International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2015). Vol. A, ch. 1.5, pp. 97-105

Table 1.5.4.4 

B. Souvignier,c G. Chapuisd and H. Wondratscheka

Table 1.5.4.4| top | pdf |
List of space-group symbols for various settings and cells

TRICLINIC SYSTEM

No. of space groupSchoenflies symbolHermann–Mauguin symbol for all settings of the same unit cell
1 [C^{1}_{1}] P1
2 [C^{1}_{i}] [P\bar{1}]

MONOCLINIC SYSTEM

No. of space groupSchoenflies symbolStandard short Hermann–Mauguin symbolExtended Hermann–Mauguin symbols for various settings and cell choices 
abc[{\bf c}{\bar{\underline{\bf b}}}{\bf a}]    Unique axis b
  abc[{\bf ba}\bar{\underline{\bf c}}]  Unique axis c
    abc[{\bar{\underline{\bf a}}}{\bf cb}]Unique axis a
3 [C_{2}^{1}] P2 P121 P121 P112 P112 P211 P211  
4 [C_{2}^{2}] [P2_{1}] [P12_{1}1] [P12_{1}1] [P112_{1}] [P112_{1}] [P2_{1}11] [P2_{1}11]  
5 [C_{2}^{3}] C2 [\!\matrix{C1 21\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{A1 21\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{A11 2\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{B11 2\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{B 211\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{C 211\hfill\cr 2_{1}\hfill\cr}] Cell choice 1
      [\!\matrix{A1 21\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{C1 21\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{B11 2\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{A11 2\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{C 211\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{B 211\hfill\cr 2_{1}\hfill\cr}] Cell choice 2
      [\!\matrix{I1 21\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{I1 21\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{I11 2\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{I11 2\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{I 211\hfill\cr 2_{1}\hfill\cr}] [\!\matrix{I 211\hfill\cr 2_{1}\hfill\cr}] Cell choice 3
6 [C_{s}^{1}] Pm P1m1 P1m1 P11m P11m Pm11 Pm11  
7 [C_{s}^{2}] Pc P1c1 P1a1 P11a P11b Pb11 Pc11 Cell choice 1
      P1n1 P1n1 P11n P11n Pn11 Pn11 Cell choice 2
      P1a1 P1c1 P11b P11a Pc11 Pb11 Cell choice 3
8 [C_{s}^{3}] Cm [\!\matrix{C1m1\hfill\cr a\hfill\cr}] [\!\matrix{A1m1\hfill\cr c\hfill\cr}] [\!\matrix{A11m\hfill\cr b\hfill\cr}] [\!\matrix{B11m\hfill\cr a\hfill\cr}] [\!\matrix{Bm11\hfill\cr c\hfill\cr}] [\!\matrix{Cm11\hfill\cr b\hfill\cr}] Cell choice 1
      [\!\matrix{A1m1\hfill\cr c\hfill\cr}] [\!\matrix{C1m1\hfill\cr a\hfill\cr}] [\!\matrix{B11m\hfill\cr a\hfill\cr}] [\!\matrix{A11m\hfill\cr b\hfill\cr}] [\!\matrix{Cm11\hfill\cr b\hfill\cr}] [\!\matrix{Bm11\hfill\cr c\hfill\cr}] Cell choice 2
      [\!\matrix{I1m1\hfill\cr n\hfill\cr}] [\!\matrix{I1m1\hfill\cr n\hfill\cr}] [\!\matrix{I11m\hfill\cr n\hfill\cr}] [\!\matrix{I11m\hfill\cr n\hfill\cr}] [\!\matrix{Im11\hfill\cr n\hfill\cr}] [\!\matrix{Im11\hfill\cr n\hfill\cr}] Cell choice 3
9 [C_{s}^{4}] Cc [\!\matrix{C1c1\hfill\cr n\hfill\cr}] [\!\matrix{A1a1\hfill\cr n\hfill\cr}] [\!\matrix{A11a\hfill\cr n\hfill\cr}] [\!\matrix{B11b\hfill\cr n\hfill\cr}] [\!\matrix{Bb11\hfill\cr n\hfill\cr}] [\!\matrix{Cc11\hfill\cr n\hfill\cr}] Cell choice 1
      [\!\matrix{A1n1\hfill\cr a\hfill\cr}] [\!\matrix{C1n1\hfill\cr c\hfill\cr}] [\!\matrix{B11n\hfill\cr b\hfill\cr}] [\!\matrix{A11n\hfill\cr a\hfill\cr}] [\!\matrix{Cn11\hfill\cr c\hfill\cr}] [\!\matrix{Bn11\hfill\cr b\hfill\cr}] Cell choice 2
      [\!\matrix{I1a1\hfill\cr c\hfill\cr}] [\!\matrix{I1c1\hfill\cr a\hfill\cr}] [\!\matrix{I11b\hfill\cr a\hfill\cr}] [\!\matrix{I11a\hfill\cr b\hfill\cr}] [\!\matrix{Ic11\hfill\cr b\hfill\cr}] [\!\matrix{Ib11\hfill\cr c\hfill\cr}] Cell choice 3
10 [C_{2h}^{1}] P2/m [P1\displaystyle{2 \over m}1] [P1\displaystyle{2 \over m}1] [P11\displaystyle{2 \over m}] [P11\displaystyle{2 \over m}] [P\displaystyle{2 \over m}11] [P\displaystyle{2 \over m}11]  
11 [C_{2h}^{2}] [P2_{1}/m] [P1\displaystyle\displaystyle{2_{1} \over m}1] [P1\displaystyle\displaystyle{2_{1} \over m}1] [P11\displaystyle\displaystyle{2_{1} \over m}] [P11\displaystyle{2_{1} \over m}] [P\displaystyle{2_{1} \over m}11] [P\displaystyle{2_{1} \over m}11]  
12 [C_{2h}^{3}] C2/m [\!\matrix{C1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{A1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] [\!\matrix{A11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] [\!\matrix{B11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{B\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] [\!\matrix{C\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] Cell choice 1
      [\!\matrix{A1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] [\!\matrix{C1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{B11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{A11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] [\!\matrix{C\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] [\!\matrix{B\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] Cell choice 2
      [\!\matrix{I1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{I1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{I11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{I11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{I\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{I\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] Cell choice 3
13 [C_{2h}^{4}] P2/c [P1\displaystyle{2 \over c}1] [P1\displaystyle{2 \over a}1] [P11\displaystyle{2 \over a}] [P11\displaystyle{2 \over b}] [P\displaystyle{2 \over b}11] [P\displaystyle{2 \over c}11] Cell choice 1
      [P1\displaystyle{2 \over n}1] [P1\displaystyle{2 \over n}1] [P11\displaystyle{2 \over n}] [P11\displaystyle{2 \over n}] [P\displaystyle{2 \over n}11] [P\displaystyle{2 \over n}11] Cell choice 2
      [P1\displaystyle{2 \over a}1] [P1\displaystyle{2 \over c}1] [P11\displaystyle{2 \over b}] [P11\displaystyle{2 \over a}] [P\displaystyle{2 \over c}11] [P\displaystyle{2 \over b}11] Cell choice 3
14 [C_{2h}^{5}] [P2_{1}/c] [P1\displaystyle{2_{1} \over c}1] [P1\displaystyle{2_{1} \over a}1] [P11\displaystyle{2_{1} \over a}] [P11\displaystyle{2_{1} \over b}] [P\displaystyle{2_{1} \over b}11] [P\displaystyle{2_{1} \over c}11] Cell choice 1
      [P1\displaystyle{2_{1} \over n}1] [P1\displaystyle{2_{1} \over n}1] [P11\displaystyle{2_{1} \over n}] [P11\displaystyle{2_{1} \over n}] [P\displaystyle{2_{1} \over n}11] [P\displaystyle{2_{1} \over n}11] Cell choice 2
      [P1\displaystyle{2_{1} \over a}1] [P1\displaystyle{2_{1} \over c}1] [P11\displaystyle{2_{1} \over b}] [P11\displaystyle{2_{1} \over a}] [P\displaystyle{2_{1} \over c}11] [P\displaystyle{2_{1} \over b}11] Cell choice 3
15 [C_{2h}^{6}] C2/c [\!\matrix{C1\displaystyle{2 \over c}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{A1\displaystyle{2 \over a}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{A11\displaystyle{2 \over a}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{B11\displaystyle{2 \over b}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{B\displaystyle{2 \over b}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] [\!\matrix{C\displaystyle{2 \over c}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}] Cell choice 1
      [\!\matrix{A1\displaystyle{2 \over n}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{C1\displaystyle{2 \over n}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] [\!\matrix{B11\displaystyle{2 \over n}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] [\!\matrix{A11\displaystyle{2 \over n}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{C\displaystyle{2 \over n}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] [\!\matrix{B\displaystyle{2 \over n}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] Cell choice 2
      [\!\matrix{I1\displaystyle{2 \over a}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] [\!\matrix{I1\displaystyle{2 \over c}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{I11\displaystyle{2 \over b}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}] [\!\matrix{I11\displaystyle{2 \over a}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] [\!\matrix{I\displaystyle{2 \over c}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}] [\!\matrix{I\displaystyle{2 \over b}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}] Cell choice 3

ORTHORHOMBIC SYSTEM

No. of space groupSchoen-flies symbolStandard full Hermann–Mauguin symbol
abc
Extended Hermann–Mauguin symbols for the six settings of the same unit cell
abc (standard)[{\bf b a} {\bar{\bf c}}]cab[{\bar{\bf c}}\bf{ b a}]bca[{\bf a}\bar{\bf c}{\bf b}]
16 [D_{2}^{1}] P222 P222 P222 P222 P222 P222 P222
17 [D_{2}^{2}] [P222_{1}] [P222_{1}] [P222_{1}] [P2_{1}22] [P2_{1}22] [P22_{1}2] [P22_{1}2]
18 [D_{2}^{3}] [P2_{1}2_{1}2] [P2_{1}2_{1}2] [P2_{1}2_{1}2] [P22_{1}2_{1}] [P22_{1}2_{1}] [P2_{1}22_{1}] [P2_{1}22_{1}]
19 [D_{2}^{4}] [P2_{1}2_{1}2_{1}] [P2_{1}2_{1}2_{1}] [P2_{1}2_{1}2_{1}] [P2_{1}2_{1}2_{1}] [P2_{1}2_{1}2_{1}] [P2_{1}2_{1}2_{1}] [P2_{1}2_{1}2_{1}]
20 [D_{2}^{5}] [C222_{1}] [\!\matrix{C222_{1}\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{C222_{1}\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{A2_{1}22\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{A2_{1}22\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{B22_{1}2\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{B22_{1}2\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]
21 [D_{2}^{6}] C222 [\!\matrix{C222\hfill\cr 2_{1}2_{1}2\hfill\cr}] [\!\matrix{C222\hfill\cr 2_{1}2_{1}2\hfill\cr}] [\!\matrix{A222\hfill\cr 22_{1}2_{1}\hfill\cr}] [\!\matrix{A222\hfill\cr 22_{1}2_{1}\hfill\cr}] [\!\matrix{B222\hfill\cr 2_{1}22_{1}\hfill\cr}] [\!\matrix{B222\hfill\cr 2_{1}22_{1}\hfill\cr}]
22 [D_{2}^{7}] F222 [\!\matrix{F222\hfill\cr 2_{1}2_{1}2\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}22_{1}\hfill\cr}] [\!\matrix{F222\hfill\cr 2_{1}2_{1}2\hfill\cr 2_{1}22_{1}\hfill\cr 22_{1}2_{1}\hfill\cr}] [\!\matrix{F222\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}22_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr}] [\!\matrix{F222\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr 2_{1}22_{1}\hfill\cr}] [\!\matrix{F222\hfill\cr 2_{1}22_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr 22_{1}2_{1}\hfill\cr}] [\!\matrix{F222\hfill\cr 2_{1}22_{1}\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr}]
23 [D_{2}^{8}] I222 [\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}] [\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]
24 [D_{2}^{9}] [I2_{1}2_{1}2_{1}] [\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}] [\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}] [\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}] [\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}] [\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}] [\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]
25 [C_{2v}^{1}] Pmm2 Pmm2 Pmm2 P2mm P2mm Pm2m Pm2m
26 [C_{2v}^{2}] [Pmc2_{1}] [Pmc2_{1}] [Pcm2_{1}] [P2_{1}ma] [P2_{1}am] [Pb2_{1}m] [Pm2_{1}b]
27 [C_{2v}^{3}] Pcc2 Pcc2 Pcc2 P2aa P2aa Pb2b Pb2b
28 [C_{2v}^{4}] Pma2 Pma2 Pbm2 P2mb P2cm Pc2m Pm2a
29 [C_{2v}^{5}] [Pca2_{1}] [Pca2_{1}] [Pbc2_{1}] [P2_{1}ab] [P2_{1}ca] [Pc2_{1}b] [Pb2_{1}a]
30 [C_{2v}^{6}] Pnc2 Pnc2 Pcn2 P2na P2an Pb2n Pn2b
31 [C_{2v}^{7}] [Pmn2_{1}] [Pmn2_{1}] [Pnm2_{1}] [P2_{1}mn] [P2_{1}nm] [Pn2_{1}m] [Pm2_{1}n]
32 [C_{2v}^{8}] Pba2 Pba2 Pba2 P2cb P2cb Pc2a Pc2a
33 [C_{2v}^{9}] [Pna2_{1}] [Pna2_{1}] [Pbn2_{1}] [P2_{1}nb] [P2_{1}cn] [Pc2_{1}n] [Pn2_{1}a]
34 [C_{2v}^{10}] Pnn2 Pnn2 Pnn2 P2nn P2nn Pn2n Pn2n
35 [C_{2v}^{11}] Cmm2 [\!\matrix{Cmm2\hfill\cr ba2\hfill\cr}] [\!\matrix{Cmm2\hfill\cr ba2\hfill\cr}] [\!\matrix{A2mm\hfill\cr 2cb\hfill\cr}] [\!\matrix{A2mm\hfill\cr 2cb\hfill\cr}] [\!\matrix{Bm2m\hfill\cr c2a\hfill\cr}] [\!\matrix{Bm2m\hfill\cr c2a\hfill\cr}]
36 [C_{2v}^{12}] [Cmc2_{1}] [\!\matrix{Cmc2_{1}\hfill\cr bn2_{1}\hfill\cr}] [\!\matrix{Ccm2_{1}\hfill\cr na2_{1}\hfill\cr}] [\!\matrix{A2_{1}ma\hfill\cr 2_{1}cn\hfill\cr}] [\!\matrix{A2_{1}am\hfill\cr 2_{1}nb\hfill\cr}] [\!\matrix{Bb2_{1}m\hfill\cr n2_{1}a\hfill\cr}] [\!\matrix{Bm2_{1}b\hfill\cr c2_{1}n\hfill\cr}]
37 [C_{2v}^{13}] Ccc2 [\!\matrix{Ccc2\cr nn2}] [\!\matrix{Ccc2\cr nn2}] [\!\matrix{A2aa\cr 2nn}] [\!\matrix{A2aa\cr 2nn}] [\!\matrix{Bb2b\cr n2n}] [\!\matrix{Bb2b\cr n2n}]
38 [C_{2v}^{14}] Amm2 [\!\matrix{Amm2\hfill\cr nc2_{1}\hfill\cr}] [\!\matrix{Bmm2\hfill\cr cn2_{1}\hfill\cr}] [\!\matrix{B2mm\hfill\cr 2_{1}na\hfill\cr}] [\!\matrix{C2mm\hfill\cr 2_{1}an\hfill\cr}] [\!\matrix{Cm2m\hfill\cr b2_{1}n\hfill\cr}] [\!\matrix{Am2m\hfill\cr n2_{1}b\hfill\cr}]
39 [C_{2v}^{15}] Aem2 [\!\matrix{Abm2\ (Aem2)\hfill\cr cc2_{1}\hfill\cr}] [\!\matrix{Bma2\ (Bme2)\hfill\cr cc2_{1}\hfill\cr}] [\!\matrix{B2cm\ (B2em)\hfill\cr 2_{1}aa\hfill\cr}] [\!\matrix{C2mb\ (C2me)\hfill\cr 2_{1}aa\hfill\cr}] [\!\matrix{Cm2a\ (Cm2e)\hfill\cr b2_{1}b\hfill\cr}] [\!\matrix{Ac2m\ (Ae2m)\hfill\cr b2_{1}b\hfill\cr}]
40 [C_{2v}^{16}] Ama2 [\!\matrix{Ama2\hfill\cr nn2_{1}\hfill\cr}] [\!\matrix{Bbm2\hfill\cr nn2_{1}\hfill\cr}] [\!\matrix{B2mb\hfill\cr 2_{1}nn\hfill\cr}] [\!\matrix{C2cm\hfill\cr 2_{1}nn\hfill\cr}] [\!\matrix{Cc2m\hfill\cr n2_{1}n\hfill\cr}] [\!\matrix{Am2a\hfill\cr n2_{1}n\hfill\cr}]
41 [C_{2v}^{17}] Aea2 [\!\matrix{Aba2\ (Aea2)\hfill\cr cn2_{1}\hfill\cr}] [\!\matrix{Bba2\ (Bbe2)\hfill\cr nc2_{1}\hfill\cr}] [\!\matrix{B2cb\ (B2eb)\hfill\cr 2_{1}an\hfill\cr}] [\!\matrix{C2cb\ (C2ce)\hfill\cr 2_{1}na\hfill\cr}] [\!\matrix{Cc2a\ (Cc2e)\hfill\cr n2_{1}b\hfill\cr}] [\!\matrix{Ac2a\ (Ae2a)\hfill\cr b2_{1}n\hfill\cr}]
42 [C_{2v}^{18}] Fmm2 [\!\matrix{Fmm2\hfill\cr ba2\hfill\cr nc2_{1}\hfill\cr cn2_{1}\hfill\cr}] [\!\matrix{Fmm2\hfill\cr ba2\hfill\cr cn2_{1}\hfill\cr nc2_{1}\hfill\cr}] [\!\matrix{F2mm\hfill\cr 2cb\hfill\cr 2_{1}na\hfill\cr 2_{1}an\hfill\cr}] [\!\matrix{F2mm\hfill\cr 2cb\hfill\cr 2_{1}an\hfill\cr 2_{1}na\hfill\cr}] [\!\matrix{Fm2m\hfill\cr c2a\hfill\cr b2_{1}n\hfill\cr n2_{1}b\hfill\cr}] [\!\matrix{Fm2m\hfill\cr c2a\hfill\cr n2_{1}b\hfill\cr b2_{1}n\hfill\cr}]
43 [C_{2v}^{19}] Fdd2 [\!\matrix{Fdd2\hfill\cr dd2_{1}\hfill\cr}] [\!\matrix{Fdd2\hfill\cr dd2_{1}\hfill\cr}] [\!\matrix{F2dd\hfill\cr 2_{1}dd\hfill\cr}] [\!\matrix{F2dd\hfill\cr 2_{1}dd\hfill\cr}] [\!\matrix{Fd2d\hfill\cr d2_{1}d\hfill\cr}] [\!\matrix{Fd2d\hfill\cr d2_{1}d\hfill\cr}]
44 [C_{2v}^{20}] Imm2 [\!\matrix{Imm2\hfill\cr nn2_{1}\hfill\cr}] [\!\matrix{Imm2\hfill\cr nn2_{1}\hfill\cr}] [\!\matrix{I2mm\hfill\cr 2_{1}nn\hfill\cr}] [\!\matrix{I2mm\hfill\cr 2_{1}nn\hfill\cr}] [\!\matrix{Im2m\hfill\cr n2_{1}n\hfill\cr}] [\!\matrix{Im2m\hfill\cr n2_{1}n\hfill\cr}]
45 [C_{2v}^{21}] Iba2 [\!\matrix{Iba2\hfill\cr cc2_{1}\hfill\cr}] [\!\matrix{Iba2\hfill\cr cc2_{1}\hfill\cr}] [\!\matrix{I2cb\hfill\cr 2_{1}aa\hfill\cr}] [\!\matrix{I2cb\hfill\cr 2_{1}aa\hfill\cr}] [\!\matrix{Ic2a\hfill\cr b2_{1}b\hfill\cr}] [\!\matrix{Ic2a\hfill\cr b2_{1}b\hfill\cr}]
46 [C_{2v}^{22}] Ima2 [\!\matrix{Ima2\hfill\cr nc2_{1}\hfill\cr}] [\!\matrix{Ibm2\hfill\cr cn2_{1}\hfill\cr}] [\!\matrix{I2mb\hfill\cr 2_{1}na\hfill\cr}] [\!\matrix{I2cm\hfill\cr 2_{1}an\hfill\cr}] [\!\matrix{Ic2m\hfill\cr b2_{1}n\hfill\cr}] [\!\matrix{Im2a\hfill\cr n2_{1}b\hfill\cr}]
47 [D_{2h}^{1}] [P\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}] Pmmm Pmmm Pmmm Pmmm Pmmm Pmmm
48 [D_{2h}^{2}] [P\displaystyle{2 \over n}\displaystyle{2 \over n}\displaystyle{2 \over n}] Pnnn Pnnn Pnnn Pnnn Pnnn Pnnn
49 [D_{2h}^{3}] [P\displaystyle{2 \over c}\displaystyle{2 \over c}\displaystyle{2 \over m}] Pccm Pccm Pmaa Pmaa Pbmb Pbmb
50 [D_{2h}^{4}] [P\displaystyle{2 \over b}\displaystyle{2 \over a}\displaystyle{2 \over n}] Pban Pban Pncb Pncb Pcna Pcna
51 [D_{2h}^{5}] [P\displaystyle{2_{1} \over m}\displaystyle{2 \over m}\displaystyle{2 \over a}] Pmma Pmmb Pbmm Pcmm Pmcm Pmam
52 [D_{2h}^{6}] [P\displaystyle{2 \over n}\displaystyle{2_{1} \over n}\displaystyle{2 \over a}] Pnna Pnnb Pbnn Pcnn Pncn Pnan
53 [D_{2h}^{7}] [P\displaystyle{2 \over m}\displaystyle{2 \over n}\displaystyle{2_{1} \over a}] Pmna Pnmb Pbmn Pcnm Pncm Pman
54 [D_{2h}^{8}] [P\displaystyle{2_{1} \over c}\displaystyle{2 \over c}\displaystyle{2 \over a}] Pcca Pccb Pbaa Pcaa Pbcb Pbab
55 [D_{2h}^{9}] [P\displaystyle{2_{1} \over b}\displaystyle{2_{1} \over a}\displaystyle{2 \over m}] Pbam Pbam Pmcb Pmcb Pcma Pcma
56 [D_{2h}^{10}] [P\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over c}\displaystyle{2 \over n}] Pccn Pccn Pnaa Pnaa Pbnb Pbnb
57 [D_{2h}^{11}] [P\displaystyle{2 \over b}\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over m}] Pbcm Pcam Pmca Pmab Pbma Pcmb
58 [D_{2h}^{12}] [P\displaystyle{2_{1} \over n}\displaystyle{2_{1} \over n}\displaystyle{2 \over m}] Pnnm Pnnm Pmnn Pmnn Pnmn Pnmn
59 [D_{2h}^{13}] [P\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over m}\displaystyle{2 \over n}] Pmmn Pmmn Pnmm Pnmm Pmnm Pmnm
60 [D_{2h}^{14}] [P\displaystyle{2_{1} \over b}\displaystyle{2 \over c}\displaystyle{2_{1} \over n}] Pbcn Pcan Pnca Pnab Pbna Pcnb
61 [D_{2h}^{15}] [P\displaystyle{2_{1} \over b}\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over a}] Pbca Pcab Pbca Pcab Pbca Pcab
62 [D_{2h}^{16}] [P\displaystyle{2_{1} \over n}\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over a}] Pnma Pmnb Pbnm Pcmn Pmcn Pnam
63 [D_{2h}^{17}] [C\displaystyle{2 \over m}\displaystyle{2 \over c}\displaystyle{2_{1} \over m}] [\!\matrix{Cmcm\hfill\cr bnn\hfill\cr}] [\!\matrix{Ccmm\hfill\cr nan\hfill\cr}] [\!\matrix{Amma\hfill\cr ncn\hfill\cr}] [\!\matrix{Amam\hfill\cr nnb\hfill\cr}] [\!\matrix{Bbmm\hfill\cr nna\hfill\cr}] [\!\matrix{Bmmb\hfill\cr cnn\hfill\cr}]
64 [D_{2h}^{18}] [C\displaystyle{2 \over m}\displaystyle{2 \over c}\displaystyle{2_{1} \over e}] [\!\matrix{Cmca\ (Cmce)\hfill\cr bnb\hfill\cr}] [\!\matrix{Ccmb\ (Ccme)\hfill\cr naa\hfill\cr}] [\!\matrix{Abma\ (Aema)\hfill\cr ccn\hfill\cr}] [\!\matrix{Acam\ (Aeam)\hfill\cr bnb\hfill\cr}] [\!\matrix{Bbcm\ (Bbem)\hfill\cr naa\hfill\cr}] [\!\matrix{Bmab\ (Bmeb)\hfill\cr cnn\hfill\cr}]
65 [D_{2h}^{19}] [C\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}] [\!\matrix{Cmmm\hfill\cr ban\hfill\cr}] [\!\matrix{Cmmm\hfill\cr ban\hfill\cr}] [\!\matrix{Ammm\hfill\cr ncb\hfill\cr}] [\!\matrix{Ammm\hfill\cr ncb\hfill\cr}] [\!\matrix{Bmmm\hfill\cr cna\hfill\cr}] [\!\matrix{Bmmm\hfill\cr cna\hfill\cr}]
66 [D_{2h}^{20}] [C\displaystyle{2 \over c}\displaystyle{2 \over c}\displaystyle{2 \over m}] [\!\matrix{Cccm\hfill\cr nnn\hfill\cr}] [\!\matrix{Cccm\hfill\cr nnn\hfill\cr}] [\!\matrix{Amaa\hfill\cr nnn\hfill\cr}] [\!\matrix{Amaa\hfill\cr nnn\hfill\cr}] [\!\matrix{Bbmb\hfill\cr nnn\hfill\cr}] [\!\matrix{Bbmb\hfill\cr nnn\hfill\cr}]
67 [D_{2h}^{21}] [C\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over e}] [\!\matrix{Cmma\ (Cmme)\hfill\cr bab\hfill\cr}] [\!\matrix{Cmmb\ (Cmme)\hfill\cr baa\hfill\cr}] [\!\matrix{Abmm\ (Aemm)\hfill\cr ccb\hfill\cr}] [\!\matrix{Acmm\ (Aemm)\hfill\cr bcb\hfill\cr}] [\!\matrix{Bmcm\ (Bmem)\hfill\cr caa\hfill\cr}] [\!\matrix{Bmam\ (Bmem)\hfill\cr cca\hfill\cr}]
68 [D_{2h}^{22}] [C\displaystyle{2 \over c}\displaystyle{2 \over c}\displaystyle{2 \over e}] [\!\matrix{Ccca\ (Ccce)\hfill\cr nnb\hfill\cr}] [\!\matrix{Cccb\ (Ccce)\hfill\cr nna\hfill\cr}] [\!\matrix{Abaa\ (Aeaa)\hfill\cr cnn\hfill\cr}] [\!\matrix{Acaa\ (Aeaa)\hfill\cr bnn\hfill\cr}] [\!\matrix{Bbcb\ (Bbeb)\hfill\cr nan\hfill\cr}] [\!\matrix{Bbab\ (Bbeb)\hfill\cr ncn\hfill\cr}]
69 [D_{2h}^{23}] [F\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}] [\!\matrix{Fmmm\hfill\cr ban\hfill\cr ncb\hfill\cr cna\hfill\cr}] [\!\matrix{Fmmm\hfill\cr ban\hfill\cr cna\hfill\cr ncb\hfill\cr}] [\!\matrix{Fmmm\hfill\cr ncb\hfill\cr cna\hfill\cr ban\hfill\cr}] [\!\matrix{Fmmm\hfill\cr ncb\hfill\cr ban\hfill\cr cna\hfill\cr}] [\!\matrix{Fmmm\hfill\cr cna\hfill\cr ban\hfill\cr ncb\hfill\cr}] [\!\matrix{Fmmm\hfill\cr cna\hfill\cr ncb\hfill\cr ban\hfill\cr}]
70 [D_{2h}^{24}] [F\displaystyle{2 \over d}\displaystyle{2 \over d}\displaystyle{2 \over d}] Fddd Fddd Fddd Fddd Fddd Fddd
71 [D_{2h}^{25}] [I\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}] [\!\matrix{I\,mmm\hfill\cr nnn\hfill\cr}] [\!\matrix{I\,mmm\hfill\cr nnn\hfill\cr}] [\!\matrix{I\,mmm\hfill\cr nnn\hfill\cr}] [\!\matrix{I\,mmm\hfill\cr nnn\hfill\cr}] [\!\matrix{I\,mmm\hfill\cr nnn\hfill\cr}] [\!\matrix{I\,mmm\hfill\cr nnn\hfill\cr}]
72 [D_{2h}^{26}] [I\displaystyle{2 \over b}\displaystyle{2 \over a}\displaystyle{2 \over m}] [\!\matrix{I\,bam\hfill\cr ccn\hfill\cr}] [\!\matrix{I\,bam\hfill\cr ccn\hfill\cr}] [\!\matrix{I\,mcb\hfill\cr naa\hfill\cr}] [\!\matrix{I\,mcb\hfill\cr naa\hfill\cr}] [\!\matrix{I\,cma\hfill\cr bnb\hfill\cr}] [\!\matrix{I\,cma\hfill\cr bnb\hfill\cr}]
73 [D_{2h}^{27}] [I\displaystyle{2_{1} \over b}\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over a}] [\!\matrix{I\,bca\hfill\cr cab\hfill\cr}] [\!\matrix{I\,cab\hfill\cr bca\hfill\cr}] [\!\matrix{I\,bca\hfill\cr cab\hfill\cr}] [\!\matrix{I\,cab\hfill\cr bca\hfill\cr}] [\!\matrix{I\,bca\hfill\cr cab\hfill\cr}] [\!\matrix{I\,cab\hfill\cr bca\hfill\cr}]
74 [D_{2h}^{28}] [I\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over a}] [\!\matrix{I\,mma\hfill\cr nnb\hfill\cr}] [\!\matrix{I\,mmb\hfill\cr nna\hfill\cr}] [\!\matrix{I\,bmm\hfill\cr cnn\hfill\cr}] [\!\matrix{I\,cmm\hfill\cr bnn\hfill\cr}] [\!\matrix{I\,mcm\hfill\cr nan\hfill\cr}] [\!\matrix{I\,mam\hfill\cr ncn\hfill\cr}]

TETRAGONAL SYSTEM

No. of space groupSchoenflies symbolHermann–Mauguin symbols for standard cell P or IMultiple cell C or F
ShortExtendedShortExtended
75 [C_{4}^{1}] P4   C4  
76 [C_{4}^{2}] [P4_{1}]   [C4_{1}]  
77 [C_{4}^{3}] [P4_{2}]   [C4_{2}]  
78 [C_{4}^{4}] [P4_{3}]   [C4_{3}]  
79 [C_{4}^{5}] I 4 [\!\matrix{I4\hfill\cr4_{2}\hfill\cr}] F4 [\!\matrix{F4\hfill\cr 4_{2}\hfill\cr}]
80 [C_{4}^{6}] [I\,4_{1}] [\!\matrix{I4_{1}\hfill\cr 4_{3}\hfill\cr}] [F4_{1}] [\!\matrix{F4_{1}\hfill\cr 4_{3}\hfill\cr}]
81 [S_{4}^{1}] [P\bar{4}]   [C\bar{4}]  
82 [S_{4}^{2}] [I \bar{4}]   [F\bar{4}]  
83 [C_{4h}^{1}] [P4/m]   [C4/m] [\!\matrix{C4_{2}/m\hfill\cr /}n\hfill\cr}]
84 [C_{4h}^{2}] [P4_{2}/m]   [C4_{2}/m] [\!\matrix{C4_{2}/m\hfill\cr /}n\hfill\cr}]
85 [C_{4h}^{3}] [P4/n]   [C4/e] [\!\matrix{C4/a\hfill\cr b\hfill\cr}]
86 [C_{4h}^{4}] [P4_{2}/n]   [C4_{2}/e] [\!\matrix{C4_{2}/a\hfill\cr /}b\hfill\cr}]
87 [C_{4h}^{5}] [I\,4/m] [\!\matrix{I4/m\hfill\cr 4_{2}/n\hfill\cr}] [F4/m] [\!\matrix{F4/m\hfill\cr 4_{2}/a\hfill\cr}]
88 [C_{4h}^{6}] [I\,4_{1}/a] [\!\matrix{I4_{1}/a\hfill\cr 4_{3}/b\hfill\cr}] [F4_{1}/d] [\!\matrix{F4_{1}/d\hfill\cr 4_{3}/d\hfill\cr}]
89 [D_{4}^{1}] P422 [\!\matrix{P422\hfill\cr 2_{1}\hfill\cr}] C422 [\!\matrix{C422\hfill\cr 2_{1}\hfill\cr}]
90 [D_{4}^{2}] [P42_{1}2] [\!\matrix{P42_{1}2\hfill\cr }2_{1}\hfill\cr}] [C422_{1}] [\!\matrix{C422_{1}\hfill\cr 2_{1}\hfill\cr}]
91 [D_{4}^{3}] [P4_{1}22] [\!\matrix{P4_{1}22\hfill\cr 2}2_{1}\hfill\cr}] [C4_{1}22] [\!\matrix{C4_{1}22\hfill\cr 2_{1}\hfill\cr}]
92 [D_{4}^{4}] [P4_{1}2_{1}2] [\!\matrix{P4_{1}2_{1}2\hfill\cr 2_{1}}2_{1}\hfill\cr}] [C4_{1}22_{1}] [\!\matrix{C4_{1}22_{1}\hfill\cr }2_{1}\hfill\cr}]
93 [D_{4}^{5}] [P4_{2}22] [\!\matrix{P4_{2}22\hfill\cr 2}2_{1}\hfill\cr}] [C4_{2}22] [\!\matrix{C4_{2}22\hfill\cr }2_{1}\hfill\cr}]
94 [D_{4}^{6}] [P4_{2}2_{1}2] [\!\matrix{P4_{2}2_{1}2\hfill\cr 2_{1}}2_{1}\hfill\cr}] [C4_{2}22_{1}] [\!\matrix{C4_{2}22_{1}\hfill\cr }2_{1}\hfill\cr}]
95 [D_{4}^{7}] [P4_{3}22] [\!\matrix{P4_{3}22\hfill\cr 2}2_{1}\hfill\cr}] [C4_{3}22] [\!\matrix{C4_{3}22\hfill\cr }2_{1}\hfill\cr}]
96 [D_{4}^{8}] [P4_{3}2_{1}2] [\!\matrix{P4_{3}2_{1}2\hfill\cr 2_{1}}2_{1}\hfill\cr}] [C4_{3}22_{1}] [\!\matrix{C4_{3}22_{1}\hfill\cr }2_{1}\hfill\cr}]
97 [D_{4}^{9}] I 422 [\!\matrix{I\,422\hfill\cr 4_{2}2_{1}2_{1}\hfill\cr}] F422 [\!\matrix{F422\hfill\cr 4_{2}2_{1}2_{1}\hfill\cr}]
98 [D_{4}^{10}] [I 4_{1}22] [\!\matrix{I\,4_{1}22\hfill\cr 4_{3}2_{1}2_{1}\hfill\cr}] [F4_{1}22] [\!\matrix{F4_{1}22\hfill\cr 4_{3}2_{1}2_{1}\hfill\cr}]
99 [C_{4v}^{1}] P4mm [\!\matrix{P4mm\hfill\cr g\hfill\cr}] C4mm [\!\matrix{C4mm\hfill\cr b\hfill\cr}]
100 [C_{4v}^{2}] P4bm [\!\matrix{P4bm\hfill\cr g\hfill\cr}] [C4mg_{1}] [\!\matrix{C4mg_{1}\hfill\cr b\hfill\cr}]
101 [C_{4v}^{3}] [P4_{2}cm] [\!\matrix{P4_{2}cm\hfill\cr c}g\hfill\cr}] [C4_{2}mc] [\!\matrix{C4_{2}mc\hfill\cr }b\hfill\cr}]
102 [C_{4v}^{4}] [P4_{2}nm] [\!\matrix{P4_{2}nm\hfill\cr n}g\hfill\cr}] [C4_{2}mg_{2}] [\!\matrix{C4_{2}mg_{2}\hfill\cr }b\hfill\cr}]
103 [C_{4v}^{5}] P4cc [\!\matrix{P4cc\hfill\cr n\hfill\cr}] C4cc [\!\matrix{C4cc\hfill\cr n\hfill\cr}]
104 [C_{4v}^{6}] P4nc [\!\matrix{P4nc\hfill\cr n\hfill\cr}] [C4cg_{2}] [\!\matrix{C4cg_{2}\hfill\cr n\hfill\cr}]
105 [C_{4v}^{7}] [P4_{2}mc] [\!\matrix{P4_{2}mc\hfill\cr m}n\hfill\cr}] [C4_{2}cm] [\!\matrix{C4_{2}cm\hfill\cr }n\hfill\cr}]
106 [C_{4v}^{8}] [P4_{2}bc] [\!\matrix{P4_{2}bc\hfill\cr b}n\hfill\cr}] [C4_{2}cg_{1}] [\!\matrix{C4_{2}cg_{1}\hfill\cr }n\hfill\cr}]
107 [C_{4v}^{9}] I 4mm [\!\matrix{I\,4mm\hfill\cr 4_{2}nc\hfill\cr}] F4mm [\!\matrix{F4mm\hfill\cr 4_{2}cg_{2}\hfill\cr}]
108 [C_{4v}^{10}] I 4cm [\!\matrix{I\,4cc\hfill\cr 4_{2}bm\hfill\cr}] F4mc [\!\matrix{F4cc\hfill\cr 4_{2}mg_{1}\hfill\cr}]
109 [C_{4v}^{11}] [I\,4_{1}md] [\!\matrix{I\,4_{1}md\hfill\cr 4_{1}nd\hfill\cr}] [F4_{1}dm] [\!\matrix{F4_{1}dm\hfill\cr 4_{3}dg_{2}\hfill\cr}]
110 [C_{4v}^{12}] [I\,4_{1}cd] [\!\matrix{I\,4_{1}cd\hfill\cr 4_{3}bd\hfill\cr}] [F4_{1}dc] [\!\matrix{F4_{1}dc\hfill\cr 4_{3}dg_{1}\hfill\cr}]
111 [D_{2d}^{1}] [P\bar{4}2m] [\!\matrix{P\bar{4}2m\hfill\cr 2}g\hfill\cr}] [C\bar{4}m2] [\!\matrix{C\bar{4}m2\hfill\cr }b\hfill\cr}]
112 [D_{2d}^{2}] [P\bar{4}2c] [\!\matrix{P\bar{4}2c\hfill\cr 2}n\hfill\cr}] [C\bar{4}c2] [\!\matrix{C\bar{4}c2\hfill\cr }n\hfill\cr}]
113 [D_{2d}^{3}] [P\bar{4}2_{1}m] [\!\matrix{P\bar{4}2_{1}m\hfill\cr 2_{1}}g\hfill\cr}] [C\bar{4}m2_{1}] [\!\matrix{C\bar{4}m2_{1}\hfill\cr }b\hfill\cr}]
114 [D_{2d}^{4}] [P\bar{4}2_{1}c] [\!\matrix{P\bar{4}2_{1}c\hfill\cr 2_{1}}n\hfill\cr}] [C\bar{4}c2_{1}] [\!\matrix{C\bar{4}c2_{1}\hfill\cr }n\hfill\cr}]
115 [D_{2d}^{5}] [P\bar{4}m2] [\!\matrix{P\bar{4}m2\hfill\cr m}2_{1}\hfill\cr}] [C\bar{4}2m] [\!\matrix{C\bar{4}2m\hfill\cr }2_{1}\hfill\cr}]
116 [D_{2d}^{6}] [P\bar{4}c2] [\!\matrix{P\bar{4}c2\hfill\cr c}2_{1}\hfill\cr}] [C\bar{4}2c] [\!\matrix{C\bar{4}2c\hfill\cr }2_{1}\hfill\cr}]
117 [D_{2d}^{7}] [P\bar{4}b2] [\!\matrix{P\bar{4}b2\hfill\cr b}2_{1}\hfill\cr}] [C\bar{4}2g_{1}] [\!\matrix{C\bar{4}2g_{1}\hfill\cr }2_{1}\hfill\cr}]
118 [D_{2d}^{8}] [P\bar{4}n2] [\!\matrix{P\bar{4}n2\hfill\cr n}2_{1}\hfill\cr}] [C\bar{4}2g_{2}] [\!\matrix{C\bar{4}2g_{2}\hfill\cr }2_{1}\hfill\cr}]
119 [D_{2d}^{9}] [I\bar{4}m2] [\!\matrix{I\,\bar{4}m2\hfill\cr }n2_{1}\hfill\cr}] [F\bar{4}2m] [\!\matrix{F\bar{4}2m\hfill\cr }2_{1}g_{2}\hfill\cr}]
120 [D_{2d}^{10}] [I\,\bar{4}c2] [\!\matrix{I\,\bar{4}c2\hfill\cr }b2_{1}\hfill\cr}] [F\bar{4}2c] [\!\matrix{F\bar{4}2c\hfill\cr }2_{1}n\hfill\cr}]
121 [D_{2d}^{11}] [I\,\bar{4}2m] [\!\matrix{I\,\bar{4}2m\hfill\cr }2_{1}c\hfill\cr}] [F\bar{4}m2] [\!\matrix{F\bar{4}m2\hfill\cr }c2_{1}\hfill\cr}]
122 [D_{2d}^{12}] [I\,\bar{4}2d] [\!\matrix{I\,\bar{4}2d\hfill\cr }2_{1}d\hfill\cr}] [F\bar{4}d2] [\!\matrix{F\bar{4}d2\hfill\cr }d2_{1}\hfill\cr}]
123 [D_{4h}^{1}] [P4/mmm] [\!\matrix{P4/m \ 2/m \ 2/m\cr 2_{1}/g\cr}] [C4/mmm] [\!\matrix{C4/mmm\hfill\cr nb\hfill\cr}]
124 [D_{4h}^{2}] [P4/mcc] [\!\matrix{P4/m \ 2/c \ 2/c\cr 2_{1}/n\cr}] [C4/mcc] [\!\matrix{C4/mcc\hfill\cr nn\hfill\cr}]
125 [D_{4h}^{3}] [P4/nbm] [\!\matrix{P4/n \ 2/b \ 2/m\cr 2_{1}/g\cr}] [C4/emg_{1}] [\!\matrix{C4/amg_{1}\hfill\cr bb\hfill\cr}]
126 [D_{4h}^{4}] [P4/nnc] [\!\matrix{P4/n \ 2/n \ 2/c\cr 2_{1}/n\cr}] [C4/ecg_{2}] [\!\matrix{C4/acg_{2}\hfill\cr bn\hfill\cr}]
127 [D_{4h}^{5}] [P4/mbm] [\!\matrix{P4/m \ 2_{1}/b \ 2/m\cr /b_1\ }2_{1}/g\cr}] [C4/mmg_{1}] [\!\matrix{C4/mmg_{1}\hfill\cr nb\hfill\cr}]
128 [D_{4h}^{6}] [P4/mnc] [\!\matrix{P4/m \ 2_{1}/n \ 2/c\cr /n_1 \ }2_{1}/n\cr}] [C4/mcg_{2}] [\!\matrix{C4/mcg_{2}\hfill\cr nn\hfill\cr}]
129 [D_{4h}^{7}] [P4/nmm] [\!\matrix{P4/n \ 2_{1}/m \ 2/m\cr /m_1 \ }2_{1}/g\cr}] [C4/emm] [\!\matrix{C4amm\hfill\cr bb\hfill\cr}]
130 [D_{4h}^{8}] [P4/ncc] [\!\matrix{P4/n \ 2_{1}/c \ 2/c\cr /c_1 \ }2_{1}/n\cr}] [C4/ecc] [\!\matrix{C4/acc\hfill\cr bn\hfill\cr}]
131 [D_{4h}^{9}] [P4_{2}/mmc] [\!\matrix{P4_{2}/m\ 2/m\ 2/c \cr /m\ 2/m_1\ }2_{1}/n \cr}] [C4_{2}/mcm] [\!\matrix{C4_{2}/mcm\hfill\cr /}nn\hfill\cr}]
132 [D_{4h}^{10}] [P4_{2}/mcm] [\!\matrix{P4_{2}/m\ 2/c\ 2/m\cr /m\ 2/c_1\ }2_{1}/g\cr}] [C4_{2}/mmc] [\!\matrix{C4_{2}/mmc\hfill\cr /}nb\hfill\cr}]
133 [D_{4h}^{11}] [P4_{2}/nbc] [\!\matrix{P4_{2}/n\ 2/b \ 2/c\cr /n\ 2/b_1 \ }2_{1}/n\cr}] [C4_{2}/ecg_{1}] [\!\matrix{C4_{2}/acg_{1}\hfill\cr /}bn\hfill\cr}]
134 [D_{4h}^{12}] [P4_{2}/nnm] [\!\matrix{P4_{2}/n\ 2/n\ 2/m\cr /n\ 2/n_1\ }2_{1}/g\cr}] [C4_{2}/emg_{2}] [\!\matrix{C4_{2}/amg_{2}\hfill\cr /}bb\hfill\cr}]
135 [D_{4h}^{13}] [P4_{2}/mbc] [\!\matrix{P4_{2}/m\ 2_{1}/b \ 2/c\cr /m\ 2_{1}/b_1 \ }2_{1}/n\cr}] [C4_{2}/mcg_{1}] [\!\matrix{C4_{2}/mcg_{1}\hfill\cr /}nn\hfill\cr}]
136 [D_{4h}^{14}] [P4_{2}/mnm] [\!\matrix{P4_{2}/m\ 2_{1}/n \ 2/m\cr /m\ 2_{1}/n_1 \ }2_{1}/g\cr}] [C4_{2}/mmg_{2}] [\!\matrix{C4_{2}/mmg_{2}\hfill\cr /}nb\hfill\cr}]
137 [D_{4h}^{15}] [P4_{2}/nmc] [\!\matrix{P4_{2}/n \ 2_{1}/m\ 2/c\cr /n \ 2_{1}/m_1\ }2_{1}/n\cr}] [C4_{2}/ecm] [\!\matrix{C4_{2}/acm\hfill\cr /}bn\hfill\cr}]
138 [D_{4h}^{16}] [P4_{2}/ncm] [\!\matrix{P4_{2}/n \ 2_{1}/c \ 2/m\cr /n \ 2_{1}/c_1 \ }2_{1}/g\cr}] [C4_{2}/emc] [\!\matrix{C4_{2}/amc\hfill\cr /}bb\hfill\cr}]
139 [D_{4h}^{17}] [I\,4/mmm] [\!\matrix{I\,4/m \ 2/m \ 2/m\cr 4_{2}/n \ 2_{1}/n \ 2_{1}/c\cr}] [F4/mmm] [\!\matrix{F4/mmm\hfill\cr 4_{2}/acg_{2}\hfill\cr}]
140 [D_{4h}^{18}] [I4/mcm] [\!\matrix{I\,4/m &\!\! 2/c\hfill &\!\! 2/c\hfill\cr \phantom{I_2\,}4_{2}/n&\!\! 2_{1}/b\!\! &2_{1}/m\cr}] [F4/mmc] [\!\matrix{F4/mcc\hfill\cr 4_{2}/amg_{1}\hfill\cr}]
141 [D_{4h}^{19}] [I\,4_{1}/amd] [\!\matrix{I\,4_{1}/a &\!\!2/m &\!\!2/d\hfill\cr \phantom{I\,}4_{3}/b &\!\!2_{1}/n &\!\!2_{1}/d\hfill\cr}] [F4_{1}/ddm] [\!\matrix{F4_{1}/ddm\hfill\cr 4_{3}/ddg_{2}\hfill\cr}]
142 [D_{4h}^{20}] [I\,4_{1}/acd] [\!\matrix{I\,4_{1}/a &\!\!2/c &\!\!2/d\hfill\cr \phantom{I\,}4_{3}/b &\!\!2_{1}/b &\!\!2_{1}/d\hfill\cr}] [F4_{1}/ddc] [\!\matrix{F4_{1}/ddc\hfill\cr 4_{3}/ddg_{1}\hfill\cr}]

TRIGONAL SYSTEM

No. of space groupSchoenflies symbolHermann–Mauguin symbols for standard cell P or RTriple cell H
ShortFullExtended
143 [C_{3}^{1}] P3     H3
144 [C_{3}^{2}] [P3_{1}]     [H3_{1}]
145 [C_{3}^{3}] [P3_{2}]     [H3_{2}]
146 [C_{3}^{4}] R3   [\!\matrix{R3\hfill\cr 3_{1,2}\hfill\cr}]  
147 [C_{3i}^{1}] [P\bar{3}]     [H\bar{3}]
148 [C_{3i}^{2}] [R\bar{3}]   [\!\matrix{R\bar{3}\hfill\cr 3_{1,2}\hfill\cr}]  
149 [D_{3}^{1}] P312   [\!\matrix{P312\hfill\cr 2_{1}\hfill\cr}] H321
150 [D_{3}^{2}] P321   [\!\matrix{P321\hfill\cr 2_{1}\hfill\cr}] H312
151 [D_{3}^{3}] [P3_{1}12]   [\!\matrix{P3_{1}12\hfill\cr 1}2_{1}\hfill\cr}] [H3_{1}21]
152 [D_{3}^{4}] [P3_{1}21]   [\!\matrix{P3_{1}21\hfill\cr }2_{1}\hfill\cr}] [H3_{1}12]
153 [D_{3}^{5}] [P3_{2}12]   [\!\matrix{P3_{2}12\hfill\cr 1}2_{1}\hfill\cr}] [H3_{2}21]
154 [D_{3}^{6}] [P3_{2}21]   [\!\matrix{P3_{2}21\hfill\cr }2_{1}\hfill\cr}] [H3_{2}12]
155 [D_{3}^{7}] R32   [\!\matrix{R3}2\hfill\cr 3_{1,2}2_{1}\hfill\cr}]  
156 [C_{3v}^{1}] P3m1   [\!\matrix{P3m1\hfill\cr b\hfill\cr}] H31m
157 [C_{3v}^{2}] P31m   [\!\matrix{P31m\hfill\cr a\hfill\cr}] H3m1
158 [C_{3v}^{3}] P3c1   [\!\matrix{P3c1\hfill\cr n\hfill\cr}] H31c
159 [C_{3v}^{4}] P31c   [\!\matrix{P31c\hfill\cr n\hfill\cr}] H3c1
160 [C_{3v}^{5}] R3m   [\!\matrix{R3} m\hfill\cr 3_{1,2} b\hfill\cr}]  
161 [C_{3v}^{6}] R3c   [\!\matrix{R3} c\hfill\cr 3_{1,2} n\hfill\cr}]  
162 [D_{3d}^{1}] [P\bar{3}1m] [P\bar{3}12/m] [\!\matrix{P\bar{3}12/m\hfill\cr 2_{1}/a\hfill\cr}] [H\bar{3}m1]
163 [D_{3d}^{2}] [P\bar{3}1c] [P\bar{3}12/c] [\!\matrix{P\bar{3}12/c\hfill\cr 2_{1}/n\hfill\cr}] [H\bar{3}c1]
164 [D_{3d}^{3}] [P\bar{3}m1] [P\bar{3}2/m1] [\!\matrix{P\bar{3}2/m1\hfill\cr 2_{1}/b\hfill\cr}] [H\bar{3}1m]
165 [D_{3d}^{4}] [P\bar{3}c1] [P\bar{3}2/c1] [\!\matrix{P\bar{3}2/c1\hfill\cr 2_{1}/n\hfill\cr}] [H\bar{3}1c]
166 [D_{3d}^{5}] [R\bar{3}m] [R\bar{3}2/m] [\!\matrix{R\bar{3}} 2/m\hfill\cr 3_{1,2} 2_{1}/b\cr}]  
167 [D_{3d}^{6}] [R\bar{3}c] [R\bar{3}2/c] [\!\matrix{R\bar{3}} 2/c\hfill\cr  3_{1,2} 2_{1}/n\hfill\cr}]  

HEXAGONAL SYSTEM

No. of space groupSchoenflies symbolHermann–Mauguin symbols for standard cell PTriple cell H
ShortFullExtended
168 [C_{6}^{1}] P6     H6
169 [C_{6}^{2}] [P6_{1}]     [H6_{1}]
170 [C_{6}^{3}] [P6_{5}]     [H6_{5}]
171 [C_{6}^{4}] [P6_{2}]     [H6_{2}]
172 [C_{6}^{5}] [P6_{4}]     [H6_{4}]
173 [C_{6}^{6}] [P6_{3}]     [H6_{3}]
174 [C_{3h}^{1}] [P\bar{6}]     [H\bar{6}]
175 [C_{6h}^{1}] P6/m     H6/m
176 [C_{6h}^{2}] [P6_{3}/m]     [H6_{3}/m]
177 [D_{6}^{1}] P622   [\!\matrix{P622\hfill\cr 2_{1}2_{1}\hfill\cr}] H622
178 [D_{6}^{2}] [P6_{1}22]   [\!\matrix{P6_{1}22\hfill\cr }2_{1}2_{1}\hfill\cr}] [H6_{1}22]
179 [D_{6}^{3}] [P6_{5}22]   [\!\matrix{P6_{5}22\hfill\cr }2_{1} 2_{1}\hfill\cr}] [H6_{5}22]
180 [D_{6}^{4}] [P6_{2}22]   [\!\matrix{P6_{2}22\hfill\cr }2_{1}2_{1}\hfill\cr}] [H6_{2}22]
181 [D_{6}^{5}] [P6_{4}22]   [\!\matrix{P6_{4}22\hfill\cr }2_{1}2_{1}\hfill\cr}] [H6_{4}22]
182 [D_{6}^{6}] [P6_{3}22]   [\!\matrix{P6_{3}22\hfill\cr }2_{1}2_{1}\hfill\cr}] [H6_{3}22]
183 [C_{6v}^{1}] P6mm   [\!\matrix{P6mm\hfill\crb\, a\hfill\cr}] H6mm
184 [C_{6v}^{2}] P6cc   [\!\matrix{P6 c c\hfill\cr nn\hfill\cr}] H6cc
185 [C_{6v}^{3}] [P6_{3}cm]   [\!\matrix{P6_{3} c m\hfill\cr }na\hfill\cr}] [H6_{3}mc]
186 [C_{6v}^{4}] [P6_{3}mc]   [\!\matrix{P6_{3} m c\hfill\cr }b\,n\hfill\cr}] [H6_{3}cm]
187 [D_{3h}^{1}] [P\bar{6}m2]   [\!\matrix{P\bar{6}m 2\hfill\cr b\,2_{1}\hfill\cr}] [H\bar{6}2m]
188 [D_{3h}^{2}] [P\bar{6}c2]   [\!\matrix{P\bar{6}c 2\hfill\cr n2_{1}\hfill\cr}] [H\bar{6}2c]
189 [D_{3h}^{3}] [P\bar{6}2m]   [\!\matrix{P\bar{6} 2m\hfill\cr 2_{1}a\hfill\cr}] [H\bar{6}m2]
190 [D_{3h}^{4}] [P\bar{6}2c]   [\!\matrix{P\bar{6}2 c\hfill\cr }2_{1} n\hfill\cr}] [H\bar{6}c2]
191 [D_{6h}^{1}] [P6/mmm] [P6/m\, 2/m2/m] [\!\matrix{P6/m\hfill &\!\!2/m\hfill &\!\!2/m\hfill\cr &\!\!2_{1}/b\hfill &\!\!2_{1}/a\hfill\cr}] [H6/mmm]
192 [D_{6h}^{2}] [P6/mcc] [P6/m\,2/c\,2/c] [\!\matrix{P6/m \hfill&\!\!2/c\hfill &\!\!2/c\hfill\cr &\!\!2_{1}/n\hfill &\!\!2_{1}/n\hfill\cr}] [H6/mcc]
193 [D_{6h}^{3}] [P6_{3}/mcm] [P6_{3}/m\,2/c\,2/m] [\!\matrix{P6_{3}/m\hfill &\!\!2/c\hfill &\!\!2/m\hfill\cr &\!\!2_{1}/b\hfill &\!\!2_{1}/a\hfill\cr}] [H6_{3}/mmc]
194 [D_{6h}^{4}] [P6_{3}/mmc] [P6_{3}/m2/m2/c] [\!\matrix{P6_{3}/m &\!\!2/m &\!\!2/c\hfill\cr &\!\!2_{1}/b &\!\!2_{1}/n\hfill\cr}] [H6_{3}/mcm]

CUBIC SYSTEM

No. of space groupSchoenflies symbolHermann–Mauguin symbols
ShortFullExtended
195 [T^{1}] P23    
196 [T^{2}] F23   [\!\matrix{F23\hfill\cr 2\hfill\cr 2_{1}\hfill\cr 2_{1}\hfill\cr}]
197 [T^{3}] I23   [\!\matrix{I23\hfill\cr 2_{1}\hfill\cr}]
198 [T^{4}] [P2_{1}3]    
199 [T^{5}] [I2_{1}3]   [\!\matrix{I2_{1}3\hfill\cr 2\hfill\cr}]
200 [T_{h}^{1}] [Pm\bar{3}] [P2/m\,\bar{3}]  
201 [T_{h}^{2}] [Pn\bar{3}] [P2/n\,\bar{3}]  
202 [T_{h}^{3}] [Fm\bar{3}] [F2/m\,\bar{3}] [\!\matrix{F2/m\,\bar{3}\hfill\cr 2/n\hfill\cr 2_{1}/b\hfill\cr 2_{1}/a\hfill\cr}]
203 [T_{h}^{4}] [Fd\bar{3}] [F2/d\,\bar{3}] [\!\matrix{F2/d\,\bar{3}\hfill\cr 2/d\hfill\cr 2_{1}/d\hfill\cr 2_{1}/d\hfill\cr}]
204 [T_{h}^{5}] [Im\bar{3}] [I2/m\,\bar{3}] [\!\matrix{I2/m\,\bar{3}\hfill\cr 2_{1}/n\hfill\cr}]
205 [T_{h}^{6}] [Pa\bar{3}]§ [P2_{1}/a \bar{3}]§  
206 [T_{h}^{7}] [Ia\bar{3}] [I2_{1}/a \bar{3}] [\!\matrix{I2_{1}/a\,\bar{3}\hfill\cr 2/b\hfill\cr}]
207 [O^{1}] P432   [\!\matrix{P4 32\hfill\cr 2_{1}\hfill\cr}]
208 [O^{2}] [P4_{2}32]   [\!\matrix{P4_{2} 32\hfill\cr2_{1}\hfill\cr}]
209 [O^{3}] F432   [\!\matrix{F432\hfill\cr 42\hfill\cr 4_{2}2_{1}\hfill\cr 4_{2} 2_{1}\hfill\cr}]
210 [O^{4}] [F4_{1}32]   [\!\matrix{F4_{1} 32\hfill\cr 4_{1} {\phantom 3}2\hfill\cr 4_{3} {\phantom 3}2_{1}\hfill\cr 4_{3} {\phantom 3}2_{1}\hfill\cr}]
211 [O^{5}] I432   [\!\matrix{I432\hfill\cr 4_{2} 2_{1}\hfill\cr}]
212 [O^{6}] [P4_{3}32]   [\!\matrix{P4_{3} 32\hfill\cr 2_{1}\hfill\cr}]
213 [O^{7}] [P4_{1}32]   [\!\matrix{P4_{1}32\hfill\cr \phantom {P4_13}2_{1}\hfill\cr}]
214 [O^{8}] [I4_{1}32]   [\!\matrix{I4_{1} 32\hfill\cr 4_{3} {\phantom 3}2_{1}\hfill\cr}]
215 [T_{d}^{1}] [P\bar{4}3m]   [\!\matrix{P\bar{4}3m\hfill\cr 3}g\hfill\cr}]
216 [T_{d}^{2}] [F\bar{4}3m]   [\!\matrix{F\bar{4}3m\hfill\cr 3}g\hfill\cr 3}g_{2}\hfill\cr 3}g_{2}\hfill\cr}]
217 [T_{d}^{3}] [I\bar{4}3m]   [\!\matrix{I\bar{4}3m\hfill\cr 3}n\hfill\cr}]
218 [T_{d}^{4}] [P\bar{4}3n]   [\!\matrix{P\bar{4}3n\hfill\cr 3}c\hfill\cr}]
219 [T_{d}^{5}] [F\bar{4}3c]   [\!\matrix{F\bar{4}3n\hfill\cr 3}c\hfill\cr 3}g_{1}\hfill\cr 3}g_{1}\hfill\cr}]
220 [T_{d}^{6}] [I\bar{4}3d]   [\!\matrix{I\bar{4}3d\hfill\cr 3}d\hfill\cr}]
221 [O_{h}^{1}] [Pm\bar{3}m] [P4/m\,\bar{3}2/m] [\!\matrix{P4/m\,\bar{3}2/m\hfill\cr }2_{1}/g\hfill\cr}]
222 [O_{h}^{2}] [Pn\bar{3}n] [P4/n\,\bar{3}2/n] [\!\matrix{P4/n\,\bar{3}2/n\hfill\cr }2_{1}/c\hfill\cr}]
223 [O_{h}^{3}] [Pm\bar{3}n] [P4_{2}/m \bar{3}2/n] [\!\matrix{P4_{2}/m\bar{3}2/n\hfill\cr /m\bar{3}}2_{1}/c\hfill\cr}]
224 [O_{h}^{4}] [Pn\bar{3}m] [P4_{2}/n \bar{3}2/m] [\!\matrix{P4_{2}/n\bar{3}2/m\hfill\cr /n\bar{3}}2_{1}/g\hfill\cr}]
225 [O_{h}^{5}] [Fm\bar{3}m] [F4/m\,\bar{3}2/m] [\!\matrix{F4/m \,\bar{3}\,2/m\hfill\cr 4/n 2/g\hfill\cr 4_{2}/b 2_{1}/g_{2}\hfill\cr 4_{2}/a 2_{1}/g_{2}\hfill\cr}]
226 [O_{h}^{6}] [Fm\bar{3}c] [F4/m\,\bar{3}2/c] [\!\matrix{F4/m \bar{3}2/n\hfill\cr 4/n 2/c\hfill\cr 4_{2}/b 2_{1}/g_{1}\hfill\cr 4_{2}/a 2_{1}/g_{1}\hfill\cr}]
227 [O_{h}^{7}] [Fd\bar{3}m] [F4_{1}/d \bar{3}2/m] [\!\matrix{F4_{1}/d \bar{3}2/m\hfill\cr 4_{1}/d 2/g\hfill\cr 4_{3}/d 2_{1}/g_{2}\hfill\cr 4_{3}/d 2_{1}/g_{2}\hfill\cr}]
228 [O_{h}^{8}] [Fd\bar{3}c] [F4_{1}/d \bar{3}2/c] [\!\matrix{F4_{1}/d \bar{3}2/n\hfill\cr 4_{1}/d 2/c\hfill\cr 4_{3}/d 2_{1}/g_{1}\hfill\cr 4_{3}/d 2_{1}/g_{1}\hfill\cr}]
229 [O_{h}^{9}] [Im\bar{3}m] [I4/m\,\bar{3}2/m] [\!\matrix{I4/m \bar{3}2/m\hfill\cr 4_{2}/n 2_{1}/n\hfill\cr}]
230 [O_{h}^{10}] [Ia\bar{3}d] [I4_{1}/a\,\bar{3}2/d] [\!\matrix{I4_{1}/a \bar{3}2/d\hfill\cr 4_{3}/b 2_{1}/d\cr}]

Note: The glide planes g, [g_{1}] and [g_{2}] have the glide components [g({1 \over 2}, {1 \over 2}, 0)], [g_{1}({1 \over 4}, {1 \over 4}, 0)] and [g_{2}({1 \over 4}, {1 \over 4}, {1 \over 2})].
For the five space groups Aem2 (39), Aea2 (41), Cmce (64), Cmme (67) and Ccce (68), the `new' space-group symbols, containing the symbol `e' for the `double' glide plane, are given for all settings. These symbols were first introduced in the fourth edition of this volume (1995[link]). For further explanations, see Sections 1.2.3[link] and 2.1.2[link] , and de Wolff et al. (1992)[link].
Axes [3_{1}] and [3_{2}] parallel to axes 3 are not indicated in the extended symbols: cf. Section 1.5.4.1[link].
§The alternative setting [Pb\bar 3] ([P2_1/b\bar 3]) of [Pa\bar 3] is of importance for diffraction studies, cf. Section 1.5.4.3[link] and Table 1.6.4.25[link] .