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

International Tables for Crystallography (2016). Vol. A, ch. 3.3, pp. 783-789

Table 3.3.3.1 

H. Burzlaffa and H. Zimmermannb*

aUniversität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail:  helmuth.zimmermann@krist.uni-erlangen.de

Table 3.3.3.1| top | pdf |
Standard space-group symbols

No.Schoenflies symbolShubnikov symbolSymbols of International TablesComments
1935 EditionPresent Edition
ShortFullShortFull
1 [C_{1}^{1}] [(a/b/c)\cdot 1] P1 P1 P1 P1  
2 [C_{i}^{1}] [(a/b/c)\cdot \overline{2}] [P\overline{1}] [P\overline{1}] [P\overline{1}] [P\overline{1}] [(a/b/c)\cdot \overline{1}] (Sh–K)
3 [C_{2}^{1}] [(b\!:\!(c/a))\!:\!2] P2 P2 P2 P121  
    [(c\!:\!(a/b))\!:\!2]       P112  
4 [C_{2}^{2}] [(b\!:\!(c/a))\!:\!2_{1}] [P2_{1}] [P2_{1}] [P2_{1}] [P12_{1}1]  
    [(c\!:\!(a/b))\!:\!2_{1}]       [P112_{1}]  
5 [C_{2}^{3}] [\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\!:\!2] C2 C2 C2 C121 B2, B112 (IT, 1952[link])
    [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\!:\!2]       A112 [\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\!:\!2] (Sh–K)
6 [C_{2}^{1}] [(b\!:\!(c/a))\cdot m] Pm Pm Pm P1m1  
    [(c\!:\!(a/b))\cdot m]       P11m  
7 [C_{s}^{2}] [(b\!:\!(c/a))\cdot \tilde{c}] Pc Pc Pc P1c1 Pb, P11b (IT, 1952[link])
    [(c\!:\!(b/a))\cdot \tilde{a}]       P11a [(c\!:\!(a/b))\cdot \tilde{b}] (Sh–K)
8 [C_{s}^{3}] [\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot m] Cm Cm Cm C1m1 Bm, B11m (IT, 1952[link])
    [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot m]       A11m [\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot m] (Sh–K)
9 [C_{s}^{4}] [\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot \tilde{c}] Cc Cc Cc C1c1 Bb, B11b (IT, 1952[link])
    [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot \tilde{a}]       A11a [\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot \tilde{b}] (Sh–K)
10 [C_{2h}^{1}] [(b\!:\!(c/a))\cdot m\!:\!2] [P2/m] [P2/m] [P2/m] [P1\ {2/m}1]  
    [(c\!:\!(a/b))\cdot m\!:\!2]       [P11\ 2/m]  
11 [C_{2h}^{2}] [(b\!:\!(c/a))\cdot m\!:\!2_{1}] [P2_{1}/m] [P2_{1}/m] [P2_{1}/m] [P1\ 2_{1}/m\ 1]  
    [(c\!:\!(a/b))\cdot m\!:\!2_{1}]       [P11\ 2_{1}/m]  
12 [C_{2h}^{3}] [\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot m\!:\!2] [C2/m] [C2/m] [C2/m] [C1\ 2/m\ 1] [B2/m, B11\ 2/m] (IT, 1952[link])
    [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot m\!:\!2]       [A11\ 2/m] [\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot m\!:\!2] (Sh–K)
13 [C_{2h}^{4}] [(b\!:\!(c/a))\cdot \tilde{c}\!:\!2] [P2/c] [P2/c] [P2/c] [P1\ 2/c\ 1] [P2/b, P11\ 2/b] (IT, 1952[link])
    [(c\!:\!(a/b))\cdot \tilde{a}\!:\!2]       [P11\ 2/a] [(c\!:\!(a/b))\cdot \tilde{b}\!:\!2] (Sh–K)
14 [C_{2h}^{5}] [(b\!:\!(c/a))\cdot \tilde{c}\!:\!2_{1}] [P2_{1}/c] [P2_{1}/c] [P2_{1}/c] [P1\ 2_{1}/c\ 1] [P2_{1}/b,P112_{1}/b] (IT, 1952[link])
    [(c\!:\!(a/b))\cdot \tilde{a}\!:\!2_{1}]       [P11\ 2_{1}/a] [(c\!:\!(a/b))\cdot b\!:\!2_{1}] (Sh–K)
15 [C_{2h}^{6}] [\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot \tilde{c}\!:\!2] [C2/c] [C2/c] [C2/c] [C1\ 2/c\ 1] [B2/b, B11\ 2/b] (IT, 1952[link])
    [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot \tilde{a}\!:\!2]       A11 2a [\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot \tilde{b}\!:\!2] (Sh–K)
16 [D_{2}^{1}] [(c\!:\!(a\!:\!b))\!:\!2\!:\!2] P222 P222 P222 P222  
17 [D_{2}^{2}] [(c\!:\!(a\!:\!b))\!:\!2_{1}\!:\!2] [P222_{1}] [P222_{1}] [P222_{1}] [P222_{1}]  
18 [D_{2}^{3}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!b))\!:\!2\circcol\,2_{1}] [P2_{1}2_{1}2] [P2_{1}2_{1}2] [P2_{1}2_{1}2] [P2_{1}2_{1}2]  
19 [D_{2}^{4}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!b))\!:\!2_{1}\circcol\, 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}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!2_{1}\!:\!2] [C222_{1}] [C222_{1}] [C222_{1}] [C222_{1}]  
21 [D_{2}^{6}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2] C222 C222 C222 C222  
22 [D_{2}^{7}] [\displaylines{\left(\displaystyle{a + c \over 2}\bigg/{b + c \over 2}\bigg/{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\hfill\cr \quad :\!2\!:\!2\hfill}] F222 F222 F222 F222  
23 [D_{2}^{8}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2] I222 I222 I222 I222  
24 [D_{2}^{9}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2_{1}] [I2_{1}2_{1}2_{1}] [I2_{1}2_{1}2_{1}] [I2_{1}2_{1}2_{1}] [I2_{1}2_{1}2_{1}]  
25 [C_{2v}^{1}] [(c\!:\!(a\!:\!b))\!:\!m\cdot 2] Pmm Pmm2 Pmm2 Pmm2  
26 [C_{2v}^{2}] [(c\!:\!(a\!:\!b))\!:\!\tilde{c}\cdot 2_{1}] Pmc [Pmc2_{1}] [Pmc2_{1}] [Pmc2_{1}]  
27 [C_{2v}^{3}] [(c\!:\!(a\!:\!b))\!:\!\tilde{c}\cdot 2] Pcc Pcc2 Pcc2 Pcc2  
28 [C_{2v}^{4}] [(c\!:\!(a\!:\!b))\!:\!\tilde{a}\cdot 2] Pma Pma2 Pma2 Pma2  
29 [C_{2v}^{5}] [(c\!:\!(a\!:\!b))\!:\!\tilde{a}\cdot 2_{1}] Pca [Pca2_{1}] [Pca2_{1}] [Pca2_{1}]  
30 [C_{2v}^{6}] [(c\!:\!(a\!:\!b))\!:\!\tilde{c} \bigodot 2] Pnc Pnc2 Pnc2 Pnc2 [(c\!:\!(a\!:\!b))\!:\!\widetilde{ac}\cdot 2] (Sh–K)
31 [C_{2v}^{7}] [(c\!:\!(a\!:\!b))\!:\!\widetilde{ac}\cdot 2_{1}] Pmn [Pmn2_{1}] [Pmn2_{1}] [Pmn2_{1}]  
32 [C_{2v}^{8}] [(c\!:\!(a\!:\!b))\!:\!\tilde{a}\bigodot 2] Pba Pba2 Pba2 Pba2  
33 [C_{2v}^{9}] [(c\!:\!(a\!:\!b))\!:\!\tilde{a}\bigodot 2_{1}] Pna [Pna2_{1}] [Pna2_{1}] [Pna2_{1}]  
34 [C_{2v}^{10}] [(c\!:\!(a\!:\!b))\!:\!\widetilde{ac}\bigodot 2] Pnn Pnn2 Pnn2 Pnn2  
35 [C_{2v}^{11}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2] Cmm Cmm2 Cmm2 Cmm2  
36 [C_{2v}^{12}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2_{1}] Cmc [Cmc2_{1}] [Cmc2_{1}] [Cmc2_{1}]  
37 [C_{2v}^{13}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2] Ccc Ccc2 Ccc2 Ccc2  
38 [C_{2v}^{14}] [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2] Amm Amm2 Amm2 Amm2  
39 [C_{2v}^{15}] [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2_{1}] Abm Abm2 Aem2 Aem2 [\cases{\!\!\left(\displaystyle{b + c \over 2}\!\big/\!c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2\cr\quad (\rm{Sh\!-\!K})\cr \hbox{Use former symbol}\cr Abm2\ \hbox{for generation}\cr}]
40 [C_{2v}^{16}] [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2] Ama Ama2 Ama2 Ama2  
41 [C_{2v}^{17}] [\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2_{1}] Aba Aba2 Aea2 Aea2 [\cases{\!\!\left(\displaystyle{b + c \over 2}\!\big/c\!:\!(a\!:\!b)\right)\!:\!\widetilde{ac}\cdot 2 \cr\quad (\rm{Sh\!-\!K})\cr \hbox{Use former symbol}\cr Aba2\ \hbox{for generation}\cr}]
42 [C_{2v}^{18}] [\displaylines{\left(\displaystyle{a + c \over 2}\bigg/{b + c \over 2}\bigg/{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\hfill\cr\quad:m\cdot 2\hfill}] Fmm Fmm2 Fmm2 Fmm2  
43 [C_{2v}^{19}] [\left(\displaystyle{a + c \over 2}\bigg/{b + c \over 2}\bigg/{a + b \over 2}\!:\!\tilde{c}\!:\!(a\!:\!b)\right)][:{1\over 2}\widetilde{ac}\bigodot 2] Fdd Fdd2 Fdd2 Fdd2  
44 [C_{2v}^{20}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2] Imm Imm2 Imm2 Imm2  
45 [C_{2v}^{21}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2] Iba Iba2 Iba2 Iba2 [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2_{1}](Sh–K)
46 [C_{2v}^{22}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2] Ima Ima2 Ima2 Ima2  
47 [D_{2h}^{1}] [(c\!:\!(a\!:\!b))\cdot m\!:\!2\cdot m] Pmmm [P2/m\ 2/m\ 2/m] Pmmm [P2/m\ 2/m\ 2/m]  
48 [D_{2h}^{2}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\circdot \widetilde{ac}] Pnnn [P2/n\ 2/n\ 2/n] Pnnn [P2/n\ 2/n\ 2/n]  
49 [D_{2h}^{3}] [(c\!:\!(a\!:\!b))\cdot m\!:\!2\cdot \tilde{c}] Pccm [P2/c\ 2/c\ 2/m] Pccm [P2/c\ 2/c\ 2/m]  
50 [D_{2h}^{4}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\circdot \tilde{a}] Pban [P2/b\ 2/a\ 2/n] Pban [P2/b\ 2/a\ 2/n]  
51 [D_{2h}^{5}] [(c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2\cdot m] Pmma [P2_{1}/m\ 2/m\ 2/a] Pmma [P2_{1}/m\ 2/m\ 2/a]  
52 [D_{2h}^{6}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2\circdot \widetilde{ac}] Pnna [P2/n\ 2_{1}/n\ 2/a] Pnna [P2/n\ 2_{1}/n\ 2/a]  
53 [D_{2h}^{7}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2_{1}\cdot \widetilde{ac}] Pmna [P2/m\ 2/n\ 2_{1}/a] Pmna [P2/m\ 2/n\ 2_{1}/a]  
54 [D_{2h}^{8}] [(c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2\cdot \tilde{c}] Pcca [P2_{1}/c\ 2/c\ 2/a] Pcca [P2_{1}/c\ 2/c\ 2/a]  
55 [D_{2h}^{9}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot m\!:\!2\circdot \tilde{a}] Pbam [P2_{1}/b\ 2_{1}/a\ 2/m] Pbam [P2_{1}/b\ 2_{1}/a\ 2/m]  
56 [D_{2h}^{10}] [(c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\cdot \tilde{c}] Pccn [P2_{1}/c\ 2_{1}/c\ 2/n] Pccn [P2_{1}/c\ 2_{1}/c\ 2/n]  
57 [D_{2h}^{11}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot m\!:\!2_{1}\circdot \tilde{c}] Pbcm [P2/b\ 2_{1}/c\ 2_{1}/m] Pbcm [P2/b\ 2_{1}/c\ 2_{1}/m]  
58 [D_{2h}^{12}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot m\!:\!2\circdot \widetilde{ac}] Pnnm [P2_{1}/n\ 2_{1}/n\ 2/m] Pnnm [P2_{1}/n\ 2_{1}/n\ 2/m]  
59 [D_{2h}^{13}] [(c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\cdot m] Pmmn [P2_{1}/m\ 2_{1}/m\ 2/n] Pmmn [P2_{1}/m\ 2_{1}/m\ 2/n]  
60 [D_{2h}^{14}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2_{1}\circdot \tilde{c}] Pbcn [P2_{1}/b\ 2/c\ 2_{1}/n] Pbcn [P2_{1}/b\ 2/c\ 2_{1}/n]  
61 [D_{2h}^{15}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2_{1}\circdot \tilde{c}] Pbca [P2_{1}/b\ 2_{1}/c\ 2_{1}/a] Pbca [P2_{1}/b\ 2_{1}/c\ 2_{1}/a]  
62 [D_{2h}^{16}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2_{1}\circdot m] Pnma [P2_{1}/n\ 2_{1}/m\ 2_{1}/a] Pnma [P2_{1}/n\ 2_{1}/m\ 2_{1}/a]  
63 [D_{2h}^{17}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot m\!:\!2_{1}\cdot \tilde{c}] Cmcm [C2/m\ 2/c\ 2_{1}/m] Cmcm [C2/m\ 2/c\ 2_{1}/m]  
64 [D_{2h}^{18}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2_{1}\cdot \tilde{c}] Cmca [C2/m\ 2/c\ 2_{1}/a] Cmce [C2/m\ 2/c\ 2_{1}/e] Use former symbol Cmca for generation
65 [D_{2h}^{19}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot m] Cmmm [C2/m\ 2/m\ 2/m] Cmmm [C2/m\ 2/m\ 2/m]  
66 [D_{2h}^{20}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot \tilde{c}] Cccm [C2/c\ 2/c\ 2/m] Cccm [C2/c\ 2/c\ 2/m]  
67 [D_{2h}^{21}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot m] Cmma [C2/m\ 2/m\ 2/a] Cmme [C2/m\ 2/m\ 2/e] Use former symbol Cmma for generation
68 [D_{2h}^{22}] [\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot \tilde{c}] Ccca [C2/c\ 2/c\ 2/a] Ccce [C2/c\ 2/c\ 2/e] Use former symbol Ccca for generation
69 [D_{2h}^{23}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\hfill\cr \quad\cdot \,m\!:\!2\cdot m\hfill\cr}] Fmmm [F2/m\ 2/m\ 2/m] Fmmm [F2/m\ 2/m\ 2/m]  
70 [D_{2h}^{24}] [\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} \displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\hfill\cr \quad\cdot\, {\textstyle{1 \over 2}}\widetilde{ab}\!:\!2\circdot {\textstyle{1 \over 2}}\widetilde{ac}\hfill\cr}] Fddd [F2/d\ 2/d\ 2/d] Fddd [F2/d\ 2/d\ 2/d]  
71 [D_{2h}^{25}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot m] Immm [I2/m\ 2/m\ 2/m] Immm I2/m 2/m 2/m  
72 [D_{2h}^{26}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot \tilde{c}] Ibam [I2/b\ 2/a\ 2/m] Ibam [I2/b\ 2/a\ 2/m]  
73 [D_{2h}^{27}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot \tilde{c}] Ibca [I2_{1}/b\ 2_{1}/c\ 2_{1}/a] Ibca [I2_{1}/b\ 2_{1}/c\ 2_{1}/a] [I2/b\ 2/c\ 2/a] (IT, 1952[link])
74 [D_{2h}^{28}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot m] Imma [I2_{1}/m\ 2_{1}/m\ 2_{1}/a] Imma [I2_{1}/m\ 2_{1}/m\ 2_{1}/a] [I2/m\ 2/m\ 2/a] (IT, 1952[link])
75 [C_{4}^{1}] [(c\!:\!(a\!:\!a))\!:\!4] P4 P4 P4 P4  
76 [C_{4}^{2}] [(c\!:\!(a\!:\!a))\!:\!4_{1}] [P4_{1}] [P4_{1}] [P4_{1}] [P4_{1}]  
77 [C_{4}^{3}] [(c\!:\!(a\!:\!a))\!:\!4_{2}] [P4_{2}] [P4_{2}] [P4_{2}] [P4_{2}]  
78 [C_{4}^{4}] [(c\!:\!(a\!:\!a))\!:\!4_{3}] [P4_{3}] [P4_{3}] [P4_{3}] [P4_{3}]  
79 [C_{4}^{5}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4] I4 I4 I4 I4  
80 [C_{4}^{6}] [\left(\displaystyle{a - b - c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}] [I4_{1}] [I4_{1}] [I4_{1}] [I4_{1}]  
81 [S_{4}^{1}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}] [P\overline{4}] [P\overline{4}] [P\overline{4}] [P\overline{4}]  
82 [S_{4}^{2}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}] [I\overline{4}] [I\overline{4}] [I\overline{4}] [I\overline{4}]  
83 [C_{4h}^{1}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4] [P4/m] [P4/m] [P4/m] [P4/m]  
84 [C_{4h}^{2}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}] [P4_{2}/m] [P4_{2}/m] [P4_{2}/m] [P4_{2}/m]  
85 [C_{4h}^{3}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4] [P4/n] [P4/n] [P4/n] [P4/n]  
86 [C_{4h}^{4}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}] [P4_{2}/n] [P4_{2}/n] [P4_{2}/n] [P4_{2}/n]  
87 [C_{4h}^{5}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\cdot m\!:\!4] [I4/m] [I4/m] [I4/m] [I4/m]  
88 [C_{4h}^{6}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\cdot \tilde{a}\!:\!4_{1}] [I4_{1}/a] [I4_{1}/a] [I4_{1}/a] [I4_{1}/a]  
89 [D_{4}^{1}] (c:(a:a)):4:2 P42 P422 P422 P422  
90 [D_{4}^{2}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4 \circcol\, 2_{1}] [P42_{1}] [P42_{1}2] [P42_{1}2] [P42_{1}2]  
91 [D_{4}^{3}] [(c\!:\!(a\!:\!a))\!:\!4_{1}\!:\!2] [P4_{1}2] [P4_{1}22] [P4_{1}22] [P4_{1}22]  
92 [D_{4}^{4}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4_{1}\circcol\, 2_{1}] [P4_{1}2_{1}] [P4_{1}2_{1}2] [P4_{1}2_{1}2] [P4_{1}2_{1}2]  
93 [D_{4}^{5}] [(c\!:\!(a\!:\!a))\!:\!4_{2}\!:\!2] [P4_{2}2] [P4_{2}22] [P4_{2}22] [P4_{2}22]  
94 [D_{4}^{6}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4_{2}\circcol\, 2_{1}] [P4_{2}2_{1}] [P4_{2}2_{1}2] [P4_{2}2_{1}2] [P4_{2}2_{1}2]  
95 [D_{4}^{7}] [(c\!:\!(a\!:\!a))\!:\!4_{3}\!:\!2] [P4_{3}2] [P4_{3}22] [P4_{3}22] [P4_{3}22]  
96 [D_{4}^{8}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4_{3}\circcol\, 2_{1}] [P4_{3}2_{1}] [P4_{3}2_{1}2] [P4_{3}2_{1}2] [P4_{3}2_{1}2]  
97 [D_{4}^{9}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4\!:\!2] I42 I422 I422 I422  
98 [D_{4}^{10}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}\!:\!2] [I4_{1}2] [I4_{1}22] [I4_{1}22] [I4_{1}22]  
99 [C_{4v}^{1}] [(c\!:\!(a\!:\!a))\!:\!4\cdot m] P4mm P4mm P4mm P4mm  
100 [C_{4v}^{2}] [ (c\!:\!(a\!:\!a))\!:\!4\bigodot \tilde{a}] P4bm P4bm P4bm P4bm  
101 [C_{4v}^{3}] [(c\!:\!(a\!:\!a))\!:\!4_{2}\cdot \tilde{c}] P4cm [P4_{2}cm] [P4_{2}cm] [P4_{2}cm]  
102 [C_{4v}^{4}] [ (c\!:\!(a\!:\!a))\!:\!4_{2}\bigodot \widetilde{ac}] P4nm [P4_{2}nm] [P4_{2}nm] [P4_{2}nm]  
103 [C_{4v}^{5}] [(c\!:\!(a\!:\!a))\!:\!4\cdot \tilde{c}] P4cc P4cc P4cc P4cc  
104 [C_{4v}^{6}] [ (c\!:\!(a\!:\!a))\!:\!4\bigodot \widetilde{ac}] P4nc P4nc P4nc P4nc  
105 [C_{4v}^{7}] [(c\!:\!(a\!:\!a))\!:\!4_{2}\cdot m] P4mc [P4_{2}mc] [P4_{2}mc] [P4_{2}mc]  
106 [C_{4v}^{8}] [(c\!:\!(a\!:\!a))\!:\!4_{2}\bigodot \tilde{a}] P4bc [P4_{2}bc] [P4_{2}bc] [P4_{2}bc]  
107 [C_{4v}^{9}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4\cdot m] I4mm I4mm I4mm I4mm  
108 [C_{4v}^{10}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4\cdot \tilde{c}] I4cm I4cm I4cm I4cm  
109 [C_{4v}^{11}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}\bigodot m] I4md [I4_{1}md] [I4_{1}md] [I4_{1}md]  
110 [C_{4v}^{12}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}\bigodot \tilde{c}] I4cd [I4_{1}cd] [I4_{1}cd] [I4_{1}cd] [\left(\displaystyle{a + b + c \over 2}\!\!\bigg/\!\!c\!:\!a\!:\!a\right)\!:\!4_{1}\cdot \tilde{a}](Sh–K)
111 [D_{2d}^{1}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\!:\!2] [P\overline{4}2m] [P\overline{4}2m] [P\overline{4}2m] [P\overline{4}2m]  
112 [D_{2d}^{2}] [\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!\tilde{4}\circcol\, 2] [P\overline{4}2c] [P\overline{4}2c] [P\overline{4}2c] [P\overline{4}2c]  
113 [D_{2d}^{3}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \widetilde{ab}] [P\overline{4}2_{1}m] [P\overline{4}2_{1}m] [P\overline{4}2_{1}m] [P\overline{4}2_{1}m]  
114 [D_{2d}^{4}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \widetilde{abc}] [P\overline{4}2_{1}c] [P\overline{4}2_{1}c] [P\overline{4}2_{1}c] [P\overline{4}2_{1}c]  
115 [D_{2d}^{5}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot m] [C\overline{4}2m] [C\overline{4}2m] [P\overline{4}m2] [P\overline{4}m2]  
116 [D_{2d}^{6}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \tilde{c}] [C\overline{4}2c] [C\overline{4}2c] [P\overline{4}c2] [P\overline{4}c2]  
117 [D_{2d}^{7}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\bigodot \tilde{a}] [C\overline{4}2b] [C\overline{4}2b] [P\overline{4}b2] [P\overline{4}b2]  
118 [D_{2d}^{8}] [(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \widetilde{ac}] [C\overline{4}2n] [C\overline{4}2n] [P\overline{4}n2] [P\overline{4}n2]  
119 [D_{2d}^{9}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\cdot m] [F\overline{4}2m] [F\overline{4}2m] [I\overline{4}m2] [I\overline{4}m2]  
120 [D_{2d}^{10}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\cdot \tilde{c}] [F\overline{4}2c] [F\overline{4}2c] [I\overline{4}c2] [I\overline{4}c2]  
121 [D_{2d}^{11}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\!:\!2] [I\overline{4}2m] [I\overline{4}2m] [I\overline{4}2m] [I\overline{4}2m]  
122 [D_{2d}^{12}] [\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\bigodot {1 \over 2}\widetilde{abc}] [I\overline{4}2d] [I\overline{4}2d] [I\overline{4}2d] [I\overline{4}2d]  
123 [D_{4h}^{1}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4\cdot m] [P4/mmm] [P4/m\ 2/m\ 2/m] [P4/mmm] [P4/m\ 2/m\ 2/m]  
124 [D_{4h}^{2}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4\cdot \tilde{c}] [P4/mcc] [P4/m\ 2/c\ 2/c] [P4/mcc] [P4/m\ 2/c\ 2/c]  
125 [D_{4h}^{3}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4\bigodot \tilde{a}] [P4/nbm] [P4/n\ 2/b\ 2/m] [P4/nbm] [P4/n\ 2/b\ 2/m] [\def\bigodot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!a\!:\!a)\cdot \widetilde{ab}\!:\!4\bigodot \tilde{b}] (Sh–K)
126 [D_{4h}^{4}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4\bigodot \widetilde{ac}] [P4/nnc] [P4/n\ 2/n\ 2/c] [P4/nnc] [P4/n\ 2/n\ 2/c]  
127 [D_{4h}^{5}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4\bigodot \tilde{a}] [P4/mbm] [P4/m\ 2_{1}/b\ 2/m] [P4/mbm] [P4/m\ 2_{1}/b\ 2/m] [\def\bigodot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!a\!:\!a)\cdot m\!:\!4\bigodot \tilde{b}] (Sh–K)
128 [D_{4h}^{6}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4\bigodot \widetilde{ac}] [P4/mnc] [P4/m\ 2_{1}/n\ 2/c] [P4/mnc] [P4/m\ 2_{1}/n\ 2/c]  
129 [D_{4h}^{7}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4\cdot m] [P4/nmm] [P4/n\ 2_{1}/m\ 2/m] [P4/nmm] [P4/n\ 2_{1}/m\ 2/m]  
130 [D_{4h}^{8}] [(c\!:\!(a\!:\!a)\cdot \widetilde{ab}\!:\!4\cdot \tilde{c}] [P4/ncc] [P4/n\ 2/c\ 2/c] [P4/ncc] [P4/n\ 2/c\ 2/c]  
131 [D_{4h}^{9}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}\cdot m] [P4/mmc] [P4_{2}/m\ 2/m\ 2/c] [P4_{2}/mmc] [P4_{2}/m\ 2/m\ 2/c]  
132 [D_{4h}^{10}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}\cdot \tilde{c}] [P4/mcm] [P4_{2}/m\ 2/c\ 2/m] [P4_{2}/mcm] [P4_{2}/m\ 2/c\ 2/m]  
133 [D_{4h}^{11}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}\bigodot \tilde{a}] [P4/nbc] [P4_{2}/n\ 2/b\ 2/c] [P4_{2}/nbc] [P4_{2}/n\ 2/b\ 2/c] [(c\!:\!a\!:\!a)\cdot \widetilde{ab}\!:\!4_{2}\bigodot \tilde{b}] (Sh–K)
134 [D_{4h}^{12}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}\bigodot \widetilde{ac}] [P4/nnm] [P4_{2}/n\ 2/n\ 2/m] [P4_{2}/nnm] [P4_{2}/n\ 2/n\ 2/m]  
135 [D_{4h}^{13}] [(c\!:\!(a\!:\!a))\cdot n\!:\!4_{2}\bigodot \tilde{a}] [P4/mbc] [P4_{2}/m\ 2_{1}/b\ 2/c] [P4_{2}/mbc] [P4_{2}/m\ 2_{1}/b\ 2/c] [(c\!:\!a\!:\!a)\cdot m\!:\!4_{2}\bigodot \tilde{b}] (Sh–K)
136 [D_{4h}^{14}] [(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}\bigodot \widetilde{ac}] [P4/mnm] [P4_{2}/m\ 2_{1}/n\ 2/m] [P4_{2}/mnm] [P4_{2}/m\ 2_{1}/n\ 2/m]  
137 [D_{4h}^{15}] [(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}\cdot m] [P4/nmc] [P4_{2}/n\ 2_{1}/m\ 2/c] [P4_{2}/nmc] [P4_{2}/n\ 2_{1}/m\ 2/c]  
138 [D_{4h}^{16}] [(c\!:\!(a\!:\!a))\cdot ab\!:\!4_{2}\cdot \tilde{c}] [P4/ncm] [P4_{2}/n\ 2_{1}/c\ 2/m] [P4_{2}/ncm] [P4_{2}/n\ 2_{1}/c\ 2/m]  
139 [D_{4h}^{17}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot m\!:\!4\cdot m] [I4/mmm] [I4/m\ 2/m\ 2/m] [I4/mmm] [I4/m\ 2/m\ 2/m]  
140 [D_{4h}^{18}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot m\!:\!4\cdot \tilde{c}] [I4/mcm] [I4/m\ 2/c\ 2/m] [I4/mcm] [I4/m\ 2/c\ 2/m]  
141 [D_{4h}^{19}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot \tilde{a}\!:\!4_{1}\bigodot m] [I4/amd] [I4_{1}/a\ 2/m\ 2/d] [I4_{1}/amd] [I4_{1}/a\ 2/m\ 2/d]  
142 [D_{4h}^{20}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot \tilde{a}\!:\!4_{1}\bigodot \tilde{c}] [I4/acd] [I4_{1}/a\ 2/c\ 2/d] [I4_{1}/acd] [I4_{1}/a\ 2/c\ 2/d]  
143 [C_{3}^{1}] [(c\!:\!(a/a))\!:\!3] C3 C3 P3 P3  
144 [C_{3}^{2}] [(c\!:\!(a/a))\!:\!3_{1}] [C3_{1}] [C3_{1}] [P3_{1}] [P3_{1}]  
145 [C_{3}^{3}] [(c\!:\!(a/a))\!:\!3_{2}] [C3_{2}] [C3_{2}] [P3_{2}] [P3_{2}]  
146 [C_{3}^{4}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\!\bigg/\!\!{a + 2b + 2c \over 3}\!\!\bigg/\!\!c\!:\!(a/a)\right)\hfill\cr\quad:3\hfill}] R3 R3 R3 R3 Hexagonal setting (Sh–K)
    [(a/a/a)/3]         Rhombohedral setting (Sh–K)
147 [C_{3i}^{1}] [(c\!:\!(a/a))\!:\!\tilde{6}] [C\overline{3}] [C\overline{3}] [P\overline{3}] [P\overline{3}]  
148 [C_{3i}^{2}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right)\hfill\cr\quad :\tilde{6}\hfill}] [R\overline{3}] [R\overline{3}] [R\overline{3}] [R\overline{3}] Hexagonal setting (Sh–K)
    [(a/a/a)/\tilde{6}]         Rhombohedral setting (Sh–K)
149 [D_{3}^{1}] [(c\!:\!(a/a))\!:\!2\!:\!3] H32 H321 P312 P312  
150 [D_{3}^{2}] [(c\!:\!(a/a))\!:\!2\!:\!3] C32 C321 P321 P321  
151 [D_{3}^{3}] [(c\!:\!(a/a))\!:\!2\!:\!3_{1}] [H3_{1}2] [H3_{1}21] [P3_{1}12] [P3_{1}12]  
152 [D_{3}^{4}] [(c\!:\!(a/a))\!:\!2\!:\!3_{1}] [C3_{1}2] [C3_{1}21] [P3_{1}21] [P3_{1}21]  
153 [D_{3}^{5}] [(c\!:\!(a/a))\!:\!2\!:\!3_{2}] [H3_{2}2] [H3_{2}21] [P3_{2}12] [P3_{2}12]  
154 [D_{3}^{6}] [(c\!:\!(a/a))\!:\!2\!:\!3_{2}] [C3_{2}2] [C3_{2}21] [P3_{2}21] [P3_{2}21]  
155 [D_{3}^{7}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right)\hfill\cr \quad\cdot 2\!:\!3\hfill\cr}] R32 R32 R32 R32 Hexagonal setting (Sh–K)
    [(a/a/a)/3\!:\!2]         Rhombohedral setting (Sh–K)
156 [C_{3v}^{1}] [(c\!:\!(a/a))\!:\!m\!:\!3] C3m C3m1 P3m1 P3m1  
157 [C_{3v}^{2}] [(a\!:\!c\!:\!a)\!:\!m\!:\!3] H3m H3m1 P31m P31m [(c\!:\!(a/a))\cdot m\cdot 3] (Sh–K) with special comment
158 [C_{3v}^{3}] [(c\!:\!(a/a))\!:\!\tilde{c}\!:\!3] C3c C3c1 P3c1 P3c1  
159 [C_{3v}^{4}] [(a\!:\!c\!:\!a)\!:\!\tilde{c}\!:\!3] H3c H3c1 P31c P31c [(c\!:\!(a/a))\cdot \tilde{c}\cdot 3] (Sh–K) with special comment
160 [C_{3v}^{5}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right)\hfill\cr \quad\cdot\, m\cdot 3\hfill\cr}] R3m R3m R3m R3m Hexagonal setting (Sh–K)
    [(a/a/a)/3\cdot m]         Rhombohedral setting (Sh–K)
161 [C_{3v}^{6}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right) \hfill\cr\quad \cdot \,\tilde{c}\cdot 3\hfill\cr}] R3c R3c R3c R3c Hexagonal setting (Sh–K)
    [(a/a/a)/3\cdot \widetilde{abc}]         Rhombohedral setting (Sh–K)
162 [D_{3d}^{1}] [(a\!:\!c\!:\!a)\cdot m\cdot \tilde{6}] [H\overline{3}m] [H\overline{3}\ 2/m\ 1] [P\overline{3}1m] [P\overline{3}1\ 2/m] [(c\!:\!(a/a))\cdot m\cdot \tilde{6}] (Sh–K) with special comment
163 [D_{3d}^{2}] [(a\!:\!c\!:\!a)\cdot \tilde{c}\cdot \tilde{6}] [H\overline{3}c] [H\overline{3}\ 2/c\ 1] [P\overline{3}1c] [P\overline{3}1\ 2/c] [(c\!:\!(a/a)\cdot \tilde{c}\cdot \tilde{6}] (Sh–K) with special comment
164 [D_{3d}^{3}] [(c\!:\!(a/a))\!:\!m\cdot \tilde{6}] [C\overline{3}m] [C\overline{3}\ 2/m\ 1] [P\overline{3}m1] [P\overline{3}\ 2/m\ 1]  
165 [D_{3d}^{4}] [(c\!:\!(a/a))\!:\!\tilde{c}\cdot \tilde{6}] [C\overline{3}c] [C\overline{3}\ 2/c\ 1] [P\overline{3}c1] [P\overline{3}\ 2/c\ 1]  
166 [D_{3d}^{5}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right) \hfill\cr \quad:m\cdot \tilde{6}\hfill\cr}] [R\overline{3}m] [R\overline{3}\ 2/m] [R\overline{3}m] [R\overline{3}\ 2/m] Hexagonal setting (Sh–K)
    [(a/a/a)/\tilde{6}\cdot m]         Rhombohedral setting (Sh–K)
167 [D_{3d}^{6}] [\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right)\hfill\cr \quad:\tilde{c}\cdot \tilde{6}\hfill\cr}] [R\overline{3}c] [R\overline{3}\ 2/c] [R\overline{3}c] [R\overline{3}\ 2/c] Hexagonal setting (Sh–K)
    [(a/a/a)/\tilde{6}\cdot \widetilde{abc}]         Rhombohedral setting (Sh–K)
168 [C_{6}^{1}] [(c\!:\!(a/a))\!:\!6] C6 C6 P6 P6  
169 [C_{6}^{2}] [(c\!:\!(a/a))\!:\!6_{1}] [C6_{1}] [C6_{1}] [P6_{1}] [P6_{1}]  
170 [C_{6}^{3}] [(c\!:\!(a/a))\!:\!6_{5}] [C6_{5}] [C6_{5}] [P6_{5}] [P6_{5}]  
171 [C_{6}^{4}] [(c\!:\!(a/a))\!:\!6_{2}] [C6_{2}] [C6_{2}] [P6_{2}] [P6_{2}]  
172 [C_{6}^{5}] [(c\!:\!(a/a))\!:\!6_{4}] [C6_{4}] [C6_{4}] [P6_{4}] [P6_{4}]  
173 [C_{6}^{6}] [(c\!:\!(a/a))\!:\!6_{3}] [C6_{3}] [C6_{3}] [P6_{3}] [P6_{3}]  
174 [C_{3h}^{1}] [(c\!:\!(a/a))\!:\!3\!:\!m] [C\overline{6}] [C\overline{6}] [P\overline{6}] [P\overline{6}]  
175 [C_{6h}^{1}] [(c\!:\!(a/a))\cdot m\!:\!6] [C6/m] [C6/m] [P6/m] [P6/m]  
176 [C_{6h}^{2}] [(c\!:\!(a/a))\cdot m\!:\!6_{3}] [C6_{3}/m] [C6_{3}/m] [P6_{3}/m] [P6_{3}/m]  
177 [D_{6}^{1}] [(c\!:\!(a/a))\cdot 2\!:\!6] C62 C622 P622 P622  
178 [D_{6}^{2}] [(c\!:\!(a/a))\cdot 2\!:\!6_{1}] [C6_{1}2] [C6_{1}22] [P6_{1}22] [P6_{1}22]  
179 [D_{6}^{3}] [(c\!:\!(a/a))\cdot 2\!:\!6_{5}] [C6_{5}2] [C6_{5}22] [P6_{5}22] [P6_{5}22]  
180 [D_{6}^{4}] [(c\!:\!(a/a))\cdot 2\!:\!6_{2}] [C6_{2}2] [C6_{2}22] [P6_{2}22] [P6_{2}22]  
181 [D_{6}^{5}] [(c\!:\!(a/a))\cdot 2\!:\!6_{4}] [C6_{4}2] [C6_{4}22] [P6_{4}22] [P6_{4}22]  
182 [D_{6}^{6}] [(c\!:\!(a/a))\cdot 2\!:\!6_{3}] [C6_{3}2] [C6_{3}22] [P6_{3}22] [P6_{3}22]  
183 [C_{6v}^{1}] [(c\!:\!(a/a))\!:\!m\cdot 6] C6mm C6mm P6mm P6mm  
184 [C_{6v}^{2}] [(c\!:\!(a/a))\!:\!\tilde{c}\cdot 6] C6cc C6cc P6cc P6cc  
185 [C_{6v}^{3}] [(c\!:\!(a/a))\!:\!\tilde{c}\cdot 6_{3}] C6cm [C6_{3}cm] [P6_{3}cm] [P6_{3}cm]  
186 [C_{6v}^{4}] [(c\!:\!(a/a))\!:\!m\cdot 6_{3}] C6mc [C6_{3}mc] [P6_{3}mc] [P6_{3}mc]  
187 [D_{3h}^{1}] [(c\!:\!(a/a))\!:\!m\cdot 3\!:\!m] [C\overline{6}m2] [C\overline{6}m2] [P\overline{6}m2] [P\overline{6}m2]  
188 [D_{3h}^{2}] [(c\!:\!(a/a))\!:\!\tilde{c}\cdot 3\!:\!m] [C\overline{6}c2] [C\overline{6}c2] [P\overline{6}c2] [P\overline{6}c2]  
189 [D_{3h}^{3}] [(c\!:\!(a/a))\cdot m\!:\!3\cdot m] [H\overline{6}m2] [H\overline{6}m2] [P\overline{6}2m] [P\overline{6}2m]  
190 [D_{3h}^{4}] [(c\!:\!(a/a))\cdot m\!:\!3\cdot \tilde{c}] [H\overline{6}c2] [H\overline{6}c2] [P\overline{6}2c] [P\overline{6}2c]  
191 [D_{6h}^{1}] [(c\!:\!(a/a))\cdot m\!:\!6\cdot m] [C6/mmm] [C6/m\ 2/m\ 2/m] [P6/mmm] [P6/m\ 2/m\ 2/m]  
192 [D_{6h}^{2}] [(c\!:\!(a/a))\cdot m\!:\!6\cdot \tilde{c}] [C6/mcc] [C6/m\ 2/c\ 2/c] [P6/mcc] [P6/m\ 2/c\ 2/c]  
193 [D_{6h}^{3}] [(c\!:\!(a/a))\cdot m\!:\!6_{3}\cdot \tilde{c}] [C6/mcm] [C6_{3}/m\ 2/c\ 2/m] [P6_{3}/mcm] [P6_{3}/m\ 2/c\ 2/m]  
194 [D_{6h}^{4}] [(c\!:\!(a/a))\cdot m\!:\!6_{3}\cdot m] [C6/mmc] [C6_{3}/m\ 2/m\ 2/c] [P6_{3}/mmc] [P6_{3}/m\ 2/m\ 2/c]  
195 [T^{1}] [(a\!:\!(a/a))\!:\!2/3] P23 P23 P23 P23  
196 [T^{2}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad:2/3\hfill}] F23 F23 F23 F23  
197 [T^{3}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!2/3] I23 I23 I23 I23  
198 [T^{4}] [(a\!:\!(a\!:\!a))\!:\!2_{1}//3] [P2_{1}3] [P2_{1}3] [P2_{1}3] [P2_{1}3]  
199 [T^{5}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!2_{1}//3] [I2_{1}3] [I2_{1}3] [I2_{1}3] [I2_{1}3]  
200 [T_{h}^{1}] [(a\!:\!(a\!:\!a))\cdot m/\tilde{6}] Pm3 [P2/m\ \overline{3}] [Pm\overline{3}] [P2/m\ \overline{3}] Pm3 (IT, 1952[link])
201 [T_{h}^{2}] [(a\!:\!(a\!:\!a))\cdot \widetilde{ab}/\tilde{6}] Pn3 [P2/n\ \overline{3}] [Pn\overline{3}] [P2/n\ \overline{3}] Pn3 (IT, 1952[link])
202 [T_{h}^{3}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad\cdot\, m/\tilde{6}\hfill}] Fm3 [F2/m\ \overline{3}] [Fm\overline{3}] [F2/m\ \overline{3}] Fm3 (IT, 1952[link])
203 [T_{h}^{4}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right) \hfill\cr\quad\cdot \,{\textstyle{1 \over 2}}ab/\tilde{6}\hfill}] Fd3 [F2/d\ \overline{3}] [Fd\overline{3}] [F2/d\ \overline{3}] Fd3 (IT, 1952[link])
204 [T_{h}^{5}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\cdot m/\tilde{6}] Im3 [I2/m\ \overline{3}] [Im\overline{3}] [I2/m\ \overline{3}] Im3 (IT, 1952[link])
205 [T_{h}^{6}] [(a\!:\!(a\!:\!a))\cdot \tilde{a}/\tilde{6}] Pa3 [P2_{1}/a\ \overline{3}] [Pa\overline{3}] [P2_{1}/a\ \overline{3}] Pa3 (IT, 1952[link])
206 [T_{h}^{7}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\cdot \tilde{a}/\tilde{6}] Ia3 [I2_{1}/a\ \overline{3}] [Ia\overline{3}] [I2_{1}/a\ \overline{3}] Ia3 (IT, 1952[link])
207 [O^{1}] [(a\!:\!(a\!:\!a))\!:\!4/3] P43 P432 P432 P432  
208 [O^{2}] [(a\!:\!(a\!:\!a))\!:\!4_{2}//3] [P4_{2}3] [P4_{2}32] [P4_{2}32] [P4_{2}32]  
209 [O^{3}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad :4/3\hfill}] F43 F432 F432 F432  
210 [O^{4}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad :4_{1}//3\hfill}] [F4_{1}3] [F4_{1}32] [F4_{1}32] [F4_{1}32]  
211 [O^{5}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4/3] I43 I432 I432 I432  
212 [O^{6}] [(a\!:\!(a\!:\!a))\!:\!4_{3}//3] [P4_{3}3] [P4_{3}32] [P4_{3}32] [P4_{3}32]  
213 [O^{7}] [(a\!:\!(a\!:\!a))\!:\!4_{1}//3] [P4_{1}3] [P4_{1}32] [P4_{1}32] [P4_{1}32]  
214 [O^{8}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4_{1}//3] [I4_{1}3] [I4_{1}32] [I4_{1}32] [I4_{1}32]  
215 [T_{d}^{1}] [(a\!:\!(a\!:\!a))\!:\!\tilde{4}/3] [P\overline{4}3m] [P\overline{4}3m] [P\overline{4}3m] [P\overline{4}3m]  
216 [T_{d}^{2}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad :\tilde{4}/3\hfill}] [F\overline{4}3m] [F\overline{4}3m] [F\overline{4}3m] [F\overline{4}3m]  
217 [T_{d}^{3}] [\displaylines{\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad :\tilde{4}/3\hfill}] [I\overline{4}3m] [I\overline{4}3m] [I\overline{4}3m] [I\overline{4}3m]  
218 [T_{d}^{4}] [(a\!:\!(a\!:\!a))\!:\!\tilde{4}//3] [P\overline{4}3n] [P\overline{4}3n] [P\overline{4}3n] [P\overline{4}3n]  
219 [T_{d}^{5}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad :\tilde{4}//3\hfill}] [F\overline{4}3c] [F\overline{4}3c] [F\overline{4}3c] [F\overline{4}3c]  
220 [T_{d}^{6}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!\tilde{4}//3] [I\overline{4}3d] [I\overline{4}3d] [I\overline{4}3d] [I\overline{4}3d]  
221 [O_{h}^{1}] [(a\!:\!(a\!:\!a))\!:\!4/\tilde{6}\cdot m] Pm3m [P4/m\ \overline{3}\ 2/m] [Pm\overline{3}m] [P4/m\ \overline{3}\ 2/m] Pm3m (IT, 1952[link])
222 [O_{h}^{2}] [(a\!:\!(a\!:\!a))\!:\!4/\tilde{6}\cdot \widetilde{abc}] Pn3n [P4/n\ \overline{3}\ 2/n] [Pn\overline{3}n] [P4/n\ \overline{3}\ 2/n] Pn3n (IT, 1952[link])
223 [O_{h}^{3}] [(a\!:\!(a\!:\!a))\!:\!4_{2}//\tilde{6}\cdot \widetilde{abc}] Pm3n [P4_{2}/m\ \overline{3}\ 2/n] [Pm\overline{3}n] [P4_{2}/m\ \overline{3}\ 2/n] Pm3n (IT, 1952[link])
224 [O_{h}^{4}] [(a\!:\!(a\!:\!a))\!:\!4_{2}//\tilde{6}\cdot m] Pn3m [P4_{2}/n\ \overline{3}\ 2/m] [Pn\overline{3}m] [P4_{2}/n\ \overline{3}\ 2/m] Pn3m (IT ,1952[link])
225 [O_{h}^{5}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right) \hfill\cr\quad :4/\tilde{6}\cdot m\hfill}] Fm3m [F4/m\ \overline{3}\ 2/m] [Fm\overline{3}m] [F4/m\ \overline{3}\ 2/m] Fm3m (IT, 1952[link])
226 [O_{h}^{6}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr\quad :4/\tilde{6}\cdot \tilde{c}\hfill}] Fm3c [F4/m\ \overline{3}\ 2/c] [Fm\overline{3}c] [F4/m\ \overline{3}\ 2/c] Fm3c (IT, 1952[link])
227 [O_{h}^{7}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a(a\!:\!a)\right)\hfill\cr\quad :\!4_{1}//\tilde{6}\cdot m\hfill\cr}] Fd3m [F4_{1}/d\ \overline{3}\ 2/m] [Fd\overline{3}m] [F4_{1}/d\ \overline{3}\ 2/m] Fd3m (IT, 1952[link])
228 [O_{h}^{8}] [\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\hfill\cr \quad:\!4_{1}//\tilde{6}\cdot \tilde{c}\hfill\cr}] Fd3c [F4_{1}/d\ \overline{3}\ 2/c] [Fd\overline{3}c] [F4_{1}/d\ \overline{3}\ 2/c] Fd3c (IT, 1952[link])
229 [O_{h}^{9}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4/\tilde{6}\cdot m] Im3m [I4/m\ \overline{3}\ 2/m] [Im\overline{3}m] [I4/m\ \overline{3}\ 2/m] Im3m (IT, 1952[link])
230 [O_{h}^{10}] [\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4_{1}//\tilde{6}\cdot {1 \over 2}\widetilde{abc}] Ia3d [I4_{1}/a\ \overline{3}\ 2/d] [Ia\overline{3}d] [I4_{1}/a\ \overline{3}\ 2/d] Ia3d (IT, 1952[link])
Abbreviations used in the column Comments: IT, 1952[link]: International Tables for X-ray Crystallography, Vol. I (1952[link]); Sh–K; Shubnikov & Koptsik (1972[link]). Note that this table contains only one notation for the b-unique setting and one notation for the c-unique setting in the monoclinic case, always referring to cell choice 1 of the space-group tables.