International
Tables for Crystallography Volume A Spacegroup symmetry Edited by Th. Hahn © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. A, ch. 4.3, pp. 6268

In IT (1935) only the b axis was considered as the unique axis. In IT (1952) two choices were given: the caxis setting was called the `first setting' and the baxis setting was designated the `second setting'.
To avoid the presence of two standard spacegroup symbols side by side, in the present tables only one standard short symbol has been chosen, that conforming to the longlasting tradition of the baxis unique (cf. Sections 2.2.4 and 2.2.16 ). However, for reasons of rigour and completeness, in Table 4.3.2.1 the full symbols are given not only for the caxis and the baxis settings but also for the aaxis setting. Thus, Table 4.3.2.1 has six columns which in pairs refer to these three settings. In the headline, the unique axis of each setting is underlined.
^{†}For the five space groups Aem2 (39), Aea2 (41), Cmce (64), Cmme (67) and Ccce (68), the `new' spacegroup 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 (IT 1995); cf. Foreword to the Fourth Edition. For further explanations, see Section 1.3.2, Note (x)
and the spacegroup diagrams.
^{‡}For space groups Cmca (64), Cmma (67) and Imma (74), the first lines of the extended symbols, as tabulated here, correspond with the symbols for the six settings in the diagrams of these space groups (Part 7). An alternative formulation which corresponds with the coordinate triplets is given in Section 4.3.3. ^{§}Axes and parallel to axes 3 are not indicated in the extended symbols: cf. Chapter 4.1 . For the glideplane symbol `e', see the Foreword to the Fourth Edition (IT 1995) and Section 1.3.2, Note (x) . 
Additional complications arise from the presence of fractional translations due to glide planes in the primitive cell [groups (7), (13), (14)], due to centred cells [ (5), (8), (12)], or due to both [ (9), (15)]. For these groups, three different choices of the two oblique axes are possible which are called `cell choices' 1, 2 and 3 (see Section 2.2.16 ). If this is combined with the three choices of the unique axis, symbols result. If we add the effect of the permutation of the two oblique axes (and simultaneously reversing the sense of the unique axis to keep the system righthanded, as in abc and ), we arrive at the symbols listed in Table 4.3.2.1 for each of the eight space groups mentioned above.
The spacegroup symbols (3), (4), (6), (10) and (11) do not depend on the cell choice: in these cases, one line of six spacegroup symbols is sufficient.
For space groups with centred lattices (A, B, C, I), extended symbols are given; the `additional symmetry elements' (due to the centring) are printed in the half line below the spacegroup symbol.
The use of the present tabulation is illustrated by two examples, Pm, which does not depend on the cell choice, and , which does.
Examples
How does a monoclinic spacegroup symbol transform for the various settings of the same unit cell? This can be easily recognized with the help of the headline of Table 4.3.2.1, completed to the following scheme: The use of this threeline scheme is illustrated by the following examples.
Examples

It is easy to read all monoclinic maximal t and k subgroups of types I and IIa directly from the extended full symbols of a space group. Maximal subgroups of types IIb and IIc cannot be recognized by simple inspection of the synoptic Table 4.3.2.1
Example: (15, unique axis a)
The t subgroups of index [2] (type I) are B211(C2); Bb11(Cc); .
The k subgroups of index [2] (type IIa) are P2b11(P2c): (); P2n11(P2c); ().
Some subgroups of index [4] (not maximal) are P211(P2); (); Pb11(Pc); Pn11(Pc); ; B1(P1).
References
Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]