In August 1995, the Executive Committee approved the publication of
this volume with H. Wondratschek as Editor. The major chapters of this
volume are: *Introduction to the
Tables*, *User's
Guide*, *Coordinate
Transformations*, and *Subgroup Tables
for Plane and Space Groups*.

The data for each space-group type are presented in two categories:

I. Maximal
*translationengleiche* subgroups;

II. Maximal *klassengleiche*
subgroups, with the subdivisions:
Loss of centring translations;
Enlarged unit cell: indices 2, 3, and 4;
Infinite series of isomorphic subgroups;
Minimal supergroups.

In contrast to the subgroup data of Volume A, the maximal subgroups of index up to 4 are listed individually, whereas the infinite number of isomorphic subgroups are presented as infinite series. For each subgroup, either its representatives (general position) or at least a set of generators are given. The transformation to the conventional coordinate system of the subgroup is indicated by the matrix for the basis transformation and the column for the origin shift.

In addition, the group-subgroup relations are displayed by two
series of diagrams:
for each crystal class, one diagram for the
*klassengleiche* subgroups:
for the *translationengleiche*
subgroups another set of diagrams which are similar to the subgroup
diagrams of crystallographic point groups.

The volume is supplemented by a theoretical section on group-theoretical aspects and by a practical section on applications of the subgroup data.

The data have been calculated completely and are available in principle. They are presently being transferred to LaTeX format, in order to enable the printing to be made directly from these files.

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[1999] IUCr Triennial Report: Volume A1. *Maximal Subgroups of Space and Plane Groups*

Updated 6th June 1999

**Copyright © 1997 International Union of Crystallography**