Chapter 13.1 Isomorphic subgroups

Space‐group symmetry

First Online Edition (2006)

Part 13. Isomorphic subgroups of space groups

  1. Y. Billiet1,
  2. E. F. Bertaut2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000528

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Billiet, Y. and Bertaut, E. F. 2006. Isomorphic subgroups. International Tables for Crystallography. A:13:13.1:836–842.

Author Information

  1. 1

    Département de Chimie, Faculté des Sciences et Techniques, Université de Bretagne Occidentale, Brest, France

  2. 2

    Laboratoire de Cristallographie, CNRS, Grenoble, France

Publication History

  1. Published Online: 1 JAN 2006



In this chapter, the (infinitely many) isomorphic subgroups of a space group are defined. The matrices relating a plane group or space group equation image and its isomorphic subgroup equation image are tabulated for each crystal system. Conditions on the coefficients of the matrices are also given, as are examples of the use of the matrices.


  • isomorphic subgroups;
  • space groups;
  • plane groups;
  • symmetry operations;
  • crystal systems