Tables for
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

International Tables for Crystallography (2011). Vol. A1, ch. 1.7, p. 58

Section Maximal isomorphic subgroups

Mois I. Aroyo,a* J. Manuel Perez-Mato,a Cesar Capillasa and Hans Wondratschekb

aDepartamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain, and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany
Correspondence e-mail: Maximal isomorphic subgroups

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Maximal subgroups of index higher than 4 have indices p, p2 or p3, where p is a prime. They are isomorphic subgroups and are infinite in number. In IT A1, the isomorphic subgroups are listed as members of series under the heading `Series of maximal isomorphic subgroups'. In addition, the isomorphic subgroups of indices 2, 3 and 4 are listed individually. The program SERIES provides access to the database of maximal isomorphic subgroups on the Bilbao Crystallographic Server. Apart from the parametric IT A1 descriptions of the series, its output provides the individual listings of all maximal isomorphic subgroups of indices as high as 27 for all space groups, except for the cubic ones where the maximum index is 125. The format and content of the subgroup data are similar to those of the MAXSUB access tool. In addition, there is a special tool (under `define a maximal index' on the SERIES web form) that permits the online generation of maximal isomorphic subgroups of any index up to 131 for all space groups. [Note that these data are only generated online and do not form part of the (static) database of isomorphic subgroups.]

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