Lemmata on subgroups of space groups
Wondratschek, H.,

International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.8,
p.

[ doi:10.1107/97809553602060000791 ]
dimensional space groups. They are valid by analogy for the (two-dimensional) plane groups.

**1.2.8.1**. General lemmata
| top | pdf |
Lemma

**1.2.8.1.1**. A subgroup of a space group is a space group again, if and only ...

Lemmata on maximal subgroups
Wondratschek, H.,

International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.8.2,
p.

[ doi:10.1107/97809553602060000791 ]
introduction to the subgroups of space groups
Even the set of all maximal subgroups of finite index is not finite, as can be seen from the following lemma.
Lemma

**1.2.8.2.1**. The index i of a maximal subgroup ...

General lemmata
Wondratschek, H.,

International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.8.1,
p.

[ doi:10.1107/97809553602060000791 ]
introduction to the subgroups of space groups
Lemma

**1.2.8.1.1**. A subgroup of a space group is a space group again, if and only if the index is finite.
In this volume, only subgroups of finite index i ...