  The symmetry of a crystal structure with a three-dimensional (3D) lattice can
be classified by one of the 230 space group types. For some types of crystals,
e.g. crystalline films, surfaces, or planar interfaces, it is more appropriate
to assume a 2D lattice. With this assumption, the structure can be classified
by one of the 80 layer group types. We have implemented an algorithm to
determine the layer group type of a 3D structure with a 2D lattice, and applied
it to more than 15,000 monolayer structures in the Computational 2D Materials
(C2DB) database. We compare the classification of monolayers by layer groups
and space groups, respectively. The latter is defined as the space group of the
3D bulk structure obtained by repeating the monolayer periodically in the
direction perpendicular to the 2D lattice (AA-stacking). By this
correspondence, nine pairs of layer group types are mapped to the same space
group type due to the inability of the space group to distinguish the in-plane
and out-of-plane axes. In total 18% of the monolayers in the C2DB belong to one
of these layer group pairs and are thus not properly classified by the space
group type.
