International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2015 
International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 4849
Section 1.4.1.5. Hermann–Mauguin symbols of the plane groups
H. Wondratschek^{e}

The principles of the HM symbols for space groups are retained in the HM symbols for plane groups (also known as wallpaper groups). The rotation axes along c of three dimensions are replaced by rotation points in the ab plane; the possible orders of rotations are the same as in threedimensional space: 2, 3, 4 and 6. The lattice (sometimes called net) of a plane group is spanned by the two basis vectors a and b, and is designated by a lowercase letter. The choice of a lattice basis, i.e. of a minimal cell, leads to a primitive lattice p, in addition a ccentred lattice is conventionally used. The nets are listed in Table 3.1.2.1 . The reflections and glide reflections through planes of the space groups are replaced by reflections and glide reflections through lines. Glide reflections are called g independent of the direction of the glide line. The arrangement of the constituents in the HM symbol is displayed in Table 1.4.1.2.

Short HM symbols are used only if there is at most one symmetry direction, e.g. p411 is replaced by p4 (no symmetry direction), p1m1 is replaced by pm (one symmetry direction) etc.
There are four crystal systems of plane groups, cf. Table 3.2.3.1 . The analogue of the triclinic crystal system is called oblique, the analogues of the monoclinic and orthorhombic crystal systems are rectangular. Both have rotations of order 2 at most. The presence of reflection or glide reflection lines in the rectangular crystal system allows one to choose a rectangular basis with one basis vector perpendicular to a symmetry line and one basis vector parallel to it. The square crystal system is analogous to the tetragonal crystal system for space groups by the occurrence of fourfold rotation points and a square net. Plane groups with threefold and sixfold rotation points are united in the hexagonal crystal system with a hexagonal net.
Plane groups occur as sections and projections of the space groups, cf. Section 1.4.5. In order to maintain the relations to the space groups, the symmetry directions of the symmetry lines are determined by their normals, not by the directions of the lines themselves. This is important because the normal of the line, not the direction of the line itself, determines the position in the HM symbol.