There are at least ten methods of naming space groups.  Some of these methods can assign several different names to the same space group, so altogether there are many thousands of different names.
; Number: The International Union of Crystallography publishes tables of all space group types, and assigns each a unique number from 1 to 230.  The numbering is arbitrary, except that groups with the same crystal system or point group are given consecutive numbers.
; Hall notation
: Space group notation with an explicit origin. Rotation, translation and axis-direction symbols are clearly separated and inversion centers are explicitly defined. The construction and format of the notation make it particularly suited to computer generation of symmetry information. For example, group number 3 has three Hall symbols: P 2y (P 1 2 1), P 2 (P 1 1 2), P 2x (P 2 1 1).
; Schönflies notation: The space groups with given point group are numbered by 1, 2, 3, ... (in the same order as their international number) and this number is added as a superscript to the Schönflies symbol for the point group. For example, groups numbers 3 to 5 whose point group is C have Schönflies symbols C, C, C.
; Coxeter notation: Spatial and point symmetry groups, represented as modifications of the pure reflectional Coxeter groups.
; Geometric notation
: A geometric algebra notation.