A system for categorizing symmetries of molecules. Cn groups contain only an n-fold rotation axis. Cnv groups, in addition to the n-fold rotation axis, have a mirror plane that contains the axis of rotation (and mirror planes associated with the existence of the n-fold axis). Cnh groups, in addition to the n-fold rotation axis, have a mirror plane perpendicular to the axis. Sn groups have an n-fold rotation-reflection axis. Dn groups have an n-fold rotation axis and a two-fold axis perpendicular to the n-fold axis (and two-fold axes associated with the existence of the n-fold axis). Dnh groups have all the symmetry operations of Dn and also a mirror plane perpendicular to the n-fold axis. Dnd groups contain all the symmetry operations of Dn and also mirror planes that contain the n-fold axis and bisect the angles between the two-fold axes. In the Schoenflies notation C stands for ‘cyclic’, S stands for ‘spiegel’ (mirror), and D stands for ‘dihedral’. The subscripts h, v, and d stand for horizontal, vertical, and diagonal respectively, where these words refer to the position of the mirror planes with respect to the n-fold axis (considered to be vertical). In addition to the noncubic groups referred to so far, there are cubic groups, which have several rotation axes with the same value of n. These are the tetrahedral groups T, Th, and Td, the octahedral groups O and Oh, and the icosahedral group I. The Schoenflies system is commonly used for isolated molecules, while the Hermann-Mauguin system is commonly used in crystallography.