* First position – primary direction – z direction, assigned to the higher-order axis. 
* Second position – symmetrically equivalent secondary directions, which are perpendicular to the z-axis. These can be 2, m, or  
* Third position – symmetrically equivalent tertiary directions, passing between secondary directions. These can be 2, m, or 
These are the crystallographic groups 3, 32, 3m, , and  (trigonal crystal system), 4, 422, 4mm, , 2m, , and  (tetragonal), and 6, 622, 6mm, , m2, , and  (hexagonal). Analogously, symbols of non-crystallographic groups (with axes of order 5, 7, 8, 9, ...) can be constructed. These groups can be arranged in the following table
It can be noticed that in groups with odd-order axes n and  the third position in symbol is always absent, because all n directions, perpendicular to higher-order axis, are symmetrically equivalent. For example, in the picture of a triangle all three mirror planes (S, S, S) are equivalent – all of them pass through one vertex and the center of the opposite side. 
For even-order axes n and  there are  secondary directions and  tertiary directions. For example, in the picture of a regular hexagon one can distinguish two sets of mirror planes – three planes go through two opposite vertexes, and three other planes go through the centers of opposite sides. In this case any of two sets can be chosen as secondary directions, the rest set will be tertiary directions. Hence groups 2m, 2m, 2m, ... can be written as m2, m2, m2, ...&thinsp;. For symbols of point groups this order usually doesnt matter; however, it will be important for Hermann–Mauguin symbols of corresponding space groups, where secondary directions are directions of symmetry elements along unit cell translations b and c, while the tertiary directions correspond to the direction between unit cell translations b and c. For example, symbols Pm2 and P2m denote two different space groups. This also applies to symbols of space groups with odd-order axes 3 and . The perpendicular symmetry elements can go along unit cell translations b and c' or between them. Space groups P321 and P312 are examples of the former and the latter cases, respectively.
The symbol of point group  may be confusing; the corresponding Schoenflies symbol is D, which means that the group consists of 3-fold axis, three perpendicular 2-fold axes, and 3 vertical diagonal planes passing between these 2-fold axes, so it seems that the group can be denoted as 32m or 3m2. However, one should remember that, unlike Schoenflies notation, the direction of a plane in a Hermann–Mauguin symbol is defined as the direction perpendicular to the plane, and in the D group all mirror planes are perpendicular to 2-fold axes, so they should be written in the same position as . Second, these  complexes generate an inversion center, which combining with the 3-fold rotation axis generates a  rotoinversion axis.
Groups with n&thinsp;=&thinsp;∞ are called limit groups or Curie groups.