Symmetry operations : 1,2,3,4,6, -1,-2,-3,-4,-6, m
| Crystal System | Point groups | Laue Class | Patterson Symmetry |
| Triclinc | 1, -1 | -1 | P-1 |
| Monoclinic | 2, m, 2/m | 2/m | P2/m, C2/m |
| Orthorhombic | 222, mm2 , mmm | mmm | Pmmm, Cmmm, Fmmm, Immm |
| Tetragonal | 4, -4, 4/m, 422, 4mm, -42m, 4/mmm | 4/m, 4/mmm | P4/m, I4/m, P4/mmm, I4/mmm |
| Trigonal | 3, -3, 32, 3m, -3 m | -3, -3m | P-3, R-3, P-3m1, P-31m, R-3m |
| Hexagonal | 6, -6, 6/m, 622, 6mm, -62m, 6/mmm | 6/m, 6/mmm | P6/m, P6/mmm |
| Cubic | 23, m-3, 432, -43m, m3m | m-3, m-3m | Pm-3, Im-3, F-3m, Pm-3m, Fm-3m, Im-3m |
Notes
| space group | polar axes |
|---|---|
| P1 | x, y, z |
| P2, P21, C2 | y |
| P4, P41, P42, P43, I4, I41 | z |
| P3, P31, P32, R3, H3 | z |
| P6, P61, P62, P63, P64, P65 | z |