- C1
- 'A'
- Cs
- 'AP', 'APP'
- Ci
- 'AG', 'AU'
- C2
- 'A', 'B'
- D2
- 'A', 'B1', 'B2', 'B3'
- D3
- 'A1', 'A2', 'E'
- C2v
- 'A1', 'A2', 'B1', 'B2'
- C3v
- 'A1', 'A2', 'E'
- C4v
- 'A1', 'A2', 'B1', 'B2', 'E'
- C2h
- 'AG', 'BG', 'AU', 'BU'
- D2h
- 'AG', 'B1G', 'B2G', 'B3G', 'AU', 'B1U', 'B2U', 'B3U'
- D3h
- 'A1P', 'A2P', 'EP', 'A1PP', 'A2PP', 'EPP'
- D6h
- 'A1G', 'A2G', 'B1G', 'B2G', 'E1G', 'E2G', 'A1U', 'A2U', 'B1U', 'B2U', 'E1U', 'E2U'
- D2d
- 'A1', 'A2', 'B1', 'B2', 'E'
- D3d
- 'A1G', 'A2G', 'EG', 'A1U', 'A2U', 'EU'
- Td
- 'A1', 'A2', 'E ', 'T1', 'T2'
- Oh
- 'A1G', 'A2G', 'EG', 'T1G', 'T2G', 'A1U', 'A2U', 'EU', 'T1U', 'T2U'
- CAv
- (C-infinity-v) 'S', 'A2', 'B1', 'B2', 'P', 'D', 'F', 'G'
- DAh
- (D-infinity-h) 'SG', 'A2G', 'B1G', 'B2G', 'PG', 'DG', 'FG', 'GG', 'SU ', 'A2U', 'B1U', 'B2U', 'PU ', 'DU ', 'FU ', 'GU '
- Ih
- 'AG', 'T1G', 'T2G', 'GG', 'HG', 'AU', 'T1U', 'T2U', 'GU', 'HU'

Note that in the case of atoms, the program uses the Ih symmetry so that 'AG' corresponds to 'S', 'T1U' corresponds to 'P', 'HG' corresponds to 'D', 'GU' and 'T2U' correspond to 'F', and 'GG' and 'HG' correspond to 'G'