Molecules grouped by symmetry

C1 g-N2H4
Ci C4H8Cl2
C2 g-H2O2, H2SO4
C3 CH(NH2)3
C2h N2H2
C3h B(OH)3
D2d B2H6
D3d t-C2H6
D4d S8
D5d Fe(C5H5)2 (staggered)
D6d Cr(C6H6)2 (staggered)
D1h t-H2O2
D2h C2H4, C10H8, C14H10
D3h c-C2H6, C13H9, PF5, ClF3
D4h XeF4
D5h IF7, Fe(C5H5)2 (eclipsed)
D6h C6H6
D∞h H2, N2, O2, F2, C2H2, CO2
C2v H2O, SO2, c-H2O2, C6H5OH, SF4
C3v NH3
C4v SClF5
C5v IClF6
C6v Cr(C6H6)(C6D6)
C∞v HF, CO
Td N4, P4, CH4, C(CH3)4, C10H16
Oh SF6, UF6, OsF8 (??), C8H8
Yh Si12, C20, C20H20, C60
E∞h H

Stable molecules with the following groups can not exist: C, C∞h, D, E, and any discrete group with rotational axis of order greater than 6 excluding D4d.

Absent groups: C4, C5, C6, C2d, C3d, C5d, C4h, C5h, C6h, D2, D3, D4, D5, D6, T, Th, O, Y.