Point groups

C1

E (not highly symmetrical or linear, no rotation axis)

Cs

sigma & E (not highly symmetrical or linear, no rotation axis)

Ci

i & E (not highly symmetrical or linear, no rotation axis)

C(infinity-v)

linear (not symmetric)

D(infinity-v)

linear (symmetric)

Cnh

nCn, sigma-h, i, nSn (not high symmetry or linear, rotation axis, no C2 norm to highest-order Cn rot axis, sigma-h)

Cnv

nCn, nsigma-v/d (not high symmetry or linear, rotation axis, no C2 norm to highest-order Cn rot axis, sigma-v)

S2n

(n/2)Sn, (n/2)Cn/2 (not high symmetry or linear, rotation axis, no C2 norm to highest-order Cn rot axis, S2n)

Cn

nCn (not high symmetry or linear, rotation axis, no C2 norm to highest-order Cn rot axis, no sigma-v or -h, no S2n)

Dnh

nCn, nC2, nsigma-v/d, sigma-h, i (not high symmetry or linear, rotation axis, C2 norm to highest-order Cn rot axis, sigma-h)

Dnd

nCn, nC2, nsigma-d, nS2n, i (not high symmetry or linear, rotation axis, C2 norm to highest-order Cn rot axis, sigma-d)

Dn

nCn, nC2 (not high symmetry or linear, rotation axis, C2 norm to highest-order Cn rot axis, no sigma-h or -d)

Td

tetrahedral (high symmetry, has >1 rot axis w/ n>2)

Oh

octahedral (high symmetry, has >1 rot axis w/ n>2)

Ih

icosahedral (high symmetry, has >1 rot axis w/ n>2)