Subgroups — C₂²×Dic₃₁ #92500

Order 496.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₁	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃₁	C₄	1	4	yes	complemented
4	C₂²×C₃₁	C₂²	1	3	yes	—
5	Dic₃₁	C₂²	1	4	yes	direct product factor
6	C₂×C₃₁	C₂×C₄	1	6	yes	complemented
7	C₂×C₃₁	C₂³	1	1	yes	characteristic
8	C₃₁	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₄	—	31	1	no	maximal, Sylow
10	C₂³	D₃₁	1	1	yes	characteristic
11	C₂×C₄	—	31	6	no	—
12	C₂²	Dic₃₁	1	4	yes	direct product factor
13	C₂²	C₂×D₃₁	1	3	yes	—
14	C₄	—	31	4	no	—
15	C₂	C₂×Dic₃₁	1	6	yes	direct product factor
16	C₂	C₂²×D₃₁	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.