Subgroups — C₅×C₃₁×Dic₃₇ #37525713

Order 22940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃₁×C₃₇	C₂×C₅	1	1	yes	characteristic
5	C₃₁×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₃₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₅×C₃₁	—	37	1	no	maximal, Hall
8	C₂×C₅×C₃₇	C₂×C₃₁	1	1	yes	characteristic
9	C₂×C₅×C₃₁	D₃₇	1	1	yes	characteristic
10	C₅×C₃₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	Dic₃₇	1	1	yes	characteristic, direct product factor, Hall
12	Dic₃₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₃₁	—	37	1	no	Hall
14	C₂×C₃₇	C₂×C₅×C₃₁	1	1	yes	characteristic
15	C₂×C₃₁	C₅×D₃₇	1	1	yes	characteristic
16	C₃₇	C₄×C₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₅×Dic₃₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₅	—	37	1	no	Hall
19	C₂×C₅	C₃₁×D₃₇	1	1	yes	characteristic
20	C₅	C₃₁×Dic₃₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	37	1	no	Sylow
22	C₂	C₅×C₃₁×D₃₇	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.