Subgroups — C₃₁×Dic₂₁₅ #40998613

Order 26660.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×Dic₄₃	—	5	1	no	maximal, Hall
4	C₂×C₃₁×C₄₃	D₅	1	1	yes	characteristic
5	C₃₁×C₄₃	Dic₅	1	1	yes	characteristic, complemented, Hall
6	Dic₂₁₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	Dic₅×C₃₁	—	43	1	no	maximal, Hall
8	C₂×C₅×C₄₃	C₂×C₃₁	1	1	yes	characteristic
9	C₂×C₅×C₃₁	D₄₃	1	1	yes	characteristic
10	C₅×C₄₃	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
11	Dic₄₃	—	5	1	no	Hall
12	C₅×C₃₁	Dic₄₃	1	1	yes	characteristic, complemented, Hall
13	C₄×C₃₁	—	215	1	no	Hall
14	C₂×C₄₃	D₅×C₃₁	1	1	yes	characteristic
15	C₂×C₃₁	D₂₁₅	1	1	yes	characteristic
16	C₄₃	Dic₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	Dic₂₁₅	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₅	—	43	1	no	Hall
19	C₂×C₅	C₃₁×D₄₃	1	1	yes	characteristic
20	C₅	C₃₁×Dic₄₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	215	1	no	Sylow
22	C₂	C₃₁×D₂₁₅	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.