Subgroups — C₅×D₃₁₇₁ #44540252

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₅₇	—	3	1	no	maximal, Hall
3	D₃₁₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₅₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₅×D₄₅₃	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	D₇	1	1	yes	characteristic, complemented, Hall
8	D₁₀₅₇	—	3	1	no	Hall
9	C₅×D₁₅₁	—	21	1	no	Hall
10	C₇×C₁₅₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
11	D₄₅₃	—	7	1	no	Hall
12	C₅×C₁₅₁	D₂₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
14	D₁₅₁	—	21	1	no	Hall
15	C₅×D₂₁	—	151	1	no	maximal, Hall
16	C₁₅₁	C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₅₁	1	1	yes	characteristic, complemented, Hall
18	C₅×D₇	—	453	1	no	Hall
19	D₂₁	—	151	1	no	Hall
20	C₅×C₇	D₄₅₃	1	1	yes	characteristic, complemented, Hall
21	C₅×D₃	—	1057	1	no	Hall
22	C₃×C₇	C₅×D₁₅₁	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₁₀₅₇	1	1	yes	characteristic, complemented, Hall
24	D₇	—	453	1	no	Hall
25	C₂×C₅	—	3171	1	no	Hall
26	C₇	C₅×D₄₅₃	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	1057	1	no	Hall
28	C₅	D₃₁₇₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₁₀₅₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3171	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₁₇₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₅₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₃×C₇×C₁₅₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₅₁	C₂	semidirect
3. D₃₁₇₁	C₅	direct (N × H)
4. C₅×C₇×C₁₅₁	D₃	semidirect
6. C₃×C₇×C₁₅₁	C₂×C₅	semidirect
7. C₃×C₅×C₁₅₁	D₇	semidirect
10. C₇×C₁₅₁	C₅×D₃	semidirect
12. C₅×C₁₅₁	D₂₁	semidirect
13. C₃×C₁₅₁	C₅×D₇	semidirect
16. C₁₅₁	C₅×D₂₁	semidirect
17. C₃×C₅×C₇	D₁₅₁	semidirect
20. C₅×C₇	D₄₅₃	semidirect
22. C₃×C₇	C₅×D₁₅₁	semidirect
23. C₃×C₅	D₁₀₅₇	semidirect
26. C₇	C₅×D₄₅₃	semidirect
28. C₅	D₃₁₇₁	direct (N × H)
29. C₃	C₅×D₁₀₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₅₁	2
C₅×D₁₀₅₇	3
D₃₁₇₁	5
C₅×D₄₅₃	7
C₅×D₂₁	151

Subgroups — C5×D3171 #44540252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₁₇₁ #44540252