Subgroups — C₅×C₇×D₁₁×C₃₁ #37558813

Order 23870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₁₁×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₇×C₃₁	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₁	D₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇×D₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₁₁×C₃₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇×C₃₁	—	11	1	no	Hall
11	C₅×C₇×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₃₁	—	11	1	no	Hall
14	C₇×C₃₁	C₅×D₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₁	C₇×D₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₇×D₁₁	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₅×D₁₁	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₇	—	11	1	no	Hall
20	C₂×C₃₁	—	11	1	no	Hall
21	C₅×C₁₁	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
22	C₅×C₇	D₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
23	C₃₁	C₅×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
24	D₁₁	C₅×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	11	1	no	Hall
26	C₁₁	C₂×C₅×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	11	1	no	Hall
28	C₇	C₅×D₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₇×D₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇×C₃₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₃₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₁×C₃₁	C₂	semidirect
2. C₇×D₁₁×C₃₁	C₅	direct (N × H)
3. C₅×D₁₁×C₃₁	C₇	direct (N × H)
4. C₇×C₁₁×C₃₁	C₂×C₅	semidirect
6. C₅×C₁₁×C₃₁	C₂×C₇	semidirect
7. C₅×C₇×C₃₁	D₁₁	direct (N × H)
8. C₅×C₇×D₁₁	C₃₁	direct (N × H)
9. D₁₁×C₃₁	C₅×C₇	direct (N × H)
11. C₅×C₇×C₁₁	C₂×C₃₁	semidirect
12. C₁₁×C₃₁	C₂×C₅×C₇	semidirect
14. C₇×C₃₁	C₅×D₁₁	direct (N × H)
15. C₅×C₃₁	C₇×D₁₁	direct (N × H)
16. C₇×D₁₁	C₅×C₃₁	direct (N × H)
17. C₅×D₁₁	C₇×C₃₁	direct (N × H)
18. C₇×C₁₁	C₂×C₅×C₃₁	semidirect
21. C₅×C₁₁	C₂×C₇×C₃₁	semidirect
22. C₅×C₇	D₁₁×C₃₁	direct (N × H)
23. C₃₁	C₅×C₇×D₁₁	direct (N × H)
24. D₁₁	C₅×C₇×C₃₁	direct (N × H)
26. C₁₁	C₂×C₅×C₇×C₃₁	semidirect
28. C₇	C₅×D₁₁×C₃₁	direct (N × H)
29. C₅	C₇×D₁₁×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₁×C₃₁	2
C₇×D₁₁×C₃₁	5
C₅×D₁₁×C₃₁	7
C₂×C₅×C₇×C₃₁	11
C₅×C₇×D₁₁	31

Subgroups — C5×C7×D11×C31 #37558813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×D₁₁×C₃₁ #37558813