Subgroups — C₇×D₅×C₁₁×C₃₁ #37558819

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	C₂×C₇×C₁₁×C₃₁	—	5	1	no	maximal, Hall
3	D₅×C₁₁×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₃₁	D₅	1	1	yes	characteristic, direct product factor, Hall
5	C₇×D₅×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₇×D₅×C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₁×C₃₁	—	5	1	no	Hall
10	C₂×C₇×C₃₁	—	5	1	no	Hall
11	C₅×C₇×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₃₁	C₇×D₅	1	1	yes	characteristic, direct product factor, Hall
13	D₅×C₃₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₃₁	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₁	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₁₁	—	5	1	no	Hall
17	D₅×C₁₁	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₁	D₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
19	C₇×D₅	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃₁	—	5	1	no	Hall
21	C₅×C₁₁	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
22	C₅×C₇	C₂×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
23	C₃₁	C₇×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₁₁	—	5	1	no	Hall
25	C₂×C₇	—	5	1	no	Hall
26	C₁₁	C₇×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
27	D₅	C₇×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₇	D₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₂×C₇×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁×C₃₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₇×C₁₁×C₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₃₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₇×C₁₁×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₁×C₃₁	C₂	semidirect
3. D₅×C₁₁×C₃₁	C₇	direct (N × H)
4. C₇×C₁₁×C₃₁	D₅	direct (N × H)
5. C₇×D₅×C₃₁	C₁₁	direct (N × H)
6. C₅×C₁₁×C₃₁	C₂×C₇	semidirect
7. C₅×C₇×C₃₁	C₂×C₁₁	semidirect
8. C₇×D₅×C₁₁	C₃₁	direct (N × H)
11. C₅×C₇×C₁₁	C₂×C₃₁	semidirect
12. C₁₁×C₃₁	C₇×D₅	direct (N × H)
13. D₅×C₃₁	C₇×C₁₁	direct (N × H)
14. C₇×C₃₁	D₅×C₁₁	direct (N × H)
15. C₅×C₃₁	C₂×C₇×C₁₁	semidirect
17. D₅×C₁₁	C₇×C₃₁	direct (N × H)
18. C₇×C₁₁	D₅×C₃₁	direct (N × H)
19. C₇×D₅	C₁₁×C₃₁	direct (N × H)
21. C₅×C₁₁	C₂×C₇×C₃₁	semidirect
22. C₅×C₇	C₂×C₁₁×C₃₁	semidirect
23. C₃₁	C₇×D₅×C₁₁	direct (N × H)
26. C₁₁	C₇×D₅×C₃₁	direct (N × H)
27. D₅	C₇×C₁₁×C₃₁	direct (N × H)
28. C₇	D₅×C₁₁×C₃₁	direct (N × H)
29. C₅	C₂×C₇×C₁₁×C₃₁	semidirect

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
C₂×C₇×C₁₁×C₃₁	5
D₅×C₁₁×C₃₁	7
C₇×D₅×C₃₁	11
C₇×D₅×C₁₁	31

Subgroups — C7×D5×C11×C31 #37558819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₅×C₁₁×C₃₁ #37558819