Subgroups — C₅×C₁₁×D₇×C₂₃ #31799313

Order 17710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₁₁×C₂₃	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×D₇×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₂₃	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×D₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₁×C₂₃	—	7	1	no	Hall
10	C₅×C₇×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	D₇×C₂₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×C₂₃	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₂₃	—	7	1	no	Hall
14	C₇×C₂₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×D₇	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₂₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₁	—	7	1	no	Hall
18	C₇×C₁₁	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₅×D₇	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₁	D₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₂₃	—	7	1	no	Hall
22	C₅×C₇	C₂×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
23	C₂₃	C₅×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₁₁	—	7	1	no	Hall
25	D₇	C₅×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁	C₅×D₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₅	—	7	1	no	Hall
28	C₇	C₂×C₅×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₅	C₁₁×D₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁×C₂₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₁₁×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₁×C₂₃	C₂	semidirect
2. C₁₁×D₇×C₂₃	C₅	direct (N × H)
4. C₇×C₁₁×C₂₃	C₂×C₅	semidirect
5. C₅×D₇×C₂₃	C₁₁	direct (N × H)
6. C₅×C₁₁×C₂₃	D₇	direct (N × H)
7. C₅×C₇×C₂₃	C₂×C₁₁	semidirect
8. C₅×C₁₁×D₇	C₂₃	direct (N × H)
10. C₅×C₇×C₁₁	C₂×C₂₃	semidirect
11. D₇×C₂₃	C₅×C₁₁	direct (N × H)
12. C₁₁×C₂₃	C₅×D₇	direct (N × H)
14. C₇×C₂₃	C₂×C₅×C₁₁	semidirect
15. C₁₁×D₇	C₅×C₂₃	direct (N × H)
16. C₅×C₂₃	C₁₁×D₇	direct (N × H)
18. C₇×C₁₁	C₂×C₅×C₂₃	semidirect
19. C₅×D₇	C₁₁×C₂₃	direct (N × H)
20. C₅×C₁₁	D₇×C₂₃	direct (N × H)
22. C₅×C₇	C₂×C₁₁×C₂₃	semidirect
23. C₂₃	C₅×C₁₁×D₇	direct (N × H)
25. D₇	C₅×C₁₁×C₂₃	direct (N × H)
26. C₁₁	C₅×D₇×C₂₃	direct (N × H)
28. C₇	C₂×C₅×C₁₁×C₂₃	semidirect
29. C₅	C₁₁×D₇×C₂₃	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×C₂₃	2
C₁₁×D₇×C₂₃	5
C₂×C₅×C₁₁×C₂₃	7
C₅×D₇×C₂₃	11
C₅×C₁₁×D₇	23

Subgroups — C5×C11×D7×C23 #31799313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×D₇×C₂₃ #31799313