Subgroups — C₅×C₂₃×D₇₇ #31799315

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	C₂₃×D₇₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₁₁×C₂₃	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×D₇×C₂₃	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₂₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₂₃	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×D₇₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₁₁×C₂₃	—	7	1	no	Hall
10	C₅×C₇×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	D₇×C₂₃	—	11	1	no	Hall
12	C₁₁×C₂₃	C₅×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₂₃	—	77	1	no	Hall
14	C₇×C₂₃	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
15	D₇₇	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₂₃	D₇₇	1	1	yes	characteristic, direct product factor, Hall
17	C₅×D₁₁	—	7	1	no	Hall
18	C₇×C₁₁	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₅×D₇	—	11	1	no	Hall
20	C₅×C₁₁	D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₃	—	77	1	no	Hall
22	C₅×C₇	D₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
23	C₂₃	C₅×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
24	D₁₁	—	7	1	no	Hall
25	D₇	—	11	1	no	Hall
26	C₁₁	C₅×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅	—	77	1	no	Hall
28	C₇	C₅×D₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₅	C₂₃×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	77	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₅×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. C₂₃×D₇₇	C₅	direct (N × H)
4. C₇×C₁₁×C₂₃	C₂×C₅	semidirect
6. C₅×C₁₁×C₂₃	D₇	semidirect
7. C₅×C₇×C₂₃	D₁₁	semidirect
8. C₅×D₇₇	C₂₃	direct (N × H)
10. C₅×C₇×C₁₁	C₂×C₂₃	semidirect
12. C₁₁×C₂₃	C₅×D₇	semidirect
14. C₇×C₂₃	C₅×D₁₁	semidirect
15. D₇₇	C₅×C₂₃	direct (N × H)
16. C₅×C₂₃	D₇₇	direct (N × H)
18. C₇×C₁₁	C₂×C₅×C₂₃	semidirect
20. C₅×C₁₁	D₇×C₂₃	semidirect
22. C₅×C₇	D₁₁×C₂₃	semidirect
23. C₂₃	C₅×D₇₇	direct (N × H)
26. C₁₁	C₅×D₇×C₂₃	semidirect
28. C₇	C₅×D₁₁×C₂₃	semidirect
29. C₅	C₂₃×D₇₇	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
C₂₃×D₇₇	5
C₅×D₁₁×C₂₃	7
C₅×D₇×C₂₃	11
C₅×D₇₇	23

Subgroups — C5×C23×D77 #31799315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₃×D₇₇ #31799315