Subgroups — C₁₁×C₂₃×D₃₅ #31799321

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	—	5	1	no	maximal, Hall
3	D₅×C₁₁×C₂₃	—	7	1	no	maximal, Hall
4	C₇×C₁₁×C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
5	C₂₃×D₃₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₂₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×D₃₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₁₁×C₂₃	—	35	1	no	Hall
10	C₅×C₇×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
11	D₇×C₂₃	—	5	1	no	Hall
12	C₁₁×C₂₃	D₃₅	1	1	yes	characteristic, direct product factor, Hall
13	D₅×C₂₃	—	7	1	no	Hall
14	C₇×C₂₃	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×D₇	—	5	1	no	Hall
16	C₅×C₂₃	C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₁	—	7	1	no	Hall
18	C₇×C₁₁	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
19	D₃₅	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₁	D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₃	—	35	1	no	Hall
22	C₅×C₇	C₂×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
23	C₂₃	C₁₁×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₁₁	—	35	1	no	Hall
25	D₇	—	5	1	no	Hall
26	C₁₁	C₂₃×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
27	D₅	—	7	1	no	Hall
28	C₇	D₅×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₅	C₁₁×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ 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
4. C₇×C₁₁×C₂₃	D₅	semidirect
5. C₂₃×D₃₅	C₁₁	direct (N × H)
6. C₅×C₁₁×C₂₃	D₇	semidirect
7. C₅×C₇×C₂₃	C₂×C₁₁	semidirect
8. C₁₁×D₃₅	C₂₃	direct (N × H)
10. C₅×C₇×C₁₁	C₂×C₂₃	semidirect
12. C₁₁×C₂₃	D₃₅	direct (N × H)
14. C₇×C₂₃	D₅×C₁₁	semidirect
16. C₅×C₂₃	C₁₁×D₇	semidirect
18. C₇×C₁₁	D₅×C₂₃	semidirect
19. D₃₅	C₁₁×C₂₃	direct (N × H)
20. C₅×C₁₁	D₇×C₂₃	semidirect
22. C₅×C₇	C₂×C₁₁×C₂₃	semidirect
23. C₂₃	C₁₁×D₃₅	direct (N × H)
26. C₁₁	C₂₃×D₃₅	direct (N × H)
28. C₇	D₅×C₁₁×C₂₃	semidirect
29. C₅	C₁₁×D₇×C₂₃	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×C₂₃	2
C₁₁×D₇×C₂₃	5
D₅×C₁₁×C₂₃	7
C₂₃×D₃₅	11
C₁₁×D₃₅	23

Subgroups — C11×C23×D35 #31799321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂₃×D₃₅ #31799321