Subgroups — C₅×D₃×C₁₁×C₇₁ #37552866

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×C₁₁×C₇₁	—	3	1	no	maximal, Hall
3	D₃×C₁₁×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₇₁	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₇₁	—	3	1	no	Hall
8	C₃×C₅×C₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₇₁	—	3	1	no	Hall
11	D₃×C₇₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₇₁	D₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅×D₃×C₁₁	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₁	—	3	1	no	Hall
17	C₂×C₅×C₁₁	—	3	1	no	Hall
18	C₇₁	C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	D₃×C₁₁	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₁	D₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	C₂×C₅×C₇₁	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	C₁₁×C₇₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₁	—	3	1	no	Hall
24	C₃×C₅	C₂×C₁₁×C₇₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₅×D₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	—	3	1	no	Hall
27	D₃	C₅×C₁₁×C₇₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅	D₃×C₁₁×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₅×C₁₁×C₇₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₁×C₇₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₁₁×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₁₁×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₇₁	C₂	semidirect
3. D₃×C₁₁×C₇₁	C₅	direct (N × H)
4. C₅×C₁₁×C₇₁	D₃	direct (N × H)
5. C₃×C₁₁×C₇₁	C₂×C₅	semidirect
6. C₅×D₃×C₇₁	C₁₁	direct (N × H)
8. C₃×C₅×C₇₁	C₂×C₁₁	semidirect
9. C₁₁×C₇₁	C₅×D₃	direct (N × H)
11. D₃×C₇₁	C₅×C₁₁	direct (N × H)
12. C₅×C₇₁	D₃×C₁₁	direct (N × H)
13. C₅×D₃×C₁₁	C₇₁	direct (N × H)
14. C₃×C₇₁	C₂×C₅×C₁₁	semidirect
15. C₃×C₅×C₁₁	C₂×C₇₁	semidirect
18. C₇₁	C₅×D₃×C₁₁	direct (N × H)
19. D₃×C₁₁	C₅×C₇₁	direct (N × H)
20. C₅×C₁₁	D₃×C₇₁	direct (N × H)
21. C₃×C₁₁	C₂×C₅×C₇₁	semidirect
22. C₅×D₃	C₁₁×C₇₁	direct (N × H)
24. C₃×C₅	C₂×C₁₁×C₇₁	semidirect
25. C₁₁	C₅×D₃×C₇₁	direct (N × H)
27. D₃	C₅×C₁₁×C₇₁	direct (N × H)
28. C₅	D₃×C₁₁×C₇₁	direct (N × H)
29. C₃	C₂×C₅×C₁₁×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁×C₇₁	2
C₂×C₅×C₁₁×C₇₁	3
D₃×C₁₁×C₇₁	5
C₅×D₃×C₇₁	11
C₅×D₃×C₁₁	71

Subgroups — C5×D3×C11×C71 #37552866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₁×C₇₁ #37552866