Subgroups — C₃×C₅×C₁₁×D₇₁ #37552859

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	C₅×C₁₁×D₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×D₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₇₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₅×C₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₇₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₇₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₇₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅×C₁₁	—	71	1	no	maximal, Hall
14	C₃×C₇₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	D₇₁	1	1	yes	characteristic, direct product factor, Hall
16	D₇₁	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₁	—	71	1	no	Hall
18	C₇₁	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₁₁	—	71	1	no	Hall
20	C₅×C₁₁	C₃×D₇₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	C₅×D₇₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅	—	71	1	no	Hall
23	C₂×C₁₁	—	71	1	no	Hall
24	C₃×C₅	C₁₁×D₇₁	1	1	yes	characteristic, direct product factor, Hall
25	C₁₁	C₃×C₅×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	—	71	1	no	Hall
27	C₂×C₃	—	71	1	no	Hall
28	C₅	C₃×C₁₁×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₁₁×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁	D₇₁
commutator, cosocle, hypocenter	C₇₁	C₂×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₇₁	C₂	semidirect
2. C₅×C₁₁×D₇₁	C₃	direct (N × H)
3. C₃×C₁₁×D₇₁	C₅	direct (N × H)
4. C₅×C₁₁×C₇₁	C₂×C₃	semidirect
5. C₃×C₁₁×C₇₁	C₂×C₅	semidirect
6. C₃×C₅×D₇₁	C₁₁	direct (N × H)
7. C₁₁×D₇₁	C₃×C₅	direct (N × H)
8. C₃×C₅×C₇₁	C₂×C₁₁	semidirect
9. C₁₁×C₇₁	C₂×C₃×C₅	semidirect
10. C₅×D₇₁	C₃×C₁₁	direct (N × H)
11. C₃×D₇₁	C₅×C₁₁	direct (N × H)
12. C₅×C₇₁	C₂×C₃×C₁₁	semidirect
14. C₃×C₇₁	C₂×C₅×C₁₁	semidirect
15. C₃×C₅×C₁₁	D₇₁	direct (N × H)
16. D₇₁	C₃×C₅×C₁₁	direct (N × H)
18. C₇₁	C₂×C₃×C₅×C₁₁	semidirect
20. C₅×C₁₁	C₃×D₇₁	direct (N × H)
21. C₃×C₁₁	C₅×D₇₁	direct (N × H)
24. C₃×C₅	C₁₁×D₇₁	direct (N × H)
25. C₁₁	C₃×C₅×D₇₁	direct (N × H)
28. C₅	C₃×C₁₁×D₇₁	direct (N × H)
29. C₃	C₅×C₁₁×D₇₁	direct (N × H)

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
C₅×C₁₁×D₇₁	3
C₃×C₁₁×D₇₁	5
C₃×C₅×D₇₁	11
C₂×C₃×C₅×C₁₁	71

Subgroups — C3×C5×C11×D71 #37552859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁×D₇₁ #37552859