Subgroups — C₁₁×D₁₅×C₇₁ #37552870

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	D₅×C₁₁×C₇₁	—	3	1	no	maximal, Hall
3	D₃×C₁₁×C₇₁	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₇₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₅×C₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₇₁	—	15	1	no	Hall
8	C₃×C₅×C₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	D₁₅	1	1	yes	characteristic, direct product factor, Hall
10	D₅×C₇₁	—	3	1	no	Hall
11	D₃×C₇₁	—	5	1	no	Hall
12	C₅×C₇₁	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₁₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇₁	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₁	—	15	1	no	Hall
17	D₅×C₁₁	—	3	1	no	Hall
18	C₇₁	C₁₁×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
19	D₃×C₁₁	—	5	1	no	Hall
20	C₅×C₁₁	D₃×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₅×C₇₁	1	1	yes	characteristic, complemented, Hall
22	D₁₅	C₁₁×C₇₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₁	—	15	1	no	Hall
24	C₃×C₅	C₂×C₁₁×C₇₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₁₅×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	3	1	no	Hall
27	D₃	—	5	1	no	Hall
28	C₅	D₃×C₁₁×C₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₁₁×C₇₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₇₁	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₁₁×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ 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
4. C₅×C₁₁×C₇₁	D₃	semidirect
5. C₃×C₁₁×C₇₁	D₅	semidirect
6. D₁₅×C₇₁	C₁₁	direct (N × H)
8. C₃×C₅×C₇₁	C₂×C₁₁	semidirect
9. C₁₁×C₇₁	D₁₅	direct (N × H)
12. C₅×C₇₁	D₃×C₁₁	semidirect
13. C₁₁×D₁₅	C₇₁	direct (N × H)
14. C₃×C₇₁	D₅×C₁₁	semidirect
15. C₃×C₅×C₁₁	C₂×C₇₁	semidirect
18. C₇₁	C₁₁×D₁₅	direct (N × H)
20. C₅×C₁₁	D₃×C₇₁	semidirect
21. C₃×C₁₁	D₅×C₇₁	semidirect
22. D₁₅	C₁₁×C₇₁	direct (N × H)
24. C₃×C₅	C₂×C₁₁×C₇₁	semidirect
25. C₁₁	D₁₅×C₇₁	direct (N × H)
28. C₅	D₃×C₁₁×C₇₁	semidirect
29. C₃	D₅×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
D₅×C₁₁×C₇₁	3
D₃×C₁₁×C₇₁	5
D₁₅×C₇₁	11
C₁₁×D₁₅	71

Subgroups — C11×D15×C71 #37552870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₅×C₇₁ #37552870