Subgroups — C₃×C₇₁×D₅₅ #37552864

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	C₇₁×D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁×C₇₁	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅×C₇₁	—	11	1	no	maximal, Hall
7	D₁₁×C₇₁	—	5	1	no	Hall
8	C₃×C₅×C₇₁	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×C₇₁	—	11	1	no	Hall
11	C₂×C₃×C₇₁	—	55	1	no	Hall
12	C₅×C₇₁	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×D₅₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇₁	D₅₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₁₁	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₁	—	55	1	no	Hall
17	D₅₅	C₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
18	C₇₁	C₃×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×D₁₁	—	5	1	no	Hall
20	C₅×C₁₁	C₂×C₃×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	D₅×C₇₁	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅	—	11	1	no	Hall
23	D₁₁	—	5	1	no	Hall
24	C₃×C₅	D₁₁×C₇₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₃×D₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	11	1	no	Hall
27	C₂×C₃	—	55	1	no	Hall
28	C₅	C₃×D₁₁×C₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇₁×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇₁	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₃×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₇₁	C₂	semidirect
2. C₇₁×D₅₅	C₃	direct (N × H)
4. C₅×C₁₁×C₇₁	C₂×C₃	semidirect
5. C₃×C₁₁×C₇₁	D₅	semidirect
8. C₃×C₅×C₇₁	D₁₁	semidirect
9. C₁₁×C₇₁	C₃×D₅	semidirect
12. C₅×C₇₁	C₃×D₁₁	semidirect
13. C₃×D₅₅	C₇₁	direct (N × H)
14. C₃×C₇₁	D₅₅	direct (N × H)
15. C₃×C₅×C₁₁	C₂×C₇₁	semidirect
17. D₅₅	C₃×C₇₁	direct (N × H)
18. C₇₁	C₃×D₅₅	direct (N × H)
20. C₅×C₁₁	C₂×C₃×C₇₁	semidirect
21. C₃×C₁₁	D₅×C₇₁	semidirect
24. C₃×C₅	D₁₁×C₇₁	semidirect
25. C₁₁	C₃×D₅×C₇₁	semidirect
28. C₅	C₃×D₁₁×C₇₁	semidirect
29. C₃	C₇₁×D₅₅	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
C₇₁×D₅₅	3
C₃×D₁₁×C₇₁	5
C₃×D₅×C₇₁	11
C₃×D₅₅	71

Subgroups — C3×C71×D55 #37552864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇₁×D₅₅ #37552864