Subgroups — C₅×D₃₃×C₇₁ #37552868

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×D₁₁×C₇₁	—	3	1	no	maximal, Hall
3	D₃₃×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₇₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₇₁	—	11	1	no	maximal, Hall
7	D₁₁×C₇₁	—	3	1	no	Hall
8	C₃×C₅×C₇₁	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇₁	—	33	1	no	Hall
11	D₃×C₇₁	—	11	1	no	Hall
12	C₅×C₇₁	D₃₃	1	1	yes	characteristic, direct product factor, Hall
13	C₅×D₃₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₇₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₁	—	33	1	no	Hall
17	C₅×D₁₁	—	3	1	no	Hall
18	C₇₁	C₅×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
19	D₃₃	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₁	D₃×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	C₂×C₅×C₇₁	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	11	1	no	Hall
23	D₁₁	—	3	1	no	Hall
24	C₃×C₅	D₁₁×C₇₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₅×D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	33	1	no	Hall
27	D₃	—	11	1	no	Hall
28	C₅	D₃₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₁₁×C₇₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇₁	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₅×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. D₃₃×C₇₁	C₅	direct (N × H)
4. C₅×C₁₁×C₇₁	D₃	semidirect
5. C₃×C₁₁×C₇₁	C₂×C₅	semidirect
8. C₃×C₅×C₇₁	D₁₁	semidirect
9. C₁₁×C₇₁	C₅×D₃	semidirect
12. C₅×C₇₁	D₃₃	direct (N × H)
13. C₅×D₃₃	C₇₁	direct (N × H)
14. C₃×C₇₁	C₅×D₁₁	semidirect
15. C₃×C₅×C₁₁	C₂×C₇₁	semidirect
18. C₇₁	C₅×D₃₃	direct (N × H)
19. D₃₃	C₅×C₇₁	direct (N × H)
20. C₅×C₁₁	D₃×C₇₁	semidirect
21. C₃×C₁₁	C₂×C₅×C₇₁	semidirect
24. C₃×C₅	D₁₁×C₇₁	semidirect
25. C₁₁	C₅×D₃×C₇₁	semidirect
28. C₅	D₃₃×C₇₁	direct (N × H)
29. C₃	C₅×D₁₁×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
C₅×D₁₁×C₇₁	3
D₃₃×C₇₁	5
C₅×D₃×C₇₁	11
C₅×D₃₃	71

Subgroups — C5×D33×C71 #37552868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₃×C₇₁ #37552868