Subgroups — C₇×C₃₇×D₆₅ #46797607

Order 33670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₃×C₃₇	—	5	1	no	maximal, Hall
3	C₃₇×D₆₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₃₇	D₅	1	1	yes	characteristic, complemented, Hall
5	C₇×D₅×C₃₇	—	13	1	no	maximal, Hall
6	C₅×C₁₃×C₃₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₃₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₁₃×C₃₇	—	5	1	no	Hall
9	C₇×D₆₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₃₇	—	65	1	no	Hall
11	C₁₃×C₃₇	C₇×D₅	1	1	yes	characteristic, complemented, Hall
12	C₅×C₇×C₁₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	D₅×C₃₇	—	13	1	no	Hall
14	C₇×C₃₇	D₆₅	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₇	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₇×D₁₃	—	5	1	no	Hall
17	D₆₅	C₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₃	D₅×C₃₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₇	—	65	1	no	Hall
20	C₇×D₅	—	13	1	no	Hall
21	C₅×C₁₃	C₂×C₇×C₃₇	1	1	yes	characteristic, complemented, Hall
22	C₃₇	C₇×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₅×C₇	D₁₃×C₃₇	1	1	yes	characteristic, complemented, Hall
24	D₁₃	—	5	1	no	Hall
25	C₂×C₇	—	65	1	no	Hall
26	C₁₃	C₇×D₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
27	D₅	—	13	1	no	Hall
28	C₇	C₃₇×D₆₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₇×D₁₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	65	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₃₇	D₆₅
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₇×C₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₃₇	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₇×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₃×C₃₇	C₂	semidirect
3. C₃₇×D₆₅	C₇	direct (N × H)
4. C₇×C₁₃×C₃₇	D₅	semidirect
6. C₅×C₁₃×C₃₇	C₂×C₇	semidirect
7. C₅×C₇×C₃₇	D₁₃	semidirect
9. C₇×D₆₅	C₃₇	direct (N × H)
11. C₁₃×C₃₇	C₇×D₅	semidirect
12. C₅×C₇×C₁₃	C₂×C₃₇	semidirect
14. C₇×C₃₇	D₆₅	direct (N × H)
15. C₅×C₃₇	C₇×D₁₃	semidirect
17. D₆₅	C₇×C₃₇	direct (N × H)
18. C₇×C₁₃	D₅×C₃₇	semidirect
21. C₅×C₁₃	C₂×C₇×C₃₇	semidirect
22. C₃₇	C₇×D₆₅	direct (N × H)
23. C₅×C₇	D₁₃×C₃₇	semidirect
26. C₁₃	C₇×D₅×C₃₇	semidirect
28. C₇	C₃₇×D₆₅	direct (N × H)
29. C₅	C₇×D₁₃×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₃×C₃₇	2
C₇×D₁₃×C₃₇	5
C₃₇×D₆₅	7
C₇×D₅×C₃₇	13
C₇×D₆₅	37

Subgroups — C7×C37×D65 #46797607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃₇×D₆₅ #46797607