Subgroups — C₇×D₁₅×C₁₁₃ #37557539

Order 23730.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₁₁₃	—	3	1	no	maximal, Hall
3	D₃×C₇×C₁₁₃	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₁₃	D₃	1	1	yes	characteristic, complemented, Hall
5	D₁₅×C₁₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×C₁₁₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₁₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×C₁₁₃	—	15	1	no	Hall
9	D₅×C₁₁₃	—	3	1	no	Hall
10	C₇×C₁₁₃	D₁₅	1	1	yes	characteristic, direct product factor, Hall
11	D₃×C₁₁₃	—	5	1	no	Hall
12	C₅×C₁₁₃	D₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁₃	C₇×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁₃	—	15	1	no	Hall
15	C₇×D₁₅	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₁₃	C₇×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅×C₇	C₂×C₁₁₃	1	1	yes	characteristic, complemented, Hall
18	C₇×D₅	—	3	1	no	Hall
19	D₃×C₇	—	5	1	no	Hall
20	C₅×C₇	D₃×C₁₁₃	1	1	yes	characteristic, complemented, Hall
21	D₁₅	C₇×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₇	D₅×C₁₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	C₂×C₇×C₁₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇	—	15	1	no	Hall
25	D₅	—	3	1	no	Hall
26	C₇	D₁₅×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	D₃	—	5	1	no	Hall
28	C₅	D₃×C₇×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇×D₅×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₇×C₁₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁₃	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₁₃	C₂	semidirect
4. C₅×C₇×C₁₁₃	D₃	semidirect
5. D₁₅×C₁₁₃	C₇	direct (N × H)
6. C₃×C₇×C₁₁₃	D₅	semidirect
7. C₃×C₅×C₁₁₃	C₂×C₇	semidirect
10. C₇×C₁₁₃	D₁₅	direct (N × H)
12. C₅×C₁₁₃	D₃×C₇	semidirect
13. C₃×C₁₁₃	C₇×D₅	semidirect
15. C₇×D₁₅	C₁₁₃	direct (N × H)
16. C₁₁₃	C₇×D₁₅	direct (N × H)
17. C₃×C₅×C₇	C₂×C₁₁₃	semidirect
20. C₅×C₇	D₃×C₁₁₃	semidirect
21. D₁₅	C₇×C₁₁₃	direct (N × H)
22. C₃×C₇	D₅×C₁₁₃	semidirect
23. C₃×C₅	C₂×C₇×C₁₁₃	semidirect
26. C₇	D₁₅×C₁₁₃	direct (N × H)
28. C₅	D₃×C₇×C₁₁₃	semidirect
29. C₃	C₇×D₅×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₁₃	2
C₇×D₅×C₁₁₃	3
D₃×C₇×C₁₁₃	5
D₁₅×C₁₁₃	7
C₇×D₁₅	113

Subgroups — C7×D15×C113 #37557539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₅×C₁₁₃ #37557539