Subgroups — C₁₃×D₉₁₅ #37558178

Order 23790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₀₅	—	3	1	no	maximal, Hall
3	C₁₃×D₁₈₃	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₆₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₆₁	D₅	1	1	yes	characteristic, complemented, Hall
6	D₉₁₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×D₆₁	—	15	1	no	Hall
8	C₃×C₅×C₆₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₆₁	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₃₀₅	—	3	1	no	Hall
11	C₁₃×D₁₅	—	61	1	no	maximal, Hall
12	D₁₈₃	—	5	1	no	Hall
13	C₅×C₆₁	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₃	D₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
16	D₅×C₁₃	—	183	1	no	Hall
17	D₆₁	—	15	1	no	Hall
18	D₃×C₁₃	—	305	1	no	Hall
19	C₅×C₁₃	D₁₈₃	1	1	yes	characteristic, complemented, Hall
20	C₆₁	C₁₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₃	D₃₀₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	61	1	no	Hall
23	C₂×C₁₃	—	915	1	no	Hall
24	C₃×C₅	C₁₃×D₆₁	1	1	yes	characteristic, complemented, Hall
25	C₁₃	D₉₁₅	1	1	yes	characteristic, direct product factor, Sylow
26	D₅	—	183	1	no	Hall
27	D₃	—	305	1	no	Hall
28	C₅	C₁₃×D₁₈₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₃×D₃₀₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	915	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₉₁₅
commutator, cosocle, hypocenter	C₃×C₅×C₆₁	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₆₁	C₂
LCS	G ▷ C₃×C₅×C₆₁
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₆₁	C₂	semidirect
4. C₅×C₁₃×C₆₁	D₃	semidirect
5. C₃×C₁₃×C₆₁	D₅	semidirect
6. D₉₁₅	C₁₃	direct (N × H)
8. C₃×C₅×C₆₁	C₂×C₁₃	semidirect
9. C₁₃×C₆₁	D₁₅	semidirect
13. C₅×C₆₁	D₃×C₁₃	semidirect
14. C₃×C₅×C₁₃	D₆₁	semidirect
15. C₃×C₆₁	D₅×C₁₃	semidirect
19. C₅×C₁₃	D₁₈₃	semidirect
20. C₆₁	C₁₃×D₁₅	semidirect
21. C₃×C₁₃	D₃₀₅	semidirect
24. C₃×C₅	C₁₃×D₆₁	semidirect
25. C₁₃	D₉₁₅	direct (N × H)
28. C₅	C₁₃×D₁₈₃	semidirect
29. C₃	C₁₃×D₃₀₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×C₆₁	2
C₁₃×D₃₀₅	3
C₁₃×D₁₈₃	5
D₉₁₅	13
C₁₃×D₁₅	61

Subgroups — C13×D915 #37558178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₉₁₅ #37558178