Subgroups — C₁₃×D₁₃₀₉ #46801351

Order 34034.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₈₇	—	7	1	no	maximal, Hall
3	C₁₃×D₁₁₉	—	11	1	no	maximal, Hall
4	D₁₃₀₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁×C₁₃×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₇₇	—	17	1	no	maximal, Hall
7	C₇×C₁₃×C₁₇	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₁×C₁₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁×C₁₃	D₁₇	1	1	yes	characteristic, complemented, Hall
10	C₁₃×D₁₇	—	77	1	no	Hall
11	D₁₈₇	—	7	1	no	Hall
12	C₁₃×D₁₁	—	119	1	no	Hall
13	D₁₁₉	—	11	1	no	Hall
14	C₁₃×C₁₇	D₇₇	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₇	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
16	C₁₃×D₇	—	187	1	no	Hall
17	D₇₇	—	17	1	no	Hall
18	C₁₁×C₁₃	D₁₁₉	1	1	yes	characteristic, complemented, Hall
19	C₇×C₁₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₇×C₁₃	D₁₈₇	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₁	C₁₃×D₁₇	1	1	yes	characteristic, complemented, Hall
22	D₁₇	—	77	1	no	Hall
23	C₂×C₁₃	—	1309	1	no	Hall
24	D₁₁	—	119	1	no	Hall
25	C₁₇	C₁₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	187	1	no	Hall
27	C₁₃	D₁₃₀₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₁₁	C₁₃×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₇	C₁₃×D₁₈₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	1309	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₁₃₀₉
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₇	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃×C₁₇	C₂
LCS	G ▷ C₇×C₁₁×C₁₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×C₁₃×C₁₇	C₂	semidirect
4. D₁₃₀₉	C₁₃	direct (N × H)
5. C₁₁×C₁₃×C₁₇	D₇	semidirect
7. C₇×C₁₃×C₁₇	D₁₁	semidirect
8. C₇×C₁₁×C₁₇	C₂×C₁₃	semidirect
9. C₇×C₁₁×C₁₃	D₁₇	semidirect
14. C₁₃×C₁₇	D₇₇	semidirect
15. C₁₁×C₁₇	C₁₃×D₇	semidirect
18. C₁₁×C₁₃	D₁₁₉	semidirect
19. C₇×C₁₇	C₁₃×D₁₁	semidirect
20. C₇×C₁₃	D₁₈₇	semidirect
21. C₇×C₁₁	C₁₃×D₁₇	semidirect
25. C₁₇	C₁₃×D₇₇	semidirect
27. C₁₃	D₁₃₀₉	direct (N × H)
28. C₁₁	C₁₃×D₁₁₉	semidirect
29. C₇	C₁₃×D₁₈₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁×C₁₃×C₁₇	2
C₁₃×D₁₈₇	7
C₁₃×D₁₁₉	11
D₁₃₀₉	13
C₁₃×D₇₇	17

Subgroups — C13×D1309 #46801351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₁₃₀₉ #46801351