Subgroups — C₇×D₁₃₀₅ #32912478

Order 18270.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₃₅	—	3	1	no	maximal
3	C₇×D₂₆₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₂₉	D₃	1	1	yes	characteristic
5	D₁₃₀₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₁₄₅	—	9	1	no	Hall
7	C₇×C₉×C₂₉	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₈₇	—	15	1	no	—
10	C₅×C₇×C₂₉	D₉	1	1	yes	characteristic, complemented, Hall
11	D₄₃₅	—	3	1	no	—
12	C₇×D₄₅	—	29	1	no	maximal, Hall
13	C₃×C₇×C₂₉	D₁₅	1	1	yes	characteristic
14	D₂₆₁	—	5	1	no	Hall
15	C₃×C₅×C₂₉	D₃×C₇	1	1	yes	characteristic
16	C₇×D₂₉	—	45	1	no	Hall
17	C₅×C₇×C₉	D₂₉	1	1	yes	characteristic, complemented, Hall
18	D₁₄₅	—	9	1	no	Hall
19	C₉×C₂₉	C₇×D₅	1	1	yes	characteristic, complemented, Hall
20	C₇×D₁₅	—	87	1	no	—
21	C₇×C₂₉	D₄₅	1	1	yes	characteristic, complemented, Hall
22	D₈₇	—	15	1	no	—
23	C₅×C₂₉	C₇×D₉	1	1	yes	characteristic, complemented, Hall
24	C₇×D₉	—	145	1	no	Hall
25	C₃×C₅×C₇	D₈₇	1	1	yes	characteristic
26	D₄₅	—	29	1	no	Hall
27	C₃×C₂₉	C₇×D₁₅	1	1	yes	characteristic
28	C₇×D₅	—	261	1	no	Hall
29	C₇×C₉	D₁₄₅	1	1	yes	characteristic, complemented, Hall
30	D₂₉	—	45	1	no	Hall
31	C₅×C₉	C₇×D₂₉	1	1	yes	characteristic, complemented, Hall
32	D₃×C₇	—	435	1	no	—
33	C₅×C₇	D₂₆₁	1	1	yes	characteristic, complemented, Hall
34	D₁₅	—	87	1	no	—
35	C₂₉	C₇×D₄₅	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	D₄₃₅	1	1	yes	characteristic
37	D₉	—	145	1	no	Hall
38	C₃×C₅	C₇×D₈₇	1	1	yes	characteristic
39	C₂×C₇	—	1305	1	no	Hall
40	D₅	—	261	1	no	Hall
41	C₉	C₇×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	D₁₃₀₅	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	435	1	no	—
44	C₅	C₇×D₂₆₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇×D₄₃₅	1	1	yes	characteristic
46	C₂	—	1305	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₃₀₅
commutator, cosocle, hypocenter	C₅×C₉×C₂₉	C₂×C₇
Frattini	C₃	C₇×D₄₃₅
Fitting	C₅×C₇×C₉×C₂₉	C₂
socle	C₃×C₅×C₇×C₂₉	D₃
LCS	G ▷ C₅×C₉×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₂₉	C₂	semidirect
5. D₁₃₀₅	C₇	direct (N × H)
7. C₇×C₉×C₂₉	D₅	semidirect
8. C₅×C₉×C₂₉	C₂×C₇	semidirect
10. C₅×C₇×C₂₉	D₉	semidirect
17. C₅×C₇×C₉	D₂₉	semidirect
19. C₉×C₂₉	C₇×D₅	semidirect
21. C₇×C₂₉	D₄₅	semidirect
23. C₅×C₂₉	C₇×D₉	semidirect
29. C₇×C₉	D₁₄₅	semidirect
31. C₅×C₉	C₇×D₂₉	semidirect
33. C₅×C₇	D₂₆₁	semidirect
35. C₂₉	C₇×D₄₅	semidirect
41. C₉	C₇×D₁₄₅	semidirect
42. C₇	D₁₃₀₅	direct (N × H)
44. C₅	C₇×D₂₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₉×C₂₉	2
C₇×D₄₃₅	3
C₇×D₂₆₁	5
D₁₃₀₅	7
C₇×D₄₅	29

Subgroups — C7×D1305 #32912478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₃₀₅ #32912478