Subgroups — C₇×C₃⋊(C₅⋊D₃₅) #20301331

Order 7350.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₅⋊D₃₅	—	3	1	no	maximal, Hall
3	C₇×D₁₀₅	—	5	6	no	maximal
4	C₅²×C₇²	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(C₅⋊D₃₅)	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×C₃⋊(C₅⋊D₅)	—	7	1	no	maximal
7	C₃×C₅×C₇²	D₅	1	6	yes	complemented
8	C₃×C₅²×C₇	—	2	3	no	—
9	C₃×C₅²×C₇	D₇	1	1	yes	characteristic, complemented
10	C₃×C₅²×C₇	C₂×C₇	1	1	yes	characteristic, complemented
11	C₇×D₃₅	—	15	6	no	—
12	C₅⋊D₃₅	—	3	1	no	—
13	C₇×C₅⋊D₅	—	21	1	no	—
14	C₇×D₂₁	—	25	1	no	Hall
15	C₅×C₇²	D₁₅	1	6	yes	complemented
16	D₁₀₅	—	5	6	no	—
17	C₇×D₁₅	—	35	6	no	—
18	C₅²×C₇	—	2	3	no	—
19	C₅²×C₇	D₃×C₇	1	1	yes	characteristic, complemented
20	C₅²×C₇	D₂₁	1	1	yes	characteristic, complemented
21	C₃⋊(C₅⋊D₅)	—	7	1	no	Hall
22	C₃×C₇²	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	—	2	18	no	—
24	C₃×C₅×C₇	C₇×D₅	1	6	yes	complemented
25	C₃×C₅×C₇	D₃₅	1	6	yes	complemented
26	C₇×D₇	—	75	1	no	Hall
27	C₃×C₅²	C₇×D₇	1	1	yes	characteristic, complemented, Hall
28	D₃₅	—	15	6	no	—
29	C₇×D₅	—	105	6	no	—
30	C₅⋊D₅	—	21	1	no	Hall
31	C₇²	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
32	D₂₁	—	25	1	no	—
33	D₃×C₇	—	175	1	no	—
34	C₅×C₇	—	2	18	no	—
35	C₅×C₇	C₇×D₁₅	1	6	yes	complemented
36	C₅×C₇	D₁₀₅	1	6	yes	complemented
37	D₁₅	—	35	6	no	—
38	C₅²	C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₇	—	2	3	no	—
40	C₃×C₇	C₇×C₅⋊D₅	1	1	yes	characteristic, complemented
41	C₃×C₇	C₅⋊D₃₅	1	1	yes	characteristic, complemented
42	C₃×C₅	C₇×D₃₅	1	6	yes	complemented
43	C₂×C₇	—	525	1	no	—
44	D₇	—	75	1	no	—
45	D₅	—	105	6	no	—
46	C₇	—	2	3	no	—
47	C₇	C₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
48	C₇	C₃⋊(C₅⋊D₃₅)	1	1	yes	characteristic, direct product factor
49	D₃	—	175	1	no	Hall
50	C₅	C₇×D₁₀₅	1	6	yes	complemented
51	C₃	C₇×C₅⋊D₃₅	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	525	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(C₅⋊D₃₅)
commutator, hypocenter	C₃×C₅²×C₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇²	C₂	semidirect
4. C₅²×C₇²	D₃	semidirect
5. C₃⋊(C₅⋊D₃₅)	C₇	direct (N × H)
7. C₃×C₅×C₇²	D₅	semidirect
9. C₃×C₅²×C₇	D₇	semidirect
10. C₃×C₅²×C₇	C₂×C₇	semidirect
15. C₅×C₇²	D₁₅	semidirect
19. C₅²×C₇	D₃×C₇	semidirect
20. C₅²×C₇	D₂₁	semidirect
22. C₃×C₇²	C₅⋊D₅	semidirect
24. C₃×C₅×C₇	C₇×D₅	semidirect
25. C₃×C₅×C₇	D₃₅	semidirect
27. C₃×C₅²	C₇×D₇	semidirect
31. C₇²	C₃⋊(C₅⋊D₅)	semidirect
35. C₅×C₇	C₇×D₁₅	semidirect
36. C₅×C₇	D₁₀₅	semidirect
38. C₅²	C₇×D₂₁	semidirect
40. C₃×C₇	C₇×C₅⋊D₅	semidirect
41. C₃×C₇	C₅⋊D₃₅	semidirect
42. C₃×C₅	C₇×D₃₅	semidirect
47. C₇	C₇×C₃⋊(C₅⋊D₅)	semidirect
48. C₇	C₃⋊(C₅⋊D₃₅)	direct (N × H)
50. C₅	C₇×D₁₀₅	semidirect
51. C₃	C₇×C₅⋊D₃₅	semidirect

Subgroups — C7×C3⋊(C5⋊D35) #20301331

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃⋊(C₅⋊D₃₅) #20301331