Subgroups — C₅×C₃⋊(C₅⋊(C₇⋊D₇)) #20301329

Order 7350.

200 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	C₅×C₅⋊(C₇⋊D₇)	—	3	1	no	maximal, Hall
3	C₃⋊(C₅⋊(C₇⋊D₇))	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₃⋊(C₇⋊D₇)	—	5	1	no	maximal
5	C₅²×C₇²	D₃	1	1	yes	characteristic, complemented, Hall
6	C₅×D₁₀₅	—	7	8	no	maximal
7	C₃×C₅×C₇²	—	2	2	no	—
8	C₃×C₅×C₇²	D₅	1	1	yes	characteristic, complemented
9	C₃×C₅×C₇²	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₅²×C₇	D₇	1	8	yes	complemented
11	C₅⋊(C₇⋊D₇)	—	3	1	no	—
12	C₅×C₇⋊D₇	—	15	1	no	—
13	C₅×D₃₅	—	21	8	no	—
14	C₃⋊(C₇⋊D₇)	—	5	1	no	Hall
15	C₅×C₇²	—	2	2	no	—
16	C₅×C₇²	C₅×D₃	1	1	yes	characteristic, complemented
17	C₅×C₇²	D₁₅	1	1	yes	characteristic, complemented
18	D₁₀₅	—	7	8	no	—
19	C₅×D₂₁	—	35	8	no	—
20	C₅²×C₇	D₂₁	1	8	yes	complemented
21	C₅×D₁₅	—	49	1	no	Hall
22	C₃×C₇²	C₅×D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	—	2	16	no	—
24	C₃×C₅×C₇	C₅×D₇	1	8	yes	complemented
25	C₃×C₅×C₇	D₃₅	1	8	yes	complemented
26	C₇⋊D₇	—	15	1	no	Hall
27	C₃×C₅²	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
28	D₃₅	—	21	8	no	—
29	C₅×D₇	—	105	8	no	—
30	C₅×D₅	—	147	1	no	Hall
31	C₇²	C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
32	D₂₁	—	35	8	no	—
33	C₅×C₇	—	2	16	no	—
34	C₅×C₇	C₅×D₂₁	1	8	yes	complemented
35	C₅×C₇	D₁₀₅	1	8	yes	complemented
36	D₁₅	—	49	1	no	—
37	C₅×D₃	—	245	1	no	—
38	C₅²	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₇	C₅×D₃₅	1	8	yes	complemented
40	C₃×C₅	—	2	2	no	—
41	C₃×C₅	C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
42	C₃×C₅	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
43	D₇	—	105	8	no	—
44	C₂×C₅	—	735	1	no	—
45	D₅	—	147	1	no	—
46	C₇	C₅×D₁₀₅	1	8	yes	complemented
47	D₃	—	245	1	no	Hall
48	C₅	—	2	2	no	—
49	C₅	C₅×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
50	C₅	C₃⋊(C₅⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor
51	C₃	C₅×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	735	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₅⋊(C₇⋊D₇))
commutator, hypocenter	C₃×C₅×C₇²	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂
LCS	G ▷ C₃×C₅×C₇²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇²	C₂	semidirect
3. C₃⋊(C₅⋊(C₇⋊D₇))	C₅	direct (N × H)
5. C₅²×C₇²	D₃	semidirect
8. C₃×C₅×C₇²	D₅	semidirect
9. C₃×C₅×C₇²	C₂×C₅	semidirect
10. C₃×C₅²×C₇	D₇	semidirect
16. C₅×C₇²	C₅×D₃	semidirect
17. C₅×C₇²	D₁₅	semidirect
20. C₅²×C₇	D₂₁	semidirect
22. C₃×C₇²	C₅×D₅	semidirect
24. C₃×C₅×C₇	C₅×D₇	semidirect
25. C₃×C₅×C₇	D₃₅	semidirect
27. C₃×C₅²	C₇⋊D₇	semidirect
31. C₇²	C₅×D₁₅	semidirect
34. C₅×C₇	C₅×D₂₁	semidirect
35. C₅×C₇	D₁₀₅	semidirect
38. C₅²	C₃⋊(C₇⋊D₇)	semidirect
39. C₃×C₇	C₅×D₃₅	semidirect
41. C₃×C₅	C₅×C₇⋊D₇	semidirect
42. C₃×C₅	C₅⋊(C₇⋊D₇)	semidirect
46. C₇	C₅×D₁₀₅	semidirect
49. C₅	C₅×C₃⋊(C₇⋊D₇)	semidirect
50. C₅	C₃⋊(C₅⋊(C₇⋊D₇))	direct (N × H)
51. C₃	C₅×C₅⋊(C₇⋊D₇)	semidirect

Subgroups — C5×C3⋊(C5⋊(C7⋊D7)) #20301329

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₃⋊(C₅⋊(C₇⋊D₇)) #20301329