Subgroups — D₇×C₃⋊(C₅⋊D₅) #14523655

Order 2100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₃₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₅⋊D₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₇×D₁₅	—	5	6	no	maximal
7	C₅⋊D₃₅	—	3	1	no	—
8	C₇×C₅⋊D₅	—	3	1	no	—
9	C₅²×D₇	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃⋊(C₅⋊D₅)	—	7	1	no	maximal, Hall
11	D₁₀₅	—	5	6	no	—
12	C₇×D₁₅	—	5	6	no	—
13	C₃×C₅×D₇	D₅	1	6	yes	complemented
14	C₅²×C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅²	—	7	1	no	—
16	C₃⋊(C₅⋊D₅)	—	7	1	no	—
17	C₃⋊(C₅⋊D₅)	D₇	1	1	yes	characteristic, direct product factor
18	D₅×D₇	—	15	6	no	—
19	C₃×C₅×C₇	C₂×D₅	1	6	yes	complemented
20	C₂×C₅⋊D₅	—	21	1	no	Hall
21	D₃×D₇	—	25	1	no	Hall
22	C₃×C₅²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	D₃₅	—	15	6	no	—
24	C₅×D₇	D₁₅	1	6	yes	complemented
25	C₇×D₅	—	15	6	no	—
26	C₂×D₁₅	—	35	6	no	—
27	C₂×C₅²	—	7	1	no	—
28	C₅⋊D₅	—	3	1	no	—
29	C₅⋊D₅	—	21	1	no	—
30	D₂₁	—	25	1	no	—
31	C₃×D₇	C₅⋊D₅	1	1	yes	characteristic, complemented
32	D₃×C₇	—	25	1	no	—
33	C₅×C₇	C₂×D₁₅	1	6	yes	complemented
34	C₂×C₃×C₅	—	7	6	no	—
35	D₁₅	—	5	6	no	—
36	D₁₅	—	35	6	no	—
37	C₂×D₇	—	75	1	no	Hall
38	C₅²	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
40	C₂×D₅	—	105	6	no	—
41	C₃×C₅	D₅×D₇	1	6	yes	complemented
42	C₂×C₇	—	75	1	no	—
43	D₇	—	75	1	no	—
44	D₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
45	C₂×D₃	—	175	1	no	Hall
46	C₂×C₅	—	7	6	no	—
47	D₅	—	15	6	no	—
48	D₅	—	105	6	no	—
49	C₇	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	7	1	no	—
51	D₃	—	25	1	no	—
52	D₃	—	175	1	no	—
53	C₅	D₇×D₁₅	1	6	yes	complemented
54	C₂²	—	525	1	no	Sylow
55	C₃	D₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	7	1	no	—
57	C₂	—	525	1	no	—
58	C₂	—	75	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₇	C₂²
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₃₅)	C₂	semidirect
2. C₇×C₃⋊(C₅⋊D₅)	C₂	semidirect
3. C₃×C₅²×D₇	C₂	semidirect
5. C₃×C₅²×C₇	C₂²	semidirect
9. C₅²×D₇	D₃	semidirect
13. C₃×C₅×D₇	D₅	semidirect
14. C₅²×C₇	C₂×D₃	semidirect
17. C₃⋊(C₅⋊D₅)	D₇	direct (N × H)
19. C₃×C₅×C₇	C₂×D₅	semidirect
22. C₃×C₅²	C₂×D₇	semidirect
24. C₅×D₇	D₁₅	semidirect
31. C₃×D₇	C₅⋊D₅	semidirect
33. C₅×C₇	C₂×D₁₅	semidirect
38. C₅²	D₃×D₇	semidirect
39. C₃×C₇	C₂×C₅⋊D₅	semidirect
41. C₃×C₅	D₅×D₇	semidirect
44. D₇	C₃⋊(C₅⋊D₅)	direct (N × H)
49. C₇	C₂×C₃⋊(C₅⋊D₅)	semidirect
53. C₅	D₇×D₁₅	semidirect
55. C₃	D₇×C₅⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₅⋊D₃₅)	2
C₇×C₃⋊(C₅⋊D₅)	2
C₃×C₅²×D₇	2
D₇×C₅⋊D₅	3
D₇×D₁₅	5
C₂×C₃⋊(C₅⋊D₅)	7

Subgroups — D7×C3⋊(C5⋊D5) #14523655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃⋊(C₅⋊D₅) #14523655