Subgroups — C₁₇×(C₅⋊D₅)⋊D₇ #26045456

Order 11900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₃₅	C₂	1	2	yes	maximal, complemented
3	C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₇×C₁₇	—	5	2	no	maximal
5	D₅²×C₁₇	—	7	1	no	maximal, Hall
6	C₁₇×D₃₅	D₅	1	2	yes	complemented
7	C₇×D₅×C₁₇	—	5	2	no	—
8	C₇×D₅×C₁₇	—	10	2	no	—
9	C₅×D₇×C₁₇	—	5	2	no	—
10	C₁₇×C₅⋊D₅	D₇	1	1	yes	characteristic, complemented
11	C₅×D₅×C₁₇	—	7	2	no	—
12	(C₅⋊D₅)⋊D₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₇×C₁₇	—	2	2	no	—
14	C₅×C₇×C₁₇	C₂×D₅	1	2	yes	complemented
15	C₂×D₇×C₁₇	—	25	1	no	Hall
16	C₅²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₅×D₃₅	C₂×C₁₇	1	2	yes	complemented
19	C₂×D₅×C₁₇	—	35	2	no	—
20	C₂×C₇×C₁₇	—	25	1	no	—
21	D₇×C₁₇	—	5	2	no	—
22	C₅²×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₁₇	—	35	2	no	—
24	D₅×C₁₇	—	5	2	no	—
25	D₅×C₁₇	—	7	2	no	—
26	D₅×C₁₇	—	10	2	no	—
27	D₅×D₇	—	5	2	no	—
28	C₇×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
29	D₅²	—	7	1	no	Hall
30	C₅×C₁₇	—	2	2	no	—
31	C₅×C₁₇	D₅×D₇	1	2	yes	complemented
32	D₃₅	D₅×C₁₇	1	2	yes	complemented
33	C₅×D₇	—	5	2	no	—
34	C₇×D₅	—	5	2	no	—
35	C₇×D₅	—	10	2	no	—
36	C₂²×C₁₇	—	175	1	no	Hall
37	C₅⋊D₅	D₇×C₁₇	1	1	yes	characteristic, complemented
38	C₅×D₅	—	7	2	no	—
39	C₅×C₇	—	2	2	no	—
40	C₅×C₇	C₂×D₅×C₁₇	1	2	yes	complemented
41	C₂×C₁₇	—	25	1	no	—
42	C₂×C₁₇	—	35	2	no	—
43	C₂×D₇	—	25	1	no	Hall
44	C₅²	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₅	—	35	2	no	—
46	C₁₇	(C₅⋊D₅)⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₇	—	25	1	no	—
48	D₇	—	5	2	no	—
49	C₂×C₅	—	35	2	no	—
50	D₅	—	5	2	no	—
51	D₅	—	7	2	no	—
52	D₅	—	10	2	no	—
53	C₇	D₅²×C₁₇	1	1	yes	characteristic, complemented, Sylow
54	C₅	—	2	2	no	—
55	C₅	D₅×D₇×C₁₇	1	2	yes	complemented
56	C₂²	—	175	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	35	2	no	—

	subgroup	G/H
center, hypercenter	C₁₇	(C₅⋊D₅)⋊D₇
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₇×C₅⋊D₅	C₂	semidirect
2. C₅×C₁₇×D₃₅	C₂	semidirect
3. C₅²×C₇×C₁₇	C₂²	semidirect
6. C₁₇×D₃₅	D₅	semidirect
10. C₁₇×C₅⋊D₅	D₇	semidirect
12. (C₅⋊D₅)⋊D₇	C₁₇	direct (N × H)
14. C₅×C₇×C₁₇	C₂×D₅	semidirect
16. C₅²×C₁₇	C₂×D₇	semidirect
17. C₇×C₅⋊D₅	C₂×C₁₇	semidirect
18. C₅×D₃₅	C₂×C₁₇	semidirect
22. C₅²×C₇	C₂²×C₁₇	semidirect
28. C₇×C₁₇	D₅²	semidirect
31. C₅×C₁₇	D₅×D₇	semidirect
32. D₃₅	D₅×C₁₇	semidirect
37. C₅⋊D₅	D₇×C₁₇	semidirect
40. C₅×C₇	C₂×D₅×C₁₇	semidirect
44. C₅²	C₂×D₇×C₁₇	semidirect
46. C₁₇	(C₅⋊D₅)⋊D₇	direct (N × H)
53. C₇	D₅²×C₁₇	semidirect
55. C₅	D₅×D₇×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₅⋊D₅	2
C₅×C₁₇×D₃₅	2
D₅×D₇×C₁₇	5
D₅²×C₁₇	7
(C₅⋊D₅)⋊D₇	17

Subgroups — C17×(C5⋊D5)⋊D7 #26045456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×(C₅⋊D₅)⋊D₇ #26045456