Subgroups — C₁₇×(C₅⋊D₅)⋊D₁₁ #34035266

Order 18700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₅₅	C₂	1	2	yes	maximal, complemented
3	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×C₁₇×D₁₁	—	5	2	no	maximal
5	C₁₇×D₅₅	D₅	1	2	yes	complemented
6	D₅×C₁₁×C₁₇	—	5	2	no	—
7	D₅×C₁₁×C₁₇	—	10	2	no	—
8	C₅×C₁₇×D₁₁	—	5	2	no	—
9	D₅²×C₁₇	—	11	1	no	maximal, Hall
10	(C₅⋊D₅)⋊D₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₇	—	2	2	no	—
12	C₅×C₁₁×C₁₇	C₂×D₅	1	2	yes	complemented
13	C₁₇×C₅⋊D₅	D₁₁	1	1	yes	characteristic, complemented
14	C₅×D₅×C₁₇	—	11	2	no	—
15	C₂×C₁₇×D₁₁	—	25	1	no	Hall
16	C₁₁×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic, complemented
17	C₅×D₅₅	C₂×C₁₇	1	2	yes	complemented
18	C₅²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×C₁₇	—	25	1	no	—
20	C₁₇×D₁₁	—	5	2	no	—
21	C₂×D₅×C₁₇	—	55	2	no	—
22	C₅²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
23	D₅×D₁₁	—	5	2	no	—
24	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₁₇	—	55	2	no	—
26	D₅×C₁₇	—	5	2	no	—
27	D₅×C₁₇	—	10	2	no	—
28	D₅×C₁₇	—	11	2	no	—
29	D₅₅	D₅×C₁₇	1	2	yes	complemented
30	C₅×D₁₁	—	5	2	no	—
31	D₅×C₁₁	—	5	2	no	—
32	D₅×C₁₁	—	10	2	no	—
33	D₅²	—	11	1	no	Hall
34	C₅×C₁₇	—	2	2	no	—
35	C₅×C₁₇	D₅×D₁₁	1	2	yes	complemented
36	C₂²×C₁₇	—	275	1	no	Hall
37	C₅×C₁₁	—	2	2	no	—
38	C₅×C₁₁	C₂×D₅×C₁₇	1	2	yes	complemented
39	C₅⋊D₅	C₁₇×D₁₁	1	1	yes	characteristic, complemented
40	C₅×D₅	—	11	2	no	—
41	C₂×D₁₁	—	25	1	no	Hall
42	C₂×C₁₇	—	25	1	no	—
43	C₂×C₁₇	—	55	2	no	—
44	C₅²	C₂×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	25	1	no	—
46	D₁₁	—	5	2	no	—
47	C₂×D₅	—	55	2	no	—
48	C₁₇	(C₅⋊D₅)⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
49	C₁₁	D₅²×C₁₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	55	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	—	11	2	no	—
54	C₅	—	2	2	no	—
55	C₅	D₅×C₁₇×D₁₁	1	2	yes	complemented
56	C₂²	—	275	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	55	2	no	—

	subgroup	G/H
center, hypercenter	C₁₇	(C₅⋊D₅)⋊D₁₁
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₅⋊D₅	C₂	semidirect
2. C₅×C₁₇×D₅₅	C₂	semidirect
3. C₅²×C₁₁×C₁₇	C₂²	semidirect
5. C₁₇×D₅₅	D₅	semidirect
10. (C₅⋊D₅)⋊D₁₁	C₁₇	direct (N × H)
12. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
13. C₁₇×C₅⋊D₅	D₁₁	semidirect
16. C₁₁×C₅⋊D₅	C₂×C₁₇	semidirect
17. C₅×D₅₅	C₂×C₁₇	semidirect
18. C₅²×C₁₇	C₂×D₁₁	semidirect
22. C₅²×C₁₁	C₂²×C₁₇	semidirect
24. C₁₁×C₁₇	D₅²	semidirect
29. D₅₅	D₅×C₁₇	semidirect
35. C₅×C₁₇	D₅×D₁₁	semidirect
38. C₅×C₁₁	C₂×D₅×C₁₇	semidirect
39. C₅⋊D₅	C₁₇×D₁₁	semidirect
44. C₅²	C₂×C₁₇×D₁₁	semidirect
48. C₁₇	(C₅⋊D₅)⋊D₁₁	direct (N × H)
49. C₁₁	D₅²×C₁₇	semidirect
55. C₅	D₅×C₁₇×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×C₅⋊D₅	2
C₅×C₁₇×D₅₅	2
D₅×C₁₇×D₁₁	5
D₅²×C₁₇	11
(C₅⋊D₅)⋊D₁₁	17

Subgroups — C17×(C5⋊D5)⋊D11 #34035266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×(C₅⋊D₅)⋊D₁₁ #34035266