Subgroups — C₁₁×(C₅⋊D₅)⋊D₁₇ #34035261

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×C₁₁×D₈₅	C₂	1	2	yes	maximal, complemented
3	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×C₁₁×D₁₇	—	5	2	no	maximal
5	C₁₁×D₈₅	D₅	1	2	yes	complemented
6	D₅×C₁₁×C₁₇	—	5	2	no	—
7	D₅×C₁₁×C₁₇	—	10	2	no	—
8	C₅×C₁₁×D₁₇	—	5	2	no	—
9	(C₅⋊D₅)⋊D₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₅²×C₁₁	—	17	1	no	maximal, Hall
11	C₅×C₁₁×C₁₇	—	2	2	no	—
12	C₅×C₁₁×C₁₇	C₂×D₅	1	2	yes	complemented
13	C₁₇×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₅×D₈₅	C₂×C₁₁	1	2	yes	complemented
15	C₂×C₁₁×D₁₇	—	25	1	no	Hall
16	C₁₁×C₅⋊D₅	D₁₇	1	1	yes	characteristic, complemented
17	C₅×D₅×C₁₁	—	17	2	no	—
18	C₅²×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×C₁₇	—	25	1	no	—
20	C₁₁×D₁₇	—	5	2	no	—
21	D₅×D₁₇	—	5	2	no	—
22	C₅²×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₁	—	85	2	no	—
24	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
25	D₈₅	D₅×C₁₁	1	2	yes	complemented
26	C₅×D₁₇	—	5	2	no	—
27	D₅×C₁₇	—	5	2	no	—
28	D₅×C₁₇	—	10	2	no	—
29	C₂×C₅×C₁₁	—	85	2	no	—
30	D₅×C₁₁	—	5	2	no	—
31	D₅×C₁₁	—	10	2	no	—
32	D₅×C₁₁	—	17	2	no	—
33	D₅²	—	17	1	no	Hall
34	C₅×C₁₇	—	2	2	no	—
35	C₅×C₁₇	C₂×D₅×C₁₁	1	2	yes	complemented
36	C₂×D₁₇	—	25	1	no	Hall
37	C₅×C₁₁	—	2	2	no	—
38	C₅×C₁₁	D₅×D₁₇	1	2	yes	complemented
39	C₅⋊D₅	C₁₁×D₁₇	1	1	yes	characteristic, complemented
40	C₅×D₅	—	17	2	no	—
41	C₂²×C₁₁	—	425	1	no	Hall
42	C₂×C₁₇	—	25	1	no	—
43	D₁₇	—	5	2	no	—
44	C₅²	C₂×C₁₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	25	1	no	—
46	C₂×C₁₁	—	85	2	no	—
47	C₂×D₅	—	85	2	no	—
48	C₁₇	D₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
49	C₁₁	(C₅⋊D₅)⋊D₁₇	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₅	—	85	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	—	17	2	no	—
54	C₅	—	2	2	no	—
55	C₅	D₅×C₁₁×D₁₇	1	2	yes	complemented
56	C₂²	—	425	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	85	2	no	—

	subgroup	G/H
center, hypercenter	C₁₁	(C₅⋊D₅)⋊D₁₇
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₁₁

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×C₁₁×D₈₅	C₂	semidirect
3. C₅²×C₁₁×C₁₇	C₂²	semidirect
5. C₁₁×D₈₅	D₅	semidirect
9. (C₅⋊D₅)⋊D₁₇	C₁₁	direct (N × H)
12. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
13. C₁₇×C₅⋊D₅	C₂×C₁₁	semidirect
14. C₅×D₈₅	C₂×C₁₁	semidirect
16. C₁₁×C₅⋊D₅	D₁₇	semidirect
18. C₅²×C₁₇	C₂²×C₁₁	semidirect
22. C₅²×C₁₁	C₂×D₁₇	semidirect
24. C₁₁×C₁₇	D₅²	semidirect
25. D₈₅	D₅×C₁₁	semidirect
35. C₅×C₁₇	C₂×D₅×C₁₁	semidirect
38. C₅×C₁₁	D₅×D₁₇	semidirect
39. C₅⋊D₅	C₁₁×D₁₇	semidirect
44. C₅²	C₂×C₁₁×D₁₇	semidirect
48. C₁₇	D₅²×C₁₁	semidirect
49. C₁₁	(C₅⋊D₅)⋊D₁₇	direct (N × H)
55. C₅	D₅×C₁₁×D₁₇	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×C₁₁×D₈₅	2
D₅×C₁₁×D₁₇	5
(C₅⋊D₅)⋊D₁₇	11
D₅²×C₁₁	17

Subgroups — C11×(C5⋊D5)⋊D17 #34035261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×(C₅⋊D₅)⋊D₁₇ #34035261