Subgroups — (C₅⋊D₅)⋊D₁₈₇ #34035268

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×D₉₃₅	C₂	1	2	yes	maximal, complemented
3	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₁₈₇	—	5	2	no	maximal
5	D₉₃₅	D₅	1	2	yes	complemented
6	D₅×C₁₁×C₁₇	—	5	2	no	—
7	D₅×C₁₁×C₁₇	—	10	2	no	—
8	C₅×D₁₈₇	—	5	2	no	—
9	(C₅⋊D₅)⋊D₁₇	—	11	1	no	maximal, Hall
10	(C₅⋊D₅)⋊D₁₁	—	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	D₁₁	1	1	yes	characteristic, complemented
14	C₅×D₈₅	—	11	2	no	—
15	C₂×D₁₈₇	—	25	1	no	Hall
16	C₁₁×C₅⋊D₅	D₁₇	1	1	yes	characteristic, complemented
17	C₅×D₅₅	—	17	2	no	—
18	C₅²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×C₁₇	—	25	1	no	—
20	D₁₈₇	—	5	2	no	—
21	D₅×D₁₇	—	55	2	no	—
22	C₅²×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
23	D₅×D₁₁	—	85	2	no	—
24	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
25	D₈₅	—	11	2	no	—
26	C₅×D₁₇	—	55	2	no	—
27	D₅×C₁₇	—	5	2	no	—
28	D₅×C₁₇	—	10	2	no	—
29	D₅₅	—	17	2	no	—
30	C₅×D₁₁	—	85	2	no	—
31	D₅×C₁₁	—	5	2	no	—
32	D₅×C₁₁	—	10	2	no	—
33	D₅²	—	187	1	no	Hall
34	C₅×C₁₇	—	2	2	no	—
35	C₅×C₁₇	D₅×D₁₁	1	2	yes	complemented
36	C₂×D₁₇	—	275	1	no	Hall
37	C₅×C₁₁	—	2	2	no	—
38	C₅×C₁₁	D₅×D₁₇	1	2	yes	complemented
39	C₅⋊D₅	D₁₈₇	1	1	yes	characteristic, complemented
40	C₅×D₅	—	187	2	no	—
41	C₂×D₁₁	—	425	1	no	Hall
42	C₂×C₁₇	—	25	1	no	—
43	D₁₇	—	55	2	no	—
44	C₅²	C₂×D₁₈₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	25	1	no	—
46	D₁₁	—	85	2	no	—
47	C₂×D₅	—	935	2	no	—
48	C₁₇	(C₅⋊D₅)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
49	C₁₁	(C₅⋊D₅)⋊D₁₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₅	—	935	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	—	187	2	no	—
54	C₅	—	2	2	no	—
55	C₅	D₅×D₁₈₇	1	2	yes	complemented
56	C₂²	—	4675	1	no	Sylow
57	C₂	—	25	1	no	—
58	C₂	—	935	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₁×C₁₇
UCS	C₁

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×D₉₃₅	C₂	semidirect
3. C₅²×C₁₁×C₁₇	C₂²	semidirect
5. D₉₃₅	D₅	semidirect
12. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
13. C₁₇×C₅⋊D₅	D₁₁	semidirect
16. C₁₁×C₅⋊D₅	D₁₇	semidirect
18. C₅²×C₁₇	C₂×D₁₁	semidirect
22. C₅²×C₁₁	C₂×D₁₇	semidirect
24. C₁₁×C₁₇	D₅²	semidirect
35. C₅×C₁₇	D₅×D₁₁	semidirect
38. C₅×C₁₁	D₅×D₁₇	semidirect
39. C₅⋊D₅	D₁₈₇	semidirect
44. C₅²	C₂×D₁₈₇	semidirect
48. C₁₇	(C₅⋊D₅)⋊D₁₁	semidirect
49. C₁₁	(C₅⋊D₅)⋊D₁₇	semidirect
55. C₅	D₅×D₁₈₇	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×D₉₃₅	2
D₅×D₁₈₇	5
(C₅⋊D₅)⋊D₁₇	11
(C₅⋊D₅)⋊D₁₁	17

Subgroups — (C5⋊D5)⋊D187 #34035268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊D₅)⋊D₁₈₇ #34035268