Subgroups — D₁₈₇⋊(C₅⋊D₅) #34035258

Order 18700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
C₁₇×C₅⋊D₅₅	2
C₁₁×C₅⋊D₈₅	2
C₅²×D₁₈₇	2
D₅₅⋊D₁₇	5
D₁₇×C₅⋊D₅	11
D₁₁×C₅⋊D₅	17

Subgroups — D187⋊(C5⋊D5) #34035258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₈₇⋊(C₅⋊D₅) #34035258