Subgroups — D₁₈₇⋊D₂₅ #34035154

Order 18700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₂₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₄₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×D₁₈₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₇×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₅⋊D₁₇	—	5	1	no	maximal
6	C₁₇×D₅₅	—	5	1	no	—
7	C₁₁×D₈₅	—	5	1	no	—
8	C₅×D₁₈₇	D₅	1	1	yes	characteristic
9	D₁₇×D₂₅	—	11	1	no	maximal, Hall
10	D₁₁×D₂₅	—	17	1	no	maximal, Hall
11	C₅×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic
12	D₄₂₅	D₁₁	1	1	yes	characteristic, complemented
13	C₂₅×D₁₇	—	11	1	no	—
14	C₁₇×D₂₅	—	11	1	no	—
15	D₁₁×D₁₇	—	25	1	no	Hall
16	D₂₇₅	D₁₇	1	1	yes	characteristic, complemented
17	D₁₁×C₂₅	—	17	1	no	—
18	C₁₁×D₂₅	—	17	1	no	—
19	C₁₇×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₁₈₇	D₂₅	1	1	yes	characteristic, complemented
21	C₁₁×D₁₇	—	25	1	no	—
22	C₁₇×D₁₁	—	25	1	no	—
23	D₅×D₁₇	—	55	1	no	—
24	C₁₁×C₂₅	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
25	D₅×D₁₁	—	85	1	no	—
26	C₁₁×C₁₇	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
27	D₈₅	—	5	1	no	—
28	C₅×D₁₇	—	11	1	no	—
29	D₅×C₁₇	—	55	1	no	—
30	D₅₅	—	5	1	no	—
31	C₅×D₁₁	—	17	1	no	—
32	D₅×C₁₁	—	85	1	no	—
33	C₂×D₂₅	—	187	1	no	Hall
34	C₅×C₁₇	D₅×D₁₁	1	1	yes	characteristic
35	C₂×D₁₇	—	275	1	no	Hall
36	C₅×C₁₁	D₅×D₁₇	1	1	yes	characteristic
37	C₂×C₂₅	—	187	1	no	—
38	D₂₅	—	11	1	no	—
39	D₂₅	—	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	C₂₅	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	1	no	—
49	C₁₇	D₁₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
50	C₁₁	D₁₇×D₂₅	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	187	1	no	—
52	D₅	—	55	1	no	—
53	D₅	—	85	1	no	—
54	C₅	D₅₅⋊D₁₇	1	1	yes	characteristic
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, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₁×C₁₇×C₂₅	C₂²
Frattini	C₅	D₅₅⋊D₁₇
socle	C₅×C₁₁×C₁₇	C₂×D₅
LCS	G ▷ C₁₁×C₁₇×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₂₇₅	C₂	semidirect
2. C₁₁×D₄₂₅	C₂	semidirect
3. C₂₅×D₁₈₇	C₂	semidirect
4. C₁₁×C₁₇×C₂₅	C₂²	semidirect
12. D₄₂₅	D₁₁	semidirect
16. D₂₇₅	D₁₇	semidirect
19. C₁₇×C₂₅	C₂×D₁₁	semidirect
20. D₁₈₇	D₂₅	semidirect
24. C₁₁×C₂₅	C₂×D₁₇	semidirect
26. C₁₁×C₁₇	C₂×D₂₅	semidirect
44. C₂₅	D₁₁×D₁₇	semidirect
49. C₁₇	D₁₁×D₂₅	semidirect
50. C₁₁	D₁₇×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×D₂₇₅	2
C₁₁×D₄₂₅	2
C₂₅×D₁₈₇	2
D₅₅⋊D₁₇	5
D₁₇×D₂₅	11
D₁₁×D₂₅	17

Subgroups — D187⋊D25 #34035154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₈₇⋊D₂₅ #34035154