Subgroups — D₈₇⋊(C₅⋊D₅) #22576485

Order 8700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅⋊D₂₉	—	5	6	no	maximal
7	C₅⋊D₁₄₅	D₃	1	1	yes	characteristic, complemented
8	C₂₉×C₅⋊D₅	—	3	1	no	—
9	C₅²×D₂₉	—	3	1	no	—
10	C₂₉×D₁₅	—	5	6	no	—
11	C₅×D₈₇	D₅	1	6	yes	complemented
12	C₃×D₁₄₅	—	5	6	no	—
13	C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₂₉	—	15	6	no	—
15	C₃×C₅×C₂₉	C₂×D₅	1	6	yes	complemented
16	D₃×D₂₉	—	25	1	no	Hall
17	D₃×C₅⋊D₅	—	29	1	no	maximal, Hall
18	D₁₄₅	—	5	6	no	—
19	C₅×D₂₉	—	3	6	no	—
20	D₅×C₂₉	—	15	6	no	—
21	D₈₇	C₅⋊D₅	1	1	yes	characteristic, complemented
22	C₃×D₂₉	—	25	1	no	—
23	D₃×C₂₉	—	25	1	no	—
24	C₃⋊(C₅⋊D₅)	D₂₉	1	1	yes	characteristic, complemented
25	C₅²×D₃	—	29	1	no	—
26	C₃×C₅⋊D₅	—	29	1	no	—
27	C₅×C₂₉	D₃×D₅	1	6	yes	complemented
28	C₂×D₂₉	—	75	1	no	Hall
29	C₂×C₅⋊D₅	—	87	1	no	Hall
30	C₃×C₂₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
32	D₃×D₅	—	145	6	no	—
33	C₂×C₂₉	—	75	1	no	—
34	D₂₉	—	3	1	no	—
35	D₂₉	—	25	1	no	—
36	C₂×C₅²	—	87	1	no	—
37	C₅⋊D₅	—	3	1	no	—
38	C₅⋊D₅	—	29	1	no	—
39	D₁₅	—	5	6	no	—
40	C₃×D₅	—	145	6	no	—
41	C₅×D₃	—	29	6	no	—
42	C₂₉	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
43	C₅²	D₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	435	6	no	—
45	C₃×C₅	D₅×D₂₉	1	6	yes	complemented
46	C₂×D₃	—	725	1	no	Hall
47	C₂×C₅	—	87	6	no	—
48	D₅	—	15	6	no	—
49	D₅	—	145	6	no	—
50	C₂×C₃	—	725	1	no	—
51	D₃	—	25	1	no	—
52	D₃	—	29	1	no	—
53	C₅	D₁₅⋊D₂₉	1	6	yes	complemented
54	C₂²	—	2175	1	no	Sylow
55	C₃	C₅⋊D₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	75	1	no	—
57	C₂	—	87	1	no	—
58	C₂	—	725	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₂₉	C₂²
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₃⋊(C₅⋊D₅)	C₂	semidirect
2. C₅²×D₈₇	C₂	semidirect
3. C₃×C₅⋊D₁₄₅	C₂	semidirect
5. C₃×C₅²×C₂₉	C₂²	semidirect
7. C₅⋊D₁₄₅	D₃	semidirect
11. C₅×D₈₇	D₅	semidirect
13. C₅²×C₂₉	C₂×D₃	semidirect
15. C₃×C₅×C₂₉	C₂×D₅	semidirect
21. D₈₇	C₅⋊D₅	semidirect
24. C₃⋊(C₅⋊D₅)	D₂₉	semidirect
27. C₅×C₂₉	D₃×D₅	semidirect
30. C₃×C₂₉	C₂×C₅⋊D₅	semidirect
31. C₃×C₅²	C₂×D₂₉	semidirect
42. C₂₉	D₃×C₅⋊D₅	semidirect
43. C₅²	D₃×D₂₉	semidirect
45. C₃×C₅	D₅×D₂₉	semidirect
53. C₅	D₁₅⋊D₂₉	semidirect
55. C₃	C₅⋊D₅×D₂₉	semidirect

Subgroups — D87⋊(C5⋊D5) #22576485

Conjugacy classes of subgroups

Complements

Subgroups — D₈₇⋊(C₅⋊D₅) #22576485