Subgroups — #22604926

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄₆₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₅⋊D₅)⋊D₃₁	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₉₃	—	5	2	no	maximal
6	C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
7	C₅×D₁₅₅	—	3	2	no	—
8	D₄₆₅	D₅	1	2	yes	complemented
9	C₅×D₉₃	—	5	2	no	—
10	C₃×D₅×C₃₁	—	5	2	no	—
11	C₃×D₅×C₃₁	—	10	2	no	—
12	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	D₅×D₃₁	—	15	2	no	—
14	C₃×C₅×C₃₁	—	2	2	no	—
15	C₃×C₅×C₃₁	C₂×D₅	1	2	yes	complemented
16	C₂×D₉₃	—	25	1	no	Hall
17	D₁₅₅	—	3	2	no	—
18	C₅×D₃₁	—	15	2	no	—
19	D₅×C₃₁	—	5	2	no	—
20	D₅×C₃₁	—	10	2	no	—
21	D₁₅⋊D₅	—	31	1	no	maximal, Hall
22	C₂×C₃×C₃₁	—	25	1	no	—
23	D₉₃	—	5	2	no	—
24	C₅×C₃₁	—	2	2	no	—
25	C₅×C₃₁	D₃×D₅	1	2	yes	complemented
26	C₅×D₁₅	—	31	2	no	—
27	C₃×C₅⋊D₅	D₃₁	1	1	yes	characteristic, complemented
28	C₂×D₃₁	—	75	1	no	Hall
29	D₅²	—	93	1	no	Hall
30	C₃×C₃₁	D₅²	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₁	—	25	1	no	—
33	D₃₁	—	15	2	no	—
34	D₃×D₅	—	155	2	no	—
35	C₅⋊D₅	D₉₃	1	1	yes	characteristic, complemented
36	C₅×D₅	—	93	2	no	—
37	C₃₁	D₁₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
38	D₁₅	—	31	2	no	—
39	C₃×D₅	—	5	2	no	—
40	C₃×D₅	—	10	2	no	—
41	C₅×D₃	—	155	2	no	—
42	C₅²	C₂×D₉₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	465	2	no	—
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	D₅×D₃₁	1	2	yes	complemented
46	C₂×D₃	—	775	1	no	Hall
47	C₂×C₅	—	465	2	no	—
48	D₅	—	5	2	no	—
49	D₅	—	10	2	no	—
50	D₅	—	93	2	no	—
51	C₂×C₃	—	25	1	no	—
52	D₃	—	155	2	no	—
53	C₅	—	2	2	no	—
54	C₅	D₅×D₉₃	1	2	yes	complemented
55	C₂²	—	2325	1	no	Sylow
56	C₃	(C₅⋊D₅)⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	25	1	no	—
58	C₂	—	465	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₃₁	C₂²
LCS	G ▷ C₃×C₅²×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₄₆₅	C₂	semidirect
2. C₃×C₃₁×C₅⋊D₅	C₂	semidirect
4. C₃×C₅²×C₃₁	C₂²	semidirect
6. C₃₁×C₅⋊D₅	D₃	semidirect
8. D₄₆₅	D₅	semidirect
12. C₅²×C₃₁	C₂×D₃	semidirect
15. C₃×C₅×C₃₁	C₂×D₅	semidirect
25. C₅×C₃₁	D₃×D₅	semidirect
27. C₃×C₅⋊D₅	D₃₁	semidirect
30. C₃×C₃₁	D₅²	semidirect
31. C₃×C₅²	C₂×D₃₁	semidirect
35. C₅⋊D₅	D₉₃	semidirect
37. C₃₁	D₁₅⋊D₅	semidirect
42. C₅²	C₂×D₉₃	semidirect
45. C₃×C₅	D₅×D₃₁	semidirect
54. C₅	D₅×D₉₃	semidirect
56. C₃	(C₅⋊D₅)⋊D₃₁	semidirect