Subgroups — #19152888

Order 5700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₈₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₅⋊D₅)⋊D₁₉	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₅₇	—	5	2	no	maximal
6	C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
7	C₅×D₉₅	—	3	2	no	—
8	D₂₈₅	D₅	1	2	yes	complemented
9	C₅×D₅₇	—	5	2	no	—
10	C₃×D₅×C₁₉	—	5	2	no	—
11	C₃×D₅×C₁₉	—	10	2	no	—
12	C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	D₅×D₁₉	—	15	2	no	—
14	D₁₅⋊D₅	—	19	1	no	maximal, Hall
15	C₃×C₅×C₁₉	—	2	2	no	—
16	C₃×C₅×C₁₉	C₂×D₅	1	2	yes	complemented
17	C₂×D₅₇	—	25	1	no	Hall
18	D₉₅	—	3	2	no	—
19	C₅×D₁₉	—	15	2	no	—
20	D₅×C₁₉	—	5	2	no	—
21	D₅×C₁₉	—	10	2	no	—
22	C₅×D₁₅	—	19	2	no	—
23	C₃×C₅⋊D₅	D₁₉	1	1	yes	characteristic, complemented
24	C₂×C₃×C₁₉	—	25	1	no	—
25	D₅₇	—	5	2	no	—
26	D₅²	—	57	1	no	Hall
27	C₅×C₁₉	—	2	2	no	—
28	C₅×C₁₉	D₃×D₅	1	2	yes	complemented
29	C₂×D₁₉	—	75	1	no	Hall
30	C₃×C₅²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	D₃×D₅	—	95	2	no	—
32	C₃×C₁₉	D₅²	1	1	yes	characteristic, complemented, Hall
33	C₅⋊D₅	D₅₇	1	1	yes	characteristic, complemented
34	C₅×D₅	—	57	2	no	—
35	C₂×C₁₉	—	25	1	no	—
36	D₁₉	—	15	2	no	—
37	D₁₅	—	19	2	no	—
38	C₃×D₅	—	5	2	no	—
39	C₃×D₅	—	10	2	no	—
40	C₅×D₃	—	95	2	no	—
41	C₅²	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₅	—	285	2	no	—
43	C₁₉	D₁₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	D₅×D₁₉	1	2	yes	complemented
46	C₂×D₃	—	475	1	no	Hall
47	C₂×C₅	—	285	2	no	—
48	D₅	—	5	2	no	—
49	D₅	—	10	2	no	—
50	D₅	—	57	2	no	—
51	C₂×C₃	—	25	1	no	—
52	D₃	—	95	2	no	—
53	C₅	—	2	2	no	—
54	C₅	D₅×D₅₇	1	2	yes	complemented
55	C₂²	—	1425	1	no	Sylow
56	C₃	(C₅⋊D₅)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	25	1	no	—
58	C₂	—	285	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₅²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₂₈₅	C₂	semidirect
2. C₃×C₁₉×C₅⋊D₅	C₂	semidirect
4. C₃×C₅²×C₁₉	C₂²	semidirect
6. C₁₉×C₅⋊D₅	D₃	semidirect
8. D₂₈₅	D₅	semidirect
12. C₅²×C₁₉	C₂×D₃	semidirect
16. C₃×C₅×C₁₉	C₂×D₅	semidirect
23. C₃×C₅⋊D₅	D₁₉	semidirect
28. C₅×C₁₉	D₃×D₅	semidirect
30. C₃×C₅²	C₂×D₁₉	semidirect
32. C₃×C₁₉	D₅²	semidirect
33. C₅⋊D₅	D₅₇	semidirect
41. C₅²	C₂×D₅₇	semidirect
43. C₁₉	D₁₅⋊D₅	semidirect
45. C₃×C₅	D₅×D₁₉	semidirect
54. C₅	D₅×D₅₇	semidirect
56. C₃	(C₅⋊D₅)⋊D₁₉	semidirect