Subgroups — D₅₇⋊(C₅⋊D₅) #19152882

Order 5700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Subgroups — D57⋊(C5⋊D5) #19152882

Conjugacy classes of subgroups

Complements

Subgroups — D₅₇⋊(C₅⋊D₅) #19152882