Subgroups — C₃×(C₅⋊D₅)⋊D₁₉ #19152863

Order 5700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃	(C₅⋊D₅)⋊D₁₉
commutator, hypocenter	C₅²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₅⋊D₅	C₂	semidirect
2. C₃×C₅×D₉₅	C₂	semidirect
3. (C₅⋊D₅)⋊D₁₉	C₃	direct (N × H)
4. C₃×C₅²×C₁₉	C₂²	semidirect
6. C₁₉×C₅⋊D₅	C₂×C₃	semidirect
7. C₅×D₉₅	C₂×C₃	semidirect
8. C₃×D₉₅	D₅	semidirect
12. C₅²×C₁₉	C₂²×C₃	semidirect
16. C₃×C₅×C₁₉	C₂×D₅	semidirect
18. D₉₅	C₃×D₅	semidirect
22. C₃×C₅⋊D₅	D₁₉	semidirect
28. C₅×C₁₉	C₂×C₃×D₅	semidirect
30. C₃×C₅²	C₂×D₁₉	semidirect
32. C₃×C₁₉	D₅²	semidirect
33. C₅⋊D₅	C₃×D₁₉	semidirect
41. C₅²	C₂×C₃×D₁₉	semidirect
43. C₁₉	C₃×D₅²	semidirect
45. C₃×C₅	D₅×D₁₉	semidirect
54. C₅	C₃×D₅×D₁₉	semidirect
56. C₃	(C₅⋊D₅)⋊D₁₉	direct (N × H)

Subgroups — C3×(C5⋊D5)⋊D19 #19152863

Conjugacy classes of subgroups

Complements

Subgroups — C₃×(C₅⋊D₅)⋊D₁₉ #19152863