Subgroups — C₃×D₅²×C₁₉ #19152861

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

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₅²
commutator, hypocenter	C₅²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₉

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×D₅×C₁₉	C₂	semidirect
3. D₅²×C₁₉	C₃	direct (N × H)
4. C₃×C₅²×C₁₉	C₂²	semidirect
6. C₁₉×C₅⋊D₅	C₂×C₃	semidirect
7. C₅×D₅×C₁₉	C₂×C₃	semidirect
11. C₃×D₅×C₁₉	D₅	direct (N × H)
12. C₅²×C₁₉	C₂²×C₃	semidirect
14. C₃×D₅²	C₁₉	direct (N × H)
16. C₃×C₅×C₁₉	C₂×D₅	semidirect
21. D₅×C₁₉	C₃×D₅	direct (N × H)
22. C₃×C₅⋊D₅	C₂×C₁₉	semidirect
23. C₃×C₅×D₅	C₂×C₁₉	semidirect
26. D₅²	C₃×C₁₉	direct (N × H)
28. C₅×C₁₉	C₂×C₃×D₅	semidirect
30. C₃×C₅²	C₂²×C₁₉	semidirect
32. C₃×C₁₉	D₅²	direct (N × H)
33. C₅⋊D₅	C₂×C₃×C₁₉	semidirect
34. C₅×D₅	C₂×C₃×C₁₉	semidirect
40. C₃×D₅	D₅×C₁₉	direct (N × H)
41. C₅²	C₂²×C₃×C₁₉	semidirect
43. C₁₉	C₃×D₅²	direct (N × H)
45. C₃×C₅	C₂×D₅×C₁₉	semidirect
50. D₅	C₃×D₅×C₁₉	direct (N × H)
54. C₅	C₂×C₃×D₅×C₁₉	semidirect
56. C₃	D₅²×C₁₉	direct (N × H)

Subgroups — C3×D52×C19 #19152861

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₅²×C₁₉ #19152861