Subgroups — D₃×C₁₉×C₅⋊D₅ #19152879

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×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×C₅⋊D₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅×C₁₉	—	5	6	no	maximal
7	C₂×C₅²×C₁₉	—	3	1	no	—
8	C₁₉×C₅⋊D₅	—	3	1	no	—
9	C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic, direct product factor
10	C₁₉×D₁₅	—	5	6	no	—
11	C₅×D₃×C₁₉	D₅	1	6	yes	complemented
12	C₃×D₅×C₁₉	—	5	6	no	—
13	C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₅×C₁₉	—	15	6	no	—
15	D₃×C₅⋊D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₅×C₁₉	C₂×D₅	1	6	yes	complemented
17	C₂×D₃×C₁₉	—	25	1	no	Hall
18	C₂×C₅×C₁₉	—	3	6	no	—
19	D₅×C₁₉	—	5	6	no	—
20	D₅×C₁₉	—	15	6	no	—
21	C₃⋊(C₅⋊D₅)	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₅²×D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₃×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic, complemented
24	C₂×C₃×C₁₉	—	25	1	no	—
25	D₃×C₁₉	—	25	1	no	—
26	D₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
27	C₂×C₅⋊D₅	—	3	1	no	Hall
28	C₅×C₁₉	D₃×D₅	1	6	yes	complemented
29	C₂²×C₁₉	—	75	1	no	Hall
30	C₃×C₅²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	D₃×D₅	—	5	6	no	—
32	C₃×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅²	—	3	1	no	—
34	C₅⋊D₅	—	3	1	no	—
35	C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic, direct product factor
36	C₂×C₁₉	—	3	1	no	—
37	C₂×C₁₉	—	25	1	no	—
38	C₂×C₁₉	—	75	1	no	—
39	D₁₅	—	5	6	no	—
40	C₃×D₅	—	5	6	no	—
41	C₅×D₃	D₅×C₁₉	1	6	yes	complemented
42	C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	15	6	no	—
44	C₁₉	D₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₃×C₅	C₂×D₅×C₁₉	1	6	yes	complemented
46	C₂×D₃	—	25	1	no	Hall
47	C₂×C₅	—	3	6	no	—
48	D₅	—	5	6	no	—
49	D₅	—	15	6	no	—
50	C₂×C₃	—	25	1	no	—
51	D₃	—	25	1	no	—
52	D₃	C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₅×C₁₉	1	6	yes	complemented
54	C₂²	—	75	1	no	Sylow
55	C₃	C₂×C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	75	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₃×C₅⋊D₅
commutator, hypocenter	C₃×C₅²	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₁₉

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×D₃×C₁₉	C₂	semidirect
3. C₃×C₁₉×C₅⋊D₅	C₂	semidirect
5. C₃×C₅²×C₁₉	C₂²	semidirect
9. C₁₉×C₅⋊D₅	D₃	direct (N × H)
11. C₅×D₃×C₁₉	D₅	semidirect
13. C₅²×C₁₉	C₂×D₃	semidirect
15. D₃×C₅⋊D₅	C₁₉	direct (N × H)
16. C₃×C₅×C₁₉	C₂×D₅	semidirect
21. C₃⋊(C₅⋊D₅)	C₂×C₁₉	semidirect
22. C₅²×D₃	C₂×C₁₉	semidirect
23. C₃×C₅⋊D₅	C₂×C₁₉	semidirect
26. D₃×C₁₉	C₅⋊D₅	direct (N × H)
28. C₅×C₁₉	D₃×D₅	semidirect
30. C₃×C₅²	C₂²×C₁₉	semidirect
32. C₃×C₁₉	C₂×C₅⋊D₅	semidirect
35. C₅⋊D₅	D₃×C₁₉	direct (N × H)
41. C₅×D₃	D₅×C₁₉	semidirect
42. C₅²	C₂×D₃×C₁₉	semidirect
44. C₁₉	D₃×C₅⋊D₅	direct (N × H)
45. C₃×C₅	C₂×D₅×C₁₉	semidirect
52. D₃	C₁₉×C₅⋊D₅	direct (N × H)
53. C₅	D₃×D₅×C₁₉	semidirect
55. C₃	C₂×C₁₉×C₅⋊D₅	semidirect

Subgroups — D3×C19×C5⋊D5 #19152879

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₉×C₅⋊D₅ #19152879