Subgroups — C₅²×D₃×D₁₉ #19152864

Order 5700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅²	D₃×D₁₉
commutator, hypocenter	C₃×C₁₉	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×D₅₇	C₂	semidirect
2. C₅²×D₃×C₁₉	C₂	semidirect
3. C₃×C₅²×D₁₉	C₂	semidirect
5. C₃×C₅²×C₁₉	C₂²	semidirect
6. C₅×D₃×D₁₉	C₅	direct (N × H)
9. C₅²×D₁₉	D₃	direct (N × H)
10. C₅×D₅₇	C₂×C₅	semidirect
11. C₅×D₃×C₁₉	C₂×C₅	semidirect
12. C₃×C₅×D₁₉	C₂×C₅	semidirect
13. C₅²×C₁₉	C₂×D₃	semidirect
16. C₃×C₅×C₁₉	C₂²×C₅	semidirect
17. D₃×D₁₉	C₅²	direct (N × H)
20. C₅×D₁₉	C₅×D₃	direct (N × H)
23. C₅²×D₃	D₁₉	direct (N × H)
24. D₅₇	C₂×C₅²	semidirect
25. C₃×D₁₉	C₂×C₅²	semidirect
26. D₃×C₁₉	C₂×C₅²	semidirect
28. C₅×C₁₉	C₂×C₅×D₃	semidirect
30. C₃×C₅²	C₂×D₁₉	semidirect
32. C₃×C₁₉	C₂²×C₅²	semidirect
38. D₁₉	C₅²×D₃	direct (N × H)
41. C₅×D₃	C₅×D₁₉	direct (N × H)
42. C₅²	D₃×D₁₉	direct (N × H)
44. C₁₉	C₂×C₅²×D₃	semidirect
45. C₃×C₅	C₂×C₅×D₁₉	semidirect
52. D₃	C₅²×D₁₉	direct (N × H)
53. C₅	C₅×D₃×D₁₉	direct (N × H)
55. C₃	C₂×C₅²×D₁₉	semidirect

Subgroups — C52×D3×D19 #19152864

Conjugacy classes of subgroups

Complements

Subgroups — C₅²×D₃×D₁₉ #19152864