Subgroups — C₂×C₅²×D₅₇ #19152903

Order 5700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₅₇
commutator, hypocenter	C₃×C₁₉	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×D₅₇	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₉	C₂	semidirect
4. C₃×C₅²×C₁₉	C₂²	semidirect
5. C₂×C₅×D₅₇	C₅	direct (N × H)
6. C₂×C₅²×C₁₉	D₃	semidirect
8. C₂×C₃×C₅×C₁₉	C₂×C₅	semidirect
9. C₅×D₅₇	C₂×C₅	direct (N × H)
10. C₅²×C₁₉	C₂×D₃	semidirect
13. C₃×C₅×C₁₉	C₂²×C₅	semidirect
14. C₂×D₅₇	C₅²	direct (N × H)
15. C₂×C₅×C₁₉	C₅×D₃	semidirect
17. C₂×C₃×C₅²	D₁₉	semidirect
19. C₂×C₃×C₁₉	C₂×C₅²	semidirect
20. D₅₇	C₂×C₅²	direct (N × H)
22. C₅×C₁₉	C₂×C₅×D₃	semidirect
24. C₃×C₅²	C₂×D₁₉	semidirect
26. C₃×C₁₉	C₂²×C₅²	semidirect
28. C₂×C₅²	D₅₇	direct (N × H)
29. C₂×C₁₉	C₅²×D₃	semidirect
31. C₂×C₃×C₅	C₅×D₁₉	semidirect
33. C₅²	C₂×D₅₇	direct (N × H)
35. C₁₉	C₂×C₅²×D₃	semidirect
36. C₃×C₅	C₂×C₅×D₁₉	semidirect
39. C₂×C₅	C₅×D₅₇	direct (N × H)
40. C₂×C₃	C₅²×D₁₉	semidirect
42. C₅	C₂×C₅×D₅₇	direct (N × H)
44. C₃	C₂×C₅²×D₁₉	semidirect
46. C₂	C₅²×D₅₇	direct (N × H)

Subgroups — C2×C52×D57 #19152903

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×D₅₇ #19152903