Subgroups — C₂×C₅²×D₅₁ #19099841

Order 5100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₁₇	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₅₁	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₅²×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₅²×D₁₇	—	3	2	no	—
8	C₂×C₃×C₅×C₁₇	C₂×C₅	1	6	yes	complemented
9	C₅×D₅₁	C₂×C₅	1	12	yes	direct product factor
10	C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₁₇	—	3	6	no	—
12	C₂×C₅²×D₃	—	17	1	no	maximal, Hall
13	C₃×C₅×C₁₇	C₂²×C₅	1	6	yes	complemented
14	C₂×D₅₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₁₇	C₅×D₃	1	6	yes	complemented
16	C₅×D₁₇	—	3	12	no	—
17	C₂×C₃×C₅²	D₁₇	1	1	yes	characteristic, complemented
18	C₅²×D₃	—	17	2	no	—
19	C₂×C₃×C₁₇	C₂×C₅²	1	1	yes	characteristic, complemented
20	D₅₁	C₂×C₅²	1	2	yes	direct product factor
21	C₂²×C₅²	—	51	1	no	Hall
22	C₅×C₁₇	C₂×C₅×D₃	1	6	yes	complemented
23	C₃×C₅²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₇	—	3	1	no	Hall
25	C₂×C₅×D₃	—	17	6	no	—
26	C₃×C₁₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅²	—	51	2	no	—
28	C₂×C₅²	D₅₁	1	1	yes	characteristic, direct product factor
29	C₂×C₁₇	C₅²×D₃	1	1	yes	characteristic, complemented
30	D₁₇	—	3	2	no	—
31	C₂×C₃×C₅	C₅×D₁₇	1	6	yes	complemented
32	C₅×D₃	—	17	12	no	—
33	C₅²	C₂×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²×C₅	—	51	6	no	—
35	C₁₇	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₅	C₂×C₅×D₁₇	1	6	yes	complemented
37	C₂×D₃	—	17	1	no	Hall
38	C₂×C₅	—	51	12	no	—
39	C₂×C₅	C₅×D₅₁	1	6	yes	direct product factor
40	C₂×C₃	C₅²×D₁₇	1	1	yes	characteristic, complemented
41	D₃	—	17	2	no	—
42	C₅	C₂×C₅×D₅₁	1	6	yes	direct product factor
43	C₂²	—	51	1	no	Sylow
44	C₃	C₂×C₅²×D₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	51	2	no	—
46	C₂	C₅²×D₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₅₁
commutator, hypocenter	C₃×C₁₇	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×D₅₁	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₇	C₂	semidirect
4. C₃×C₅²×C₁₇	C₂²	semidirect
5. C₂×C₅×D₅₁	C₅	direct (N × H)
6. C₂×C₅²×C₁₇	D₃	semidirect
8. C₂×C₃×C₅×C₁₇	C₂×C₅	semidirect
9. C₅×D₅₁	C₂×C₅	direct (N × H)
10. C₅²×C₁₇	C₂×D₃	semidirect
13. C₃×C₅×C₁₇	C₂²×C₅	semidirect
14. C₂×D₅₁	C₅²	direct (N × H)
15. C₂×C₅×C₁₇	C₅×D₃	semidirect
17. C₂×C₃×C₅²	D₁₇	semidirect
19. C₂×C₃×C₁₇	C₂×C₅²	semidirect
20. D₅₁	C₂×C₅²	direct (N × H)
22. C₅×C₁₇	C₂×C₅×D₃	semidirect
23. C₃×C₅²	C₂×D₁₇	semidirect
26. C₃×C₁₇	C₂²×C₅²	semidirect
28. C₂×C₅²	D₅₁	direct (N × H)
29. C₂×C₁₇	C₅²×D₃	semidirect
31. C₂×C₃×C₅	C₅×D₁₇	semidirect
33. C₅²	C₂×D₅₁	direct (N × H)
35. C₁₇	C₂×C₅²×D₃	semidirect
36. C₃×C₅	C₂×C₅×D₁₇	semidirect
39. C₂×C₅	C₅×D₅₁	direct (N × H)
40. C₂×C₃	C₅²×D₁₇	semidirect
42. C₅	C₂×C₅×D₅₁	direct (N × H)
44. C₃	C₂×C₅²×D₁₇	semidirect
46. C₂	C₅²×D₅₁	direct (N × H)

Subgroups — C2×C52×D51 #19099841

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×D₅₁ #19099841