Subgroups — C₃×C₅×C₇×D₅₁ #24924241

Order 10710.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×C₇×D₁₇	—	3	1	no	maximal
4	C₃×C₇×D₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₁₇	—	2	1	no	—
6	C₃×C₅×C₇×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₅×D₅₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇×D₁₇	—	3	1	no	Hall
10	C₃²×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₅×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₅₁	C₃×C₅	1	1	yes	characteristic, direct product factor
13	C₃×C₇×D₁₇	—	3	1	no	—
14	C₃×C₅×D₃×C₇	—	17	1	no	maximal, Hall
15	C₅×C₇×C₁₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
16	C₅×D₅₁	C₃×C₇	1	1	yes	characteristic, direct product factor
17	C₃×C₅×D₁₇	—	3	1	no	—
18	C₃×C₇×C₁₇	—	2	1	no	—
19	C₃×C₇×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₃²×C₅×C₇	D₁₇	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₇	—	2	1	no	—
24	C₃×C₅×C₁₇	D₃×C₇	1	1	yes	characteristic, complemented
25	C₃×C₅×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
26	C₇×D₁₇	—	3	1	no	Hall
27	C₂×C₃×C₅×C₇	—	51	1	no	—
28	C₅×D₃×C₇	—	17	1	no	—
29	C₅×D₁₇	—	3	1	no	Hall
30	C₃²×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
31	C₃×D₃×C₇	—	17	1	no	Hall
32	C₇×C₁₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₅×C₇	—	2	1	no	—
34	C₃×C₅×C₇	C₃×D₁₇	1	1	yes	characteristic, complemented
35	C₃×C₅×C₇	D₅₁	1	1	yes	characteristic, direct product factor
36	D₅₁	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor
37	C₃×D₁₇	—	3	1	no	—
38	C₃×C₅×D₃	—	17	1	no	Hall
39	C₅×C₁₇	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅×C₇	—	51	1	no	Hall
41	C₃²×C₇	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₇	—	2	1	no	—
43	C₃×C₁₇	C₅×D₃×C₇	1	1	yes	characteristic, complemented
44	C₃×C₁₇	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
45	C₃²×C₅	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₇	—	51	1	no	—
47	D₃×C₇	—	17	1	no	—
48	C₅×C₇	C₃×D₅₁	1	1	yes	characteristic, direct product factor, Hall
49	D₁₇	—	3	1	no	Hall
50	C₂×C₃×C₅	—	51	1	no	—
51	C₅×D₃	—	17	1	no	—
52	C₃×C₇	—	2	1	no	—
53	C₃×C₇	C₃×C₅×D₁₇	1	1	yes	characteristic, complemented
54	C₃×C₇	C₅×D₅₁	1	1	yes	characteristic, direct product factor
55	C₃×D₃	—	17	1	no	Hall
56	C₁₇	C₃×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
57	C₃×C₅	—	2	1	no	—
58	C₃×C₅	C₃×C₇×D₁₇	1	1	yes	characteristic, complemented
59	C₃×C₅	C₇×D₅₁	1	1	yes	characteristic, direct product factor
60	C₂×C₇	—	51	1	no	Hall
61	C₂×C₅	—	51	1	no	Hall
62	C₃²	C₅×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
63	C₇	C₃×C₅×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	51	1	no	—
65	D₃	—	17	1	no	—
66	C₅	C₃×C₇×D₅₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₅×C₇×D₁₇	1	1	yes	characteristic, complemented
69	C₃	C₅×C₇×D₅₁	1	1	yes	characteristic, direct product factor
70	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₇	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₃×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₇	C₂	semidirect
2. C₅×C₇×D₅₁	C₃	direct (N × H)
4. C₃×C₇×D₅₁	C₅	direct (N × H)
6. C₃×C₅×C₇×C₁₇	D₃	semidirect
7. C₃×C₅×C₇×C₁₇	C₂×C₃	semidirect
8. C₃×C₅×D₅₁	C₇	direct (N × H)
10. C₃²×C₇×C₁₇	C₂×C₅	semidirect
11. C₃²×C₅×C₁₇	C₂×C₇	semidirect
12. C₇×D₅₁	C₃×C₅	direct (N × H)
15. C₅×C₇×C₁₇	C₃×D₃	semidirect
16. C₅×D₅₁	C₃×C₇	direct (N × H)
19. C₃×C₇×C₁₇	C₅×D₃	semidirect
20. C₃×C₇×C₁₇	C₂×C₃×C₅	semidirect
21. C₃²×C₅×C₇	D₁₇	semidirect
22. C₃×D₅₁	C₅×C₇	direct (N × H)
24. C₃×C₅×C₁₇	D₃×C₇	semidirect
25. C₃×C₅×C₁₇	C₂×C₃×C₇	semidirect
30. C₃²×C₁₇	C₂×C₅×C₇	semidirect
32. C₇×C₁₇	C₃×C₅×D₃	semidirect
34. C₃×C₅×C₇	C₃×D₁₇	semidirect
35. C₃×C₅×C₇	D₅₁	direct (N × H)
36. D₅₁	C₃×C₅×C₇	direct (N × H)
39. C₅×C₁₇	C₃×D₃×C₇	semidirect
41. C₃²×C₇	C₅×D₁₇	semidirect
43. C₃×C₁₇	C₅×D₃×C₇	semidirect
44. C₃×C₁₇	C₂×C₃×C₅×C₇	semidirect
45. C₃²×C₅	C₇×D₁₇	semidirect
48. C₅×C₇	C₃×D₅₁	direct (N × H)
53. C₃×C₇	C₃×C₅×D₁₇	semidirect
54. C₃×C₇	C₅×D₅₁	direct (N × H)
56. C₁₇	C₃×C₅×D₃×C₇	semidirect
58. C₃×C₅	C₃×C₇×D₁₇	semidirect
59. C₃×C₅	C₇×D₅₁	direct (N × H)
62. C₃²	C₅×C₇×D₁₇	semidirect
63. C₇	C₃×C₅×D₅₁	direct (N × H)
66. C₅	C₃×C₇×D₅₁	direct (N × H)
68. C₃	C₃×C₅×C₇×D₁₇	semidirect
69. C₃	C₅×C₇×D₅₁	direct (N × H)

Subgroups — C3×C5×C7×D51 #24924241

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×C₇×D₅₁ #24924241