Subgroups — C₂×C₅×D₃×C₇×C₅₉ #37613435

Order 24780.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₇×C₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₇×C₅₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₇×C₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₅₉	—	3	2	no	—
7	C₂×C₅×C₇×C₅₉	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₅×D₃×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₇×C₅₉	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₇×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₅₉	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₅×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented
13	C₅×D₃×C₅₉	C₂×C₇	1	2	yes	direct product factor
14	C₂²×C₇×C₅₉	—	3	1	no	Hall
15	C₃×C₇×C₅₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₅×C₅₉	—	3	1	no	Hall
17	C₃×C₅×C₅₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₅₉	—	3	2	no	—
19	C₂×C₇×C₅₉	C₅×D₃	1	1	yes	characteristic, direct product factor
20	C₂×D₃×C₅₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₅₉	—	3	2	no	—
22	C₂×C₅×C₅₉	D₃×C₇	1	1	yes	characteristic, direct product factor
23	C₂×C₅×D₃×C₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₇×C₅₉	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
26	D₃×C₅₉	C₂×C₅×C₇	1	2	yes	direct product factor
27	C₅×C₅₉	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₅₉	—	3	1	no	Hall
29	C₂×C₃×C₅×C₇	C₂×C₅₉	1	1	yes	characteristic, complemented
30	C₅×D₃×C₇	C₂×C₅₉	1	2	yes	direct product factor
31	C₃×C₅₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₅×C₇	—	3	1	no	Hall
33	C₂×C₅₉	—	3	2	no	—
34	C₂×C₅₉	C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₇	C₂²×C₅₉	1	1	yes	characteristic, complemented, Hall
36	C₂×D₃×C₇	C₅×C₅₉	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₅×C₇	—	3	2	no	—
38	C₂×C₅×C₇	D₃×C₅₉	1	1	yes	characteristic, direct product factor
39	C₂×C₅×D₃	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
40	C₅₉	C₂×C₅×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃×C₇	C₂×C₅×C₅₉	1	1	yes	characteristic, complemented
42	D₃×C₇	C₂×C₅×C₅₉	1	2	yes	direct product factor
43	C₅×C₇	C₂×D₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃×C₅	C₂×C₇×C₅₉	1	1	yes	characteristic, complemented
45	C₅×D₃	C₂×C₇×C₅₉	1	2	yes	direct product factor
46	C₂²×C₇	—	3	1	no	Hall
47	C₃×C₇	C₂²×C₅×C₅₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅	—	3	1	no	Hall
49	C₃×C₅	C₂²×C₇×C₅₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	—	3	2	no	—
51	C₂×C₇	C₅×D₃×C₅₉	1	1	yes	characteristic, direct product factor
52	C₂×D₃	C₅×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₅	—	3	2	no	—
54	C₂×C₅	D₃×C₇×C₅₉	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	C₂×C₅×C₇×C₅₉	1	1	yes	characteristic, complemented
57	D₃	C₂×C₅×C₇×C₅₉	1	2	yes	direct product factor
58	C₅	C₂×D₃×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	3	1	no	Sylow
60	C₃	C₂²×C₅×C₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	3	2	no	—
62	C₂	C₅×D₃×C₇×C₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₅₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₅₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₇×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₇×C₅₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₅₉	C₂	semidirect
4. C₃×C₅×C₇×C₅₉	C₂²	semidirect
5. C₂×D₃×C₇×C₅₉	C₅	direct (N × H)
7. C₂×C₅×C₇×C₅₉	D₃	direct (N × H)
8. C₂×C₅×D₃×C₅₉	C₇	direct (N × H)
9. D₃×C₇×C₅₉	C₂×C₅	direct (N × H)
10. C₂×C₃×C₇×C₅₉	C₂×C₅	semidirect
11. C₅×C₇×C₅₉	C₂×D₃	direct (N × H)
12. C₂×C₃×C₅×C₅₉	C₂×C₇	semidirect
13. C₅×D₃×C₅₉	C₂×C₇	direct (N × H)
15. C₃×C₇×C₅₉	C₂²×C₅	semidirect
17. C₃×C₅×C₅₉	C₂²×C₇	semidirect
19. C₂×C₇×C₅₉	C₅×D₃	direct (N × H)
20. C₂×D₃×C₅₉	C₅×C₇	direct (N × H)
22. C₂×C₅×C₅₉	D₃×C₇	direct (N × H)
23. C₂×C₅×D₃×C₇	C₅₉	direct (N × H)
24. C₇×C₅₉	C₂×C₅×D₃	direct (N × H)
25. C₂×C₃×C₅₉	C₂×C₅×C₇	semidirect
26. D₃×C₅₉	C₂×C₅×C₇	direct (N × H)
27. C₅×C₅₉	C₂×D₃×C₇	direct (N × H)
29. C₂×C₃×C₅×C₇	C₂×C₅₉	semidirect
30. C₅×D₃×C₇	C₂×C₅₉	direct (N × H)
31. C₃×C₅₉	C₂²×C₅×C₇	semidirect
34. C₂×C₅₉	C₅×D₃×C₇	direct (N × H)
35. C₃×C₅×C₇	C₂²×C₅₉	semidirect
36. C₂×D₃×C₇	C₅×C₅₉	direct (N × H)
38. C₂×C₅×C₇	D₃×C₅₉	direct (N × H)
39. C₂×C₅×D₃	C₇×C₅₉	direct (N × H)
40. C₅₉	C₂×C₅×D₃×C₇	direct (N × H)
41. C₂×C₃×C₇	C₂×C₅×C₅₉	semidirect
42. D₃×C₇	C₂×C₅×C₅₉	direct (N × H)
43. C₅×C₇	C₂×D₃×C₅₉	direct (N × H)
44. C₂×C₃×C₅	C₂×C₇×C₅₉	semidirect
45. C₅×D₃	C₂×C₇×C₅₉	direct (N × H)
47. C₃×C₇	C₂²×C₅×C₅₉	semidirect
49. C₃×C₅	C₂²×C₇×C₅₉	semidirect
51. C₂×C₇	C₅×D₃×C₅₉	direct (N × H)
52. C₂×D₃	C₅×C₇×C₅₉	direct (N × H)
54. C₂×C₅	D₃×C₇×C₅₉	direct (N × H)
55. C₇	C₂×C₅×D₃×C₅₉	direct (N × H)
56. C₂×C₃	C₂×C₅×C₇×C₅₉	semidirect
57. D₃	C₂×C₅×C₇×C₅₉	direct (N × H)
58. C₅	C₂×D₃×C₇×C₅₉	direct (N × H)
60. C₃	C₂²×C₅×C₇×C₅₉	semidirect
62. C₂	C₅×D₃×C₇×C₅₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×D₃×C₇×C₅₉	2
C₂×C₃×C₅×C₇×C₅₉	2
C₂²×C₅×C₇×C₅₉	3
C₂×D₃×C₇×C₅₉	5
C₂×C₅×D₃×C₅₉	7
C₂×C₅×D₃×C₇	59

Subgroups — C2×C5×D3×C7×C59 #37613435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₇×C₅₉ #37613435