Subgroups — C₂×C₃×C₅×C₇×D₅₉ #37613428

Order 24780.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×D₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×D₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×D₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₅₉	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₇×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₅×D₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇×D₅₉	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₇×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₅₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented
13	C₃×C₅×D₅₉	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₇×D₅₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇×C₅₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₅₉	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅×C₅₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₅₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₇×D₅₉	C₂×C₃×C₅	1	2	yes	direct product factor
20	C₂×C₃×D₅₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₅₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
22	C₅×D₅₉	C₂×C₃×C₇	1	2	yes	direct product factor
23	C₂²×C₃×C₅×C₇	—	59	1	no	maximal, Hall
24	C₇×C₅₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₅₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
26	C₃×D₅₉	C₂×C₅×C₇	1	2	yes	direct product factor
27	C₅×C₅₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
28	C₂×D₅₉	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₅×C₇	—	59	2	no	—
30	C₂×C₃×C₅×C₇	D₅₉	1	1	yes	characteristic, direct product factor
31	C₃×C₅₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₅×C₇	—	59	1	no	Hall
33	C₂×C₅₉	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
34	D₅₉	C₂×C₃×C₅×C₇	1	2	yes	direct product factor
35	C₃×C₅×C₇	C₂×D₅₉	1	1	yes	characteristic, direct product factor, Hall
36	C₂²×C₃×C₇	—	59	1	no	Hall
37	C₂×C₅×C₇	—	59	2	no	—
38	C₂×C₅×C₇	C₃×D₅₉	1	1	yes	characteristic, direct product factor
39	C₂²×C₃×C₅	—	59	1	no	Hall
40	C₅₉	C₂²×C₃×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃×C₇	—	59	2	no	—
42	C₂×C₃×C₇	C₅×D₅₉	1	1	yes	characteristic, direct product factor
43	C₅×C₇	C₂×C₃×D₅₉	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃×C₅	—	59	2	no	—
45	C₂×C₃×C₅	C₇×D₅₉	1	1	yes	characteristic, direct product factor
46	C₂²×C₇	—	59	1	no	Hall
47	C₃×C₇	C₂×C₅×D₅₉	1	1	yes	characteristic, direct product factor, Hall
48	C₂²×C₅	—	59	1	no	Hall
49	C₃×C₅	C₂×C₇×D₅₉	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₇	—	59	2	no	—
51	C₂×C₇	C₃×C₅×D₅₉	1	1	yes	characteristic, direct product factor
52	C₂²×C₃	—	59	1	no	Hall
53	C₂×C₅	—	59	2	no	—
54	C₂×C₅	C₃×C₇×D₅₉	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₃×C₅×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	—	59	2	no	—
57	C₂×C₃	C₅×C₇×D₅₉	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₇×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	59	1	no	Sylow
60	C₃	C₂×C₅×C₇×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	59	2	no	—
62	C₂	C₃×C₅×C₇×D₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₇	D₅₉
commutator, cosocle, hypocenter	C₅₉	C₂²×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₅₉	C₂
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₂×C₃×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×D₅₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₅₉	C₂	semidirect
3. C₂×C₅×C₇×D₅₉	C₃	direct (N × H)
4. C₃×C₅×C₇×C₅₉	C₂²	semidirect
5. C₂×C₃×C₇×D₅₉	C₅	direct (N × H)
6. C₅×C₇×D₅₉	C₂×C₃	direct (N × H)
7. C₂×C₅×C₇×C₅₉	C₂×C₃	semidirect
8. C₂×C₃×C₅×D₅₉	C₇	direct (N × H)
9. C₃×C₇×D₅₉	C₂×C₅	direct (N × H)
10. C₂×C₃×C₇×C₅₉	C₂×C₅	semidirect
11. C₅×C₇×C₅₉	C₂²×C₃	semidirect
12. C₂×C₃×C₅×C₅₉	C₂×C₇	semidirect
13. C₃×C₅×D₅₉	C₂×C₇	direct (N × H)
14. C₂×C₇×D₅₉	C₃×C₅	direct (N × H)
15. C₃×C₇×C₅₉	C₂²×C₅	semidirect
16. C₂×C₅×D₅₉	C₃×C₇	direct (N × H)
17. C₃×C₅×C₅₉	C₂²×C₇	semidirect
18. C₂×C₇×C₅₉	C₂×C₃×C₅	semidirect
19. C₇×D₅₉	C₂×C₃×C₅	direct (N × H)
20. C₂×C₃×D₅₉	C₅×C₇	direct (N × H)
21. C₂×C₅×C₅₉	C₂×C₃×C₇	semidirect
22. C₅×D₅₉	C₂×C₃×C₇	direct (N × H)
24. C₇×C₅₉	C₂²×C₃×C₅	semidirect
25. C₂×C₃×C₅₉	C₂×C₅×C₇	semidirect
26. C₃×D₅₉	C₂×C₅×C₇	direct (N × H)
27. C₅×C₅₉	C₂²×C₃×C₇	semidirect
28. C₂×D₅₉	C₃×C₅×C₇	direct (N × H)
30. C₂×C₃×C₅×C₇	D₅₉	direct (N × H)
31. C₃×C₅₉	C₂²×C₅×C₇	semidirect
33. C₂×C₅₉	C₂×C₃×C₅×C₇	semidirect
34. D₅₉	C₂×C₃×C₅×C₇	direct (N × H)
35. C₃×C₅×C₇	C₂×D₅₉	direct (N × H)
38. C₂×C₅×C₇	C₃×D₅₉	direct (N × H)
40. C₅₉	C₂²×C₃×C₅×C₇	semidirect
42. C₂×C₃×C₇	C₅×D₅₉	direct (N × H)
43. C₅×C₇	C₂×C₃×D₅₉	direct (N × H)
45. C₂×C₃×C₅	C₇×D₅₉	direct (N × H)
47. C₃×C₇	C₂×C₅×D₅₉	direct (N × H)
49. C₃×C₅	C₂×C₇×D₅₉	direct (N × H)
51. C₂×C₇	C₃×C₅×D₅₉	direct (N × H)
54. C₂×C₅	C₃×C₇×D₅₉	direct (N × H)
55. C₇	C₂×C₃×C₅×D₅₉	direct (N × H)
57. C₂×C₃	C₅×C₇×D₅₉	direct (N × H)
58. C₅	C₂×C₃×C₇×D₅₉	direct (N × H)
60. C₃	C₂×C₅×C₇×D₅₉	direct (N × H)
62. C₂	C₃×C₅×C₇×D₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×D₅₉	2
C₂×C₃×C₅×C₇×C₅₉	2
C₂×C₅×C₇×D₅₉	3
C₂×C₃×C₇×D₅₉	5
C₂×C₃×C₅×D₅₉	7
C₂²×C₃×C₅×C₇	59

Subgroups — C2×C3×C5×C7×D59 #37613428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₇×D₅₉ #37613428