Subgroups — C₂×C₅×D₃×C₇×C₇₁ #44447281

Order 29820.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₇×C₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₇×C₇₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₇×C₇₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₇₁	—	3	2	no	—
7	C₂×C₅×C₇×C₇₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₅×D₃×C₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₇×C₇₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₇×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
12	C₅×D₃×C₇₁	C₂×C₇	1	2	yes	direct product factor
13	C₂×C₃×C₅×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂²×C₇×C₇₁	—	3	1	no	Hall
15	C₃×C₇×C₇₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₅×C₇₁	—	3	1	no	Hall
17	C₃×C₅×C₇₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₇₁	—	3	2	no	—
19	C₂×C₇×C₇₁	C₅×D₃	1	1	yes	characteristic, direct product factor
20	C₂×D₃×C₇₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₅×C₇₁	—	3	2	no	—
22	C₂×C₅×C₇₁	D₃×C₇	1	1	yes	characteristic, direct product factor
23	C₇×C₇₁	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₇₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
25	D₃×C₇₁	C₂×C₅×C₇	1	2	yes	direct product factor
26	C₂×C₅×D₃×C₇	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×C₇₁	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₇₁	—	3	1	no	Hall
29	C₃×C₇₁	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₇	C₂×C₇₁	1	1	yes	characteristic, complemented
31	C₅×D₃×C₇	C₂×C₇₁	1	2	yes	direct product factor
32	C₂×C₇₁	—	3	2	no	—
33	C₂×C₇₁	C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
34	C₂²×C₅×C₇	—	3	1	no	Hall
35	C₃×C₅×C₇	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
36	C₂×D₃×C₇	C₅×C₇₁	1	1	yes	characteristic, direct product factor, Hall
37	C₇₁	C₂×C₅×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₅×C₇	—	3	2	no	—
39	C₂×C₅×C₇	D₃×C₇₁	1	1	yes	characteristic, direct product factor
40	C₂×C₅×D₃	C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₃×C₇	C₂×C₅×C₇₁	1	1	yes	characteristic, complemented
42	D₃×C₇	C₂×C₅×C₇₁	1	2	yes	direct product factor
43	C₅×C₇	C₂×D₃×C₇₁	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₃×C₅	C₂×C₇×C₇₁	1	1	yes	characteristic, complemented
45	C₅×D₃	C₂×C₇×C₇₁	1	2	yes	direct product factor
46	C₂²×C₇	—	3	1	no	Hall
47	C₃×C₇	C₂²×C₅×C₇₁	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅	—	3	1	no	Hall
49	C₃×C₅	C₂²×C₇×C₇₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	—	3	2	no	—
51	C₂×C₇	C₅×D₃×C₇₁	1	1	yes	characteristic, direct product factor
52	C₂×D₃	C₅×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₅	—	3	2	no	—
54	C₂×C₅	D₃×C₇×C₇₁	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	C₂×C₅×C₇×C₇₁	1	1	yes	characteristic, complemented
57	D₃	C₂×C₅×C₇×C₇₁	1	2	yes	direct product factor
58	C₅	C₂×D₃×C₇×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	3	1	no	Sylow
60	C₃	C₂²×C₅×C₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	3	2	no	—
62	C₂	C₅×D₃×C₇×C₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₇₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₇×C₇₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₇₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₇×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₇×C₇₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₇₁	C₂	semidirect
4. C₃×C₅×C₇×C₇₁	C₂²	semidirect
5. C₂×D₃×C₇×C₇₁	C₅	direct (N × H)
7. C₂×C₅×C₇×C₇₁	D₃	direct (N × H)
8. C₂×C₅×D₃×C₇₁	C₇	direct (N × H)
9. D₃×C₇×C₇₁	C₂×C₅	direct (N × H)
10. C₂×C₃×C₇×C₇₁	C₂×C₅	semidirect
11. C₅×C₇×C₇₁	C₂×D₃	direct (N × H)
12. C₅×D₃×C₇₁	C₂×C₇	direct (N × H)
13. C₂×C₃×C₅×C₇₁	C₂×C₇	semidirect
15. C₃×C₇×C₇₁	C₂²×C₅	semidirect
17. C₃×C₅×C₇₁	C₂²×C₇	semidirect
19. C₂×C₇×C₇₁	C₅×D₃	direct (N × H)
20. C₂×D₃×C₇₁	C₅×C₇	direct (N × H)
22. C₂×C₅×C₇₁	D₃×C₇	direct (N × H)
23. C₇×C₇₁	C₂×C₅×D₃	direct (N × H)
24. C₂×C₃×C₇₁	C₂×C₅×C₇	semidirect
25. D₃×C₇₁	C₂×C₅×C₇	direct (N × H)
26. C₂×C₅×D₃×C₇	C₇₁	direct (N × H)
27. C₅×C₇₁	C₂×D₃×C₇	direct (N × H)
29. C₃×C₇₁	C₂²×C₅×C₇	semidirect
30. C₂×C₃×C₅×C₇	C₂×C₇₁	semidirect
31. C₅×D₃×C₇	C₂×C₇₁	direct (N × H)
33. C₂×C₇₁	C₅×D₃×C₇	direct (N × H)
35. C₃×C₅×C₇	C₂²×C₇₁	semidirect
36. C₂×D₃×C₇	C₅×C₇₁	direct (N × H)
37. C₇₁	C₂×C₅×D₃×C₇	direct (N × H)
39. C₂×C₅×C₇	D₃×C₇₁	direct (N × H)
40. C₂×C₅×D₃	C₇×C₇₁	direct (N × H)
41. C₂×C₃×C₇	C₂×C₅×C₇₁	semidirect
42. D₃×C₇	C₂×C₅×C₇₁	direct (N × H)
43. C₅×C₇	C₂×D₃×C₇₁	direct (N × H)
44. C₂×C₃×C₅	C₂×C₇×C₇₁	semidirect
45. C₅×D₃	C₂×C₇×C₇₁	direct (N × H)
47. C₃×C₇	C₂²×C₅×C₇₁	semidirect
49. C₃×C₅	C₂²×C₇×C₇₁	semidirect
51. C₂×C₇	C₅×D₃×C₇₁	direct (N × H)
52. C₂×D₃	C₅×C₇×C₇₁	direct (N × H)
54. C₂×C₅	D₃×C₇×C₇₁	direct (N × H)
55. C₇	C₂×C₅×D₃×C₇₁	direct (N × H)
56. C₂×C₃	C₂×C₅×C₇×C₇₁	semidirect
57. D₃	C₂×C₅×C₇×C₇₁	direct (N × H)
58. C₅	C₂×D₃×C₇×C₇₁	direct (N × H)
60. C₃	C₂²×C₅×C₇×C₇₁	semidirect
62. C₂	C₅×D₃×C₇×C₇₁	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×C₇₁	2
C₂×C₃×C₅×C₇×C₇₁	2
C₂²×C₅×C₇×C₇₁	3
C₂×D₃×C₇×C₇₁	5
C₂×C₅×D₃×C₇₁	7
C₂×C₅×D₃×C₇	71

Subgroups — C2×C5×D3×C7×C71 #44447281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₇×C₇₁ #44447281