Subgroups — C₂×C₇×D₅×C₁₁×C₂₃ #47978484

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₁₁×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₇×C₁₁×C₂₃	—	5	1	no	maximal, Hall
5	C₂×D₅×C₁₁×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇×C₁₁×C₂₃	—	5	2	no	—
7	C₂×C₇×C₁₁×C₂₃	D₅	1	1	yes	characteristic, direct product factor
8	C₂×C₇×D₅×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₅×C₁₁×C₂₃	C₂×C₇	1	2	yes	direct product factor
10	C₂×C₅×C₁₁×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
11	C₇×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₇×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₇×D₅×C₂₃	C₂×C₁₁	1	2	yes	direct product factor
14	C₂×C₇×D₅×C₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₁₁×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₁₁×C₂₃	—	5	1	no	Hall
17	C₅×C₇×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₇×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented
19	C₇×D₅×C₁₁	C₂×C₂₃	1	2	yes	direct product factor
20	C₂²×C₇×C₂₃	—	5	1	no	Hall
21	C₂×C₁₁×C₂₃	—	5	2	no	—
22	C₂×C₁₁×C₂₃	C₇×D₅	1	1	yes	characteristic, direct product factor
23	C₂×D₅×C₂₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₇×C₁₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₂₃	—	5	2	no	—
26	C₂×C₇×C₂₃	D₅×C₁₁	1	1	yes	characteristic, direct product factor
27	C₂²×C₇×C₁₁	—	5	1	no	Hall
28	C₁₁×C₂₃	C₂×C₇×D₅	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅×C₂₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
30	D₅×C₂₃	C₂×C₇×C₁₁	1	2	yes	direct product factor
31	C₂×D₅×C₁₁	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
32	C₇×C₂₃	C₂×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₇×C₁₁	—	5	2	no	—
34	C₂×C₇×C₁₁	D₅×C₂₃	1	1	yes	characteristic, direct product factor
35	C₂×C₇×D₅	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₂₃	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₅×C₁₁	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
38	D₅×C₁₁	C₂×C₇×C₂₃	1	2	yes	direct product factor
39	C₂²×C₂₃	—	5	1	no	Hall
40	C₇×C₁₁	C₂×D₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅×C₇	C₂×C₁₁×C₂₃	1	1	yes	characteristic, complemented
42	C₇×D₅	C₂×C₁₁×C₂₃	1	2	yes	direct product factor
43	C₅×C₁₁	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₂₃	—	5	2	no	—
45	C₂×C₂₃	C₇×D₅×C₁₁	1	1	yes	characteristic, direct product factor
46	C₂²×C₁₁	—	5	1	no	Hall
47	C₅×C₇	C₂²×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₇	—	5	1	no	Hall
49	C₂₃	C₂×C₇×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₁₁	—	5	2	no	—
51	C₂×C₁₁	C₇×D₅×C₂₃	1	1	yes	characteristic, direct product factor
52	C₂×D₅	C₇×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₇	—	5	2	no	—
54	C₂×C₇	D₅×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor
55	C₁₁	C₂×C₇×D₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₅	C₂×C₇×C₁₁×C₂₃	1	1	yes	characteristic, complemented
57	D₅	C₂×C₇×C₁₁×C₂₃	1	2	yes	direct product factor
58	C₇	C₂×D₅×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₅	C₂²×C₇×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
60	C₂²	—	5	1	no	Sylow
61	C₂	—	5	2	no	—
62	C₂	C₇×D₅×C₁₁×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₁×C₂₃	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₇×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₇×C₁₁×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇×D₅×C₁₁×C₂₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₁×C₂₃	C₂	semidirect
3. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
5. C₂×D₅×C₁₁×C₂₃	C₇	direct (N × H)
7. C₂×C₇×C₁₁×C₂₃	D₅	direct (N × H)
8. C₂×C₇×D₅×C₂₃	C₁₁	direct (N × H)
9. D₅×C₁₁×C₂₃	C₂×C₇	direct (N × H)
10. C₂×C₅×C₁₁×C₂₃	C₂×C₇	semidirect
11. C₇×C₁₁×C₂₃	C₂×D₅	direct (N × H)
12. C₂×C₅×C₇×C₂₃	C₂×C₁₁	semidirect
13. C₇×D₅×C₂₃	C₂×C₁₁	direct (N × H)
14. C₂×C₇×D₅×C₁₁	C₂₃	direct (N × H)
15. C₅×C₁₁×C₂₃	C₂²×C₇	semidirect
17. C₅×C₇×C₂₃	C₂²×C₁₁	semidirect
18. C₂×C₅×C₇×C₁₁	C₂×C₂₃	semidirect
19. C₇×D₅×C₁₁	C₂×C₂₃	direct (N × H)
22. C₂×C₁₁×C₂₃	C₇×D₅	direct (N × H)
23. C₂×D₅×C₂₃	C₇×C₁₁	direct (N × H)
24. C₅×C₇×C₁₁	C₂²×C₂₃	semidirect
26. C₂×C₇×C₂₃	D₅×C₁₁	direct (N × H)
28. C₁₁×C₂₃	C₂×C₇×D₅	direct (N × H)
29. C₂×C₅×C₂₃	C₂×C₇×C₁₁	semidirect
30. D₅×C₂₃	C₂×C₇×C₁₁	direct (N × H)
31. C₂×D₅×C₁₁	C₇×C₂₃	direct (N × H)
32. C₇×C₂₃	C₂×D₅×C₁₁	direct (N × H)
34. C₂×C₇×C₁₁	D₅×C₂₃	direct (N × H)
35. C₂×C₇×D₅	C₁₁×C₂₃	direct (N × H)
36. C₅×C₂₃	C₂²×C₇×C₁₁	semidirect
37. C₂×C₅×C₁₁	C₂×C₇×C₂₃	semidirect
38. D₅×C₁₁	C₂×C₇×C₂₃	direct (N × H)
40. C₇×C₁₁	C₂×D₅×C₂₃	direct (N × H)
41. C₂×C₅×C₇	C₂×C₁₁×C₂₃	semidirect
42. C₇×D₅	C₂×C₁₁×C₂₃	direct (N × H)
43. C₅×C₁₁	C₂²×C₇×C₂₃	semidirect
45. C₂×C₂₃	C₇×D₅×C₁₁	direct (N × H)
47. C₅×C₇	C₂²×C₁₁×C₂₃	semidirect
49. C₂₃	C₂×C₇×D₅×C₁₁	direct (N × H)
51. C₂×C₁₁	C₇×D₅×C₂₃	direct (N × H)
52. C₂×D₅	C₇×C₁₁×C₂₃	direct (N × H)
54. C₂×C₇	D₅×C₁₁×C₂₃	direct (N × H)
55. C₁₁	C₂×C₇×D₅×C₂₃	direct (N × H)
56. C₂×C₅	C₂×C₇×C₁₁×C₂₃	semidirect
57. D₅	C₂×C₇×C₁₁×C₂₃	direct (N × H)
58. C₇	C₂×D₅×C₁₁×C₂₃	direct (N × H)
59. C₅	C₂²×C₇×C₁₁×C₂₃	semidirect
62. C₂	C₇×D₅×C₁₁×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₅×C₁₁×C₂₃	2
C₂×C₅×C₇×C₁₁×C₂₃	2
C₂²×C₇×C₁₁×C₂₃	5
C₂×D₅×C₁₁×C₂₃	7
C₂×C₇×D₅×C₂₃	11
C₂×C₇×D₅×C₁₁	23

Subgroups — C2×C7×D5×C11×C23 #47978484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₅×C₁₁×C₂₃ #47978484