Subgroups — C₂×C₅×C₇×D₁₁×C₂₃ #47978478

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₁₁×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	C₂×C₇×D₁₁×C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₁₁×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₁₁×C₂₃	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₇×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
8	C₂²×C₅×C₇×C₂₃	—	11	1	no	maximal, Hall
9	C₅×D₁₁×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	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇×C₂₃	—	11	2	no	—
13	C₂×C₅×C₇×C₂₃	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×C₅×C₇×D₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₁₁×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×D₁₁×C₂₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₇×C₂₃	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₇×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented
19	C₅×C₇×D₁₁	C₂×C₂₃	1	2	yes	direct product factor
20	C₂²×C₇×C₂₃	—	11	1	no	Hall
21	C₂×C₁₁×C₂₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
22	D₁₁×C₂₃	C₂×C₅×C₇	1	2	yes	direct product factor
23	C₂²×C₅×C₂₃	—	11	1	no	Hall
24	C₅×C₇×C₁₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₂₃	—	11	2	no	—
26	C₂×C₇×C₂₃	C₅×D₁₁	1	1	yes	characteristic, direct product factor
27	C₂×C₇×D₁₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
28	C₁₁×C₂₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₂₃	—	11	2	no	—
30	C₂×C₅×C₂₃	C₇×D₁₁	1	1	yes	characteristic, direct product factor
31	C₂×C₅×D₁₁	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
32	C₇×C₂₃	C₂×C₅×D₁₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₇×C₁₁	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
34	C₇×D₁₁	C₂×C₅×C₂₃	1	2	yes	direct product factor
35	C₂²×C₅×C₇	—	11	1	no	Hall
36	C₅×C₂₃	C₂×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₅×C₁₁	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
38	C₅×D₁₁	C₂×C₇×C₂₃	1	2	yes	direct product factor
39	C₂²×C₂₃	—	11	1	no	Hall
40	C₇×C₁₁	C₂²×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₇	—	11	2	no	—
42	C₂×C₅×C₇	D₁₁×C₂₃	1	1	yes	characteristic, direct product factor
43	C₅×C₁₁	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
44	C₂×C₂₃	—	11	2	no	—
45	C₂×C₂₃	C₅×C₇×D₁₁	1	1	yes	characteristic, direct product factor
46	C₂×D₁₁	C₅×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
47	C₅×C₇	C₂×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂²×C₇	—	11	1	no	Hall
49	C₂₃	C₂×C₅×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₁₁	C₂×C₅×C₇×C₂₃	1	1	yes	characteristic, complemented
51	D₁₁	C₂×C₅×C₇×C₂₃	1	2	yes	direct product factor
52	C₂²×C₅	—	11	1	no	Hall
53	C₂×C₇	—	11	2	no	—
54	C₂×C₇	C₅×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor
55	C₁₁	C₂²×C₅×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	11	2	no	—
57	C₂×C₅	C₇×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor
58	C₇	C₂×C₅×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₅	C₂×C₇×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	—	11	1	no	Sylow
61	C₂	—	11	2	no	—
62	C₂	C₅×C₇×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₂₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₅×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₁₁×C₂₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₁×C₂₃	C₂	semidirect
3. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
4. C₂×C₇×D₁₁×C₂₃	C₅	direct (N × H)
5. C₂×C₅×D₁₁×C₂₃	C₇	direct (N × H)
6. C₇×D₁₁×C₂₃	C₂×C₅	direct (N × H)
7. C₂×C₇×C₁₁×C₂₃	C₂×C₅	semidirect
9. C₅×D₁₁×C₂₃	C₂×C₇	direct (N × H)
10. C₂×C₅×C₁₁×C₂₃	C₂×C₇	semidirect
11. C₇×C₁₁×C₂₃	C₂²×C₅	semidirect
13. C₂×C₅×C₇×C₂₃	D₁₁	direct (N × H)
14. C₂×C₅×C₇×D₁₁	C₂₃	direct (N × H)
15. C₅×C₁₁×C₂₃	C₂²×C₇	semidirect
16. C₂×D₁₁×C₂₃	C₅×C₇	direct (N × H)
17. C₅×C₇×C₂₃	C₂×D₁₁	direct (N × H)
18. C₂×C₅×C₇×C₁₁	C₂×C₂₃	semidirect
19. C₅×C₇×D₁₁	C₂×C₂₃	direct (N × H)
21. C₂×C₁₁×C₂₃	C₂×C₅×C₇	semidirect
22. D₁₁×C₂₃	C₂×C₅×C₇	direct (N × H)
24. C₅×C₇×C₁₁	C₂²×C₂₃	semidirect
26. C₂×C₇×C₂₃	C₅×D₁₁	direct (N × H)
27. C₂×C₇×D₁₁	C₅×C₂₃	direct (N × H)
28. C₁₁×C₂₃	C₂²×C₅×C₇	semidirect
30. C₂×C₅×C₂₃	C₇×D₁₁	direct (N × H)
31. C₂×C₅×D₁₁	C₇×C₂₃	direct (N × H)
32. C₇×C₂₃	C₂×C₅×D₁₁	direct (N × H)
33. C₂×C₇×C₁₁	C₂×C₅×C₂₃	semidirect
34. C₇×D₁₁	C₂×C₅×C₂₃	direct (N × H)
36. C₅×C₂₃	C₂×C₇×D₁₁	direct (N × H)
37. C₂×C₅×C₁₁	C₂×C₇×C₂₃	semidirect
38. C₅×D₁₁	C₂×C₇×C₂₃	direct (N × H)
40. C₇×C₁₁	C₂²×C₅×C₂₃	semidirect
42. C₂×C₅×C₇	D₁₁×C₂₃	direct (N × H)
43. C₅×C₁₁	C₂²×C₇×C₂₃	semidirect
45. C₂×C₂₃	C₅×C₇×D₁₁	direct (N × H)
46. C₂×D₁₁	C₅×C₇×C₂₃	direct (N × H)
47. C₅×C₇	C₂×D₁₁×C₂₃	direct (N × H)
49. C₂₃	C₂×C₅×C₇×D₁₁	direct (N × H)
50. C₂×C₁₁	C₂×C₅×C₇×C₂₃	semidirect
51. D₁₁	C₂×C₅×C₇×C₂₃	direct (N × H)
54. C₂×C₇	C₅×D₁₁×C₂₃	direct (N × H)
55. C₁₁	C₂²×C₅×C₇×C₂₃	semidirect
57. C₂×C₅	C₇×D₁₁×C₂₃	direct (N × H)
58. C₇	C₂×C₅×D₁₁×C₂₃	direct (N × H)
59. C₅	C₂×C₇×D₁₁×C₂₃	direct (N × H)
62. C₂	C₅×C₇×D₁₁×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
C₅×C₇×D₁₁×C₂₃	2
C₂×C₅×C₇×C₁₁×C₂₃	2
C₂×C₇×D₁₁×C₂₃	5
C₂×C₅×D₁₁×C₂₃	7
C₂²×C₅×C₇×C₂₃	11
C₂×C₅×C₇×D₁₁	23

Subgroups — C2×C5×C7×D11×C23 #47978478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×D₁₁×C₂₃ #47978478