Subgroups — C₂×C₅×C₇×C₁₁×D₂₃ #47978477

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁×D₂₃	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×C₁₁×D₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×D₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁×D₂₃	C₂×C₅	1	2	yes	direct product factor
7	C₂×C₇×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
8	C₂×C₅×C₇×D₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×D₂₃	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	C₂×C₁₁	1	1	yes	characteristic, complemented
13	C₅×C₇×D₂₃	C₂×C₁₁	1	2	yes	direct product factor
14	C₂²×C₅×C₇×C₁₁	—	23	1	no	maximal, Hall
15	C₅×C₁₁×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×D₂₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₇×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₇×C₁₁	—	23	2	no	—
19	C₂×C₅×C₇×C₁₁	D₂₃	1	1	yes	characteristic, direct product factor
20	C₂×C₇×D₂₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₁×C₂₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
22	C₁₁×D₂₃	C₂×C₅×C₇	1	2	yes	direct product factor
23	C₂×C₅×D₂₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₇×C₁₁	C₂×D₂₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇×C₂₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
26	C₇×D₂₃	C₂×C₅×C₁₁	1	2	yes	direct product factor
27	C₂²×C₇×C₁₁	—	23	1	no	Hall
28	C₁₁×C₂₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₂₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
30	C₅×D₂₃	C₂×C₇×C₁₁	1	2	yes	direct product factor
31	C₂²×C₅×C₁₁	—	23	1	no	Hall
32	C₇×C₂₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₇×C₁₁	—	23	2	no	—
34	C₂×C₇×C₁₁	C₅×D₂₃	1	1	yes	characteristic, direct product factor
35	C₂²×C₅×C₇	—	23	1	no	Hall
36	C₅×C₂₃	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₅×C₁₁	—	23	2	no	—
38	C₂×C₅×C₁₁	C₇×D₂₃	1	1	yes	characteristic, direct product factor
39	C₂×D₂₃	C₅×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
40	C₇×C₁₁	C₂×C₅×D₂₃	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅×C₇	—	23	2	no	—
42	C₂×C₅×C₇	C₁₁×D₂₃	1	1	yes	characteristic, direct product factor
43	C₅×C₁₁	C₂×C₇×D₂₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₂₃	C₂×C₅×C₇×C₁₁	1	1	yes	characteristic, complemented
45	D₂₃	C₂×C₅×C₇×C₁₁	1	2	yes	direct product factor
46	C₂²×C₁₁	—	23	1	no	Hall
47	C₅×C₇	C₂×C₁₁×D₂₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂²×C₇	—	23	1	no	Hall
49	C₂₃	C₂²×C₅×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₁₁	—	23	2	no	—
51	C₂×C₁₁	C₅×C₇×D₂₃	1	1	yes	characteristic, direct product factor
52	C₂²×C₅	—	23	1	no	Hall
53	C₂×C₇	—	23	2	no	—
54	C₂×C₇	C₅×C₁₁×D₂₃	1	1	yes	characteristic, direct product factor
55	C₁₁	C₂×C₅×C₇×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₅	—	23	2	no	—
57	C₂×C₅	C₇×C₁₁×D₂₃	1	1	yes	characteristic, direct product factor
58	C₇	C₂×C₅×C₁₁×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₅	C₂×C₇×C₁₁×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	—	23	1	no	Sylow
61	C₂	—	23	2	no	—
62	C₂	C₅×C₇×C₁₁×D₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₁	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²×C₅×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₁×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₅×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₁×D₂₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₁×C₂₃	C₂	semidirect
3. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
4. C₂×C₇×C₁₁×D₂₃	C₅	direct (N × H)
5. C₂×C₅×C₁₁×D₂₃	C₇	direct (N × H)
6. C₇×C₁₁×D₂₃	C₂×C₅	direct (N × H)
7. C₂×C₇×C₁₁×C₂₃	C₂×C₅	semidirect
8. C₂×C₅×C₇×D₂₃	C₁₁	direct (N × H)
9. C₅×C₁₁×D₂₃	C₂×C₇	direct (N × H)
10. C₂×C₅×C₁₁×C₂₃	C₂×C₇	semidirect
11. C₇×C₁₁×C₂₃	C₂²×C₅	semidirect
12. C₂×C₅×C₇×C₂₃	C₂×C₁₁	semidirect
13. C₅×C₇×D₂₃	C₂×C₁₁	direct (N × H)
15. C₅×C₁₁×C₂₃	C₂²×C₇	semidirect
16. C₂×C₁₁×D₂₃	C₅×C₇	direct (N × H)
17. C₅×C₇×C₂₃	C₂²×C₁₁	semidirect
19. C₂×C₅×C₇×C₁₁	D₂₃	direct (N × H)
20. C₂×C₇×D₂₃	C₅×C₁₁	direct (N × H)
21. C₂×C₁₁×C₂₃	C₂×C₅×C₇	semidirect
22. C₁₁×D₂₃	C₂×C₅×C₇	direct (N × H)
23. C₂×C₅×D₂₃	C₇×C₁₁	direct (N × H)
24. C₅×C₇×C₁₁	C₂×D₂₃	direct (N × H)
25. C₂×C₇×C₂₃	C₂×C₅×C₁₁	semidirect
26. C₇×D₂₃	C₂×C₅×C₁₁	direct (N × H)
28. C₁₁×C₂₃	C₂²×C₅×C₇	semidirect
29. C₂×C₅×C₂₃	C₂×C₇×C₁₁	semidirect
30. C₅×D₂₃	C₂×C₇×C₁₁	direct (N × H)
32. C₇×C₂₃	C₂²×C₅×C₁₁	semidirect
34. C₂×C₇×C₁₁	C₅×D₂₃	direct (N × H)
36. C₅×C₂₃	C₂²×C₇×C₁₁	semidirect
38. C₂×C₅×C₁₁	C₇×D₂₃	direct (N × H)
39. C₂×D₂₃	C₅×C₇×C₁₁	direct (N × H)
40. C₇×C₁₁	C₂×C₅×D₂₃	direct (N × H)
42. C₂×C₅×C₇	C₁₁×D₂₃	direct (N × H)
43. C₅×C₁₁	C₂×C₇×D₂₃	direct (N × H)
44. C₂×C₂₃	C₂×C₅×C₇×C₁₁	semidirect
45. D₂₃	C₂×C₅×C₇×C₁₁	direct (N × H)
47. C₅×C₇	C₂×C₁₁×D₂₃	direct (N × H)
49. C₂₃	C₂²×C₅×C₇×C₁₁	semidirect
51. C₂×C₁₁	C₅×C₇×D₂₃	direct (N × H)
54. C₂×C₇	C₅×C₁₁×D₂₃	direct (N × H)
55. C₁₁	C₂×C₅×C₇×D₂₃	direct (N × H)
57. C₂×C₅	C₇×C₁₁×D₂₃	direct (N × H)
58. C₇	C₂×C₅×C₁₁×D₂₃	direct (N × H)
59. C₅	C₂×C₇×C₁₁×D₂₃	direct (N × H)
62. C₂	C₅×C₇×C₁₁×D₂₃	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×C₁₁×D₂₃	2
C₂×C₅×C₇×C₁₁×C₂₃	2
C₂×C₇×C₁₁×D₂₃	5
C₂×C₅×C₁₁×D₂₃	7
C₂×C₅×C₇×D₂₃	11
C₂²×C₅×C₇×C₁₁	23

Subgroups — C2×C5×C7×C11×D23 #47978477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₁₁×D₂₃ #47978477