Subgroups — C₂×C₅²×D₁₁×C₂₃ #38760816

Order 25300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₁₁×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₁₁×C₂₃	C₅	1	6	yes	maximal, direct product factor
5	C₅×D₁₁×C₂₃	C₂×C₅	1	12	yes	direct product factor
6	C₂×C₅×C₁₁×C₂₃	C₂×C₅	1	6	yes	complemented
7	C₂²×C₅²×C₂₃	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₂₃	C₂²×C₅	1	6	yes	complemented
9	C₂×C₅²×C₂₃	—	11	2	no	—
10	C₂×C₅²×C₂₃	D₁₁	1	1	yes	characteristic, direct product factor
11	C₂×C₅²×D₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×D₁₁×C₂₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₅²×C₂₃	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅²×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented
15	C₅²×D₁₁	C₂×C₂₃	1	2	yes	direct product factor
16	C₂×C₁₁×C₂₃	C₂×C₅²	1	1	yes	characteristic, complemented
17	D₁₁×C₂₃	C₂×C₅²	1	2	yes	direct product factor
18	C₂²×C₅×C₂₃	—	11	6	no	—
19	C₅²×C₁₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₁₁×C₂₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₂₃	—	11	12	no	—
22	C₂×C₅×C₂₃	C₅×D₁₁	1	6	yes	direct product factor
23	C₂×C₅×D₁₁	C₅×C₂₃	1	6	yes	direct product factor
24	C₅×C₂₃	C₂×C₅×D₁₁	1	6	yes	direct product factor
25	C₂×C₅×C₁₁	C₂×C₅×C₂₃	1	6	yes	complemented
26	C₅×D₁₁	C₂×C₅×C₂₃	1	12	yes	direct product factor
27	C₂²×C₅²	—	11	1	no	Hall
28	C₂²×C₂₃	—	11	1	no	Hall
29	C₅×C₁₁	C₂²×C₅×C₂₃	1	6	yes	complemented
30	C₂×C₅²	—	11	2	no	—
31	C₂×C₅²	D₁₁×C₂₃	1	1	yes	characteristic, direct product factor
32	C₂×C₂₃	—	11	2	no	—
33	C₂×C₂₃	C₅²×D₁₁	1	1	yes	characteristic, direct product factor
34	C₂×D₁₁	C₅²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
35	C₅²	C₂×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂₃	C₂×C₅²×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₁₁	C₂×C₅²×C₂₃	1	1	yes	characteristic, complemented
38	D₁₁	C₂×C₅²×C₂₃	1	2	yes	direct product factor
39	C₂²×C₅	—	11	6	no	—
40	C₁₁	C₂²×C₅²×C₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	11	12	no	—
42	C₂×C₅	C₅×D₁₁×C₂₃	1	6	yes	direct product factor
43	C₅	C₂×C₅×D₁₁×C₂₃	1	6	yes	direct product factor
44	C₂²	—	11	1	no	Sylow
45	C₂	—	11	2	no	—
46	C₂	C₅²×D₁₁×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₂₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₅²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁×C₂₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅²×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅²×D₁₁×C₂₃	C₂	direct (N × H)
2. C₂×C₅²×C₁₁×C₂₃	C₂	semidirect
3. C₅²×C₁₁×C₂₃	C₂²	semidirect
4. C₂×C₅×D₁₁×C₂₃	C₅	direct (N × H)
5. C₅×D₁₁×C₂₃	C₂×C₅	direct (N × H)
6. C₂×C₅×C₁₁×C₂₃	C₂×C₅	semidirect
8. C₅×C₁₁×C₂₃	C₂²×C₅	semidirect
10. C₂×C₅²×C₂₃	D₁₁	direct (N × H)
11. C₂×C₅²×D₁₁	C₂₃	direct (N × H)
12. C₂×D₁₁×C₂₃	C₅²	direct (N × H)
13. C₅²×C₂₃	C₂×D₁₁	direct (N × H)
14. C₂×C₅²×C₁₁	C₂×C₂₃	semidirect
15. C₅²×D₁₁	C₂×C₂₃	direct (N × H)
16. C₂×C₁₁×C₂₃	C₂×C₅²	semidirect
17. D₁₁×C₂₃	C₂×C₅²	direct (N × H)
19. C₅²×C₁₁	C₂²×C₂₃	semidirect
20. C₁₁×C₂₃	C₂²×C₅²	semidirect
22. C₂×C₅×C₂₃	C₅×D₁₁	direct (N × H)
23. C₂×C₅×D₁₁	C₅×C₂₃	direct (N × H)
24. C₅×C₂₃	C₂×C₅×D₁₁	direct (N × H)
25. C₂×C₅×C₁₁	C₂×C₅×C₂₃	semidirect
26. C₅×D₁₁	C₂×C₅×C₂₃	direct (N × H)
29. C₅×C₁₁	C₂²×C₅×C₂₃	semidirect
31. C₂×C₅²	D₁₁×C₂₃	direct (N × H)
33. C₂×C₂₃	C₅²×D₁₁	direct (N × H)
34. C₂×D₁₁	C₅²×C₂₃	direct (N × H)
35. C₅²	C₂×D₁₁×C₂₃	direct (N × H)
36. C₂₃	C₂×C₅²×D₁₁	direct (N × H)
37. C₂×C₁₁	C₂×C₅²×C₂₃	semidirect
38. D₁₁	C₂×C₅²×C₂₃	direct (N × H)
40. C₁₁	C₂²×C₅²×C₂₃	semidirect
42. C₂×C₅	C₅×D₁₁×C₂₃	direct (N × H)
43. C₅	C₂×C₅×D₁₁×C₂₃	direct (N × H)
46. C₂	C₅²×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
C₅²×D₁₁×C₂₃	2
C₂×C₅²×C₁₁×C₂₃	2
C₂×C₅×D₁₁×C₂₃	5
C₂²×C₅²×C₂₃	11
C₂×C₅²×D₁₁	23

Subgroups — C2×C52×D11×C23 #38760816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×D₁₁×C₂₃ #38760816