Subgroups — C₂×C₅²×AGL(1,𝔽₂₃) #38760751

Order 25300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×AGL(1,𝔽₂₃)	C₂	1	2	yes	maximal, direct product factor
3	C₅²×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×AGL(1,𝔽₂₃)	C₅	1	6	yes	maximal, direct product factor
5	C₅×AGL(1,𝔽₂₃)	C₂×C₅	1	12	yes	direct product factor
6	C₂×C₅×C₂₃⋊C₁₁	C₂×C₅	1	6	yes	complemented
7	C₂×C₅²×D₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
8	C₅×C₂₃⋊C₁₁	C₂²×C₅	1	6	yes	complemented
9	C₂×C₅²×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
10	C₅²×D₂₃	C₂×C₁₁	1	2	yes	complemented
11	C₂²×C₅²×C₁₁	—	23	1	no	maximal, Hall
12	C₂×AGL(1,𝔽₂₃)	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₅²×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅²×C₁₁	—	23	2	no	—
15	C₂×C₅²×C₁₁	—	23	1	no	—
16	C₂×C₂₃⋊C₁₁	C₂×C₅²	1	1	yes	characteristic, complemented
17	AGL(1,𝔽₂₃)	C₂×C₅²	1	2	yes	direct product factor
18	C₂×C₅×D₂₃	C₅×C₁₁	1	6	yes	complemented
19	C₅²×C₁₁	—	23	1	no	Hall
20	C₂₃⋊C₁₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₂₃	C₂×C₅×C₁₁	1	6	yes	complemented
22	C₅×D₂₃	C₂×C₅×C₁₁	1	12	yes	complemented
23	C₂²×C₅×C₁₁	—	23	6	no	—
24	C₅×C₂₃	C₂²×C₅×C₁₁	1	6	yes	complemented
25	C₂×C₅×C₁₁	—	23	12	no	—
26	C₂×C₅×C₁₁	—	23	6	no	—
27	C₂²×C₅²	—	23	1	no	Hall
28	C₂×D₂₃	C₅²×C₁₁	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₁	—	23	6	no	—
30	C₂×C₅²	—	23	2	no	—
31	C₂×C₅²	AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor
32	C₂×C₂₃	C₂×C₅²×C₁₁	1	1	yes	characteristic, complemented
33	D₂₃	C₂×C₅²×C₁₁	1	2	yes	complemented
34	C₂²×C₁₁	—	23	1	no	Hall
35	C₅²	C₂×AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor, Sylow
36	C₂₃	C₂²×C₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₁	—	23	2	no	—
38	C₂×C₁₁	—	23	1	no	—
39	C₂²×C₅	—	23	6	no	—
40	C₁₁	—	23	1	no	Sylow
41	C₂×C₅	—	23	12	no	—
42	C₂×C₅	C₅×AGL(1,𝔽₂₃)	1	6	yes	direct product factor
43	C₅	C₂×C₅×AGL(1,𝔽₂₃)	1	6	yes	direct product factor
44	C₂²	—	23	1	no	Sylow
45	C₂	—	23	2	no	—
46	C₂	C₅²×AGL(1,𝔽₂₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²	AGL(1,𝔽₂₃)
commutator, cosocle, hypocenter	C₂₃	C₂²×C₅²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₂₃	C₂×C₁₁
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×C₂₃⋊C₁₁	C₂	semidirect
2. C₅²×AGL(1,𝔽₂₃)	C₂	direct (N × H)
3. C₅²×C₂₃⋊C₁₁	C₂²	semidirect
4. C₂×C₅×AGL(1,𝔽₂₃)	C₅	direct (N × H)
5. C₅×AGL(1,𝔽₂₃)	C₂×C₅	direct (N × H)
6. C₂×C₅×C₂₃⋊C₁₁	C₂×C₅	semidirect
7. C₂×C₅²×D₂₃	C₁₁	semidirect
8. C₅×C₂₃⋊C₁₁	C₂²×C₅	semidirect
9. C₂×C₅²×C₂₃	C₂×C₁₁	semidirect
10. C₅²×D₂₃	C₂×C₁₁	semidirect
12. C₂×AGL(1,𝔽₂₃)	C₅²	direct (N × H)
13. C₅²×C₂₃	C₂²×C₁₁	semidirect
16. C₂×C₂₃⋊C₁₁	C₂×C₅²	semidirect
17. AGL(1,𝔽₂₃)	C₂×C₅²	direct (N × H)
18. C₂×C₅×D₂₃	C₅×C₁₁	semidirect
20. C₂₃⋊C₁₁	C₂²×C₅²	semidirect
21. C₂×C₅×C₂₃	C₂×C₅×C₁₁	semidirect
22. C₅×D₂₃	C₂×C₅×C₁₁	semidirect
24. C₅×C₂₃	C₂²×C₅×C₁₁	semidirect
28. C₂×D₂₃	C₅²×C₁₁	semidirect
31. C₂×C₅²	AGL(1,𝔽₂₃)	direct (N × H)
32. C₂×C₂₃	C₂×C₅²×C₁₁	semidirect
33. D₂₃	C₂×C₅²×C₁₁	semidirect
35. C₅²	C₂×AGL(1,𝔽₂₃)	direct (N × H)
36. C₂₃	C₂²×C₅²×C₁₁	semidirect
42. C₂×C₅	C₅×AGL(1,𝔽₂₃)	direct (N × H)
43. C₅	C₂×C₅×AGL(1,𝔽₂₃)	direct (N × H)
46. C₂	C₅²×AGL(1,𝔽₂₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₂₃⋊C₁₁	2
C₅²×AGL(1,𝔽₂₃)	2
C₂×C₅×AGL(1,𝔽₂₃)	5
C₂×C₅²×D₂₃	11
C₂²×C₅²×C₁₁	23

Subgroups — C2×C52×AGL(1,𝔽23) #38760751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×AGL(1,𝔽₂₃) #38760751