Subgroups — C₂₃×C₁₁⋊#1043 #38760809

Order 25300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃×C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	maximal
4	D₅×C₁₁×C₂₃	—	5	6	no	—
5	C₂₃×#1043	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₂₃	AGL(1,𝔽₅)	1	6	yes	complemented
7	C₂₃×C₅⋊D₅	D₁₁	1	1	yes	characteristic
8	C₁₁⋊#1043	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₃×Dic₁₁	—	25	1	no	Hall
10	C₅²×C₂₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₅⋊D₅	C₂×C₂₃	1	1	yes	characteristic
12	C₂×C₁₁×C₂₃	—	25	1	no	—
13	AGL(1,𝔽₅)×C₂₃	—	55	6	no	—
14	C₅²×C₁₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₂₃	#1043	1	1	yes	characteristic, complemented, Hall
16	D₅×C₂₃	—	5	6	no	—
17	C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	—
18	C₅×C₂₃	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
19	D₅×C₁₁	—	5	6	no	—
20	#1043	—	11	1	no	Hall
21	C₄×C₂₃	—	275	1	no	Hall
22	C₅×C₁₁	AGL(1,𝔽₅)×C₂₃	1	6	yes	complemented
23	C₅⋊D₅	D₁₁×C₂₃	1	1	yes	characteristic
24	C₂×C₂₃	—	25	1	no	—
25	Dic₁₁	—	25	1	no	Hall
26	C₅²	C₂₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	C₁₁⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₁	—	25	1	no	—
29	AGL(1,𝔽₅)	—	55	6	no	—
30	C₁₁	C₂₃×#1043	1	1	yes	characteristic, complemented, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₂₃×C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
33	C₄	—	275	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	C₁₁⋊#1043
commutator, hypocenter	C₅²×C₁₁	C₄×C₂₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₃	C₄
prime radical	C₁₁×C₂₃×C₅⋊D₅	C₂
cosocle	C₁₁×C₅⋊D₅	C₂×C₂₃
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₂₃	C₄	semidirect
6. C₅×C₁₁×C₂₃	AGL(1,𝔽₅)	semidirect
8. C₁₁⋊#1043	C₂₃	direct (N × H)
10. C₅²×C₂₃	Dic₁₁	semidirect
14. C₅²×C₁₁	C₄×C₂₃	semidirect
15. C₁₁×C₂₃	#1043	semidirect
18. C₅×C₂₃	C₁₁⋊AGL(1,𝔽₅)	semidirect
22. C₅×C₁₁	AGL(1,𝔽₅)×C₂₃	semidirect
26. C₅²	C₂₃×Dic₁₁	semidirect
27. C₂₃	C₁₁⋊#1043	direct (N × H)
30. C₁₁	C₂₃×#1043	semidirect
32. C₅	C₂₃×C₁₁⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₂₃×C₅⋊D₅	2
C₂₃×C₁₁⋊AGL(1,𝔽₅)	5
C₂₃×#1043	11
C₁₁⋊#1043	23

Subgroups — C23×C11⋊#1043 #38760809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×C₁₁⋊#1043 #38760809