Subgroups — C₁₁×C₂₃×#1043 #38760807

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	C₁₁×AGL(1,𝔽₅)×C₂₃	—	5	6	no	maximal
4	D₅×C₁₁×C₂₃	—	5	6	no	—
5	C₂₃×#1043	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₂₃	AGL(1,𝔽₅)	1	6	yes	complemented
7	C₂₃×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
8	C₁₁×#1043	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₁₁×C₂₃	—	25	1	no	Hall
10	C₅²×C₂₃	C₄×C₁₁	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	—	5	6	no	—
14	C₅²×C₁₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₂₃	#1043	1	1	yes	characteristic, direct product factor, 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	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₂₃	—	25	1	no	Hall
22	C₅×C₁₁	AGL(1,𝔽₅)×C₂₃	1	6	yes	complemented
23	C₅⋊D₅	C₂×C₁₁×C₂₃	1	1	yes	characteristic
24	C₂×C₂₃	—	25	1	no	—
25	C₄×C₁₁	—	25	1	no	Hall
26	C₅²	C₄×C₁₁×C₂₃	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)	—	5	6	no	—
30	C₁₁	C₂₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₁₁×AGL(1,𝔽₅)×C₂₃	1	6	yes	complemented
33	C₄	—	25	1	no	Sylow
34	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₂₃	C₄	semidirect
5. C₂₃×#1043	C₁₁	direct (N × H)
6. C₅×C₁₁×C₂₃	AGL(1,𝔽₅)	semidirect
8. C₁₁×#1043	C₂₃	direct (N × H)
10. C₅²×C₂₃	C₄×C₁₁	semidirect
14. C₅²×C₁₁	C₄×C₂₃	semidirect
15. C₁₁×C₂₃	#1043	direct (N × H)
18. C₅×C₂₃	C₁₁×AGL(1,𝔽₅)	semidirect
20. #1043	C₁₁×C₂₃	direct (N × H)
22. C₅×C₁₁	AGL(1,𝔽₅)×C₂₃	semidirect
26. C₅²	C₄×C₁₁×C₂₃	semidirect
27. C₂₃	C₁₁×#1043	direct (N × H)
30. C₁₁	C₂₃×#1043	direct (N × H)
32. C₅	C₁₁×AGL(1,𝔽₅)×C₂₃	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
C₁₁×AGL(1,𝔽₅)×C₂₃	5
C₂₃×#1043	11
C₁₁×#1043	23

Subgroups — C11×C23×#1043 #38760807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂₃×#1043 #38760807