Subgroups — C₁₁×C₂₃×#1044 #38760811

Order 25300.

64 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	2	no	maximal
4	D₅×C₁₁×C₂₃	—	5	2	no	—
5	D₅×C₁₁×C₂₃	—	10	2	no	—
6	C₂₃×#1044	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₂₃	—	2	2	no	—
8	C₅×C₁₁×C₂₃	AGL(1,𝔽₅)	1	2	yes	complemented
9	C₂₃×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
10	C₁₁×#1044	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₄×C₁₁×C₂₃	—	25	1	no	Hall
12	C₅²×C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×C₅⋊D₅	C₂×C₂₃	1	1	yes	characteristic
14	C₂×C₁₁×C₂₃	—	25	1	no	—
15	AGL(1,𝔽₅)×C₂₃	—	5	2	no	—
16	C₅²×C₁₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
17	C₁₁×C₂₃	#1044	1	1	yes	characteristic, direct product factor, Hall
18	D₅×C₂₃	—	5	2	no	—
19	D₅×C₂₃	—	10	2	no	—
20	C₁₁×AGL(1,𝔽₅)	—	5	2	no	—
21	C₅×C₂₃	—	2	2	no	—
22	C₅×C₂₃	C₁₁×AGL(1,𝔽₅)	1	2	yes	complemented
23	D₅×C₁₁	—	5	2	no	—
24	D₅×C₁₁	—	10	2	no	—
25	#1044	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
26	C₄×C₂₃	—	25	1	no	Hall
27	C₅×C₁₁	—	2	2	no	—
28	C₅×C₁₁	AGL(1,𝔽₅)×C₂₃	1	2	yes	complemented
29	C₅⋊D₅	C₂×C₁₁×C₂₃	1	1	yes	characteristic
30	C₂×C₂₃	—	25	1	no	—
31	C₄×C₁₁	—	25	1	no	Hall
32	C₅²	C₄×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
33	C₂₃	C₁₁×#1044	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₁	—	25	1	no	—
35	AGL(1,𝔽₅)	—	5	2	no	—
36	C₁₁	C₂₃×#1044	1	1	yes	characteristic, direct product factor, Sylow
37	D₅	—	5	2	no	—
38	D₅	—	10	2	no	—
39	C₅	—	2	2	no	—
40	C₅	C₁₁×AGL(1,𝔽₅)×C₂₃	1	2	yes	complemented
41	C₄	—	25	1	no	Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	#1044
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
6. C₂₃×#1044	C₁₁	direct (N × H)
8. C₅×C₁₁×C₂₃	AGL(1,𝔽₅)	semidirect
10. C₁₁×#1044	C₂₃	direct (N × H)
12. C₅²×C₂₃	C₄×C₁₁	semidirect
16. C₅²×C₁₁	C₄×C₂₃	semidirect
17. C₁₁×C₂₃	#1044	direct (N × H)
22. C₅×C₂₃	C₁₁×AGL(1,𝔽₅)	semidirect
25. #1044	C₁₁×C₂₃	direct (N × H)
28. C₅×C₁₁	AGL(1,𝔽₅)×C₂₃	semidirect
32. C₅²	C₄×C₁₁×C₂₃	semidirect
33. C₂₃	C₁₁×#1044	direct (N × H)
36. C₁₁	C₂₃×#1044	direct (N × H)
40. 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×#1044	11
C₁₁×#1044	23

Subgroups — C11×C23×#1044 #38760811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂₃×#1044 #38760811