Subgroups — C₁₁⋊(C₂₃⋊#1043) #38760810

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⋊(C₂₃⋊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	—	23	1	no	maximal, Hall
9	Dic₂₅₃	—	25	1	no	Hall
10	C₅²×C₂₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₅⋊D₅	D₂₃	1	1	yes	characteristic
12	C₂×C₁₁×C₂₃	—	25	1	no	—
13	C₂₃⋊AGL(1,𝔽₅)	—	55	6	no	—
14	C₅²×C₁₁	Dic₂₃	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)	—	115	6	no	—
18	C₅×C₂₃	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
19	D₅×C₁₁	—	5	6	no	—
20	#1043	—	253	1	no	Hall
21	Dic₂₃	—	275	1	no	Hall
22	C₅×C₁₁	C₂₃⋊AGL(1,𝔽₅)	1	6	yes	complemented
23	C₅⋊D₅	D₂₅₃	1	1	yes	characteristic
24	C₂×C₂₃	—	25	1	no	—
25	Dic₁₁	—	575	1	no	Hall
26	C₅²	Dic₂₅₃	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	C₁₁⋊#1043	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	—	25	1	no	—
29	AGL(1,𝔽₅)	—	1265	6	no	—
30	C₁₁	C₂₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₁₁⋊(C₂₃⋊AGL(1,𝔽₅))	1	6	yes	complemented
33	C₄	—	6325	1	no	Sylow
34	C₂	—	25	1	no	—

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

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

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