Subgroups — #1035×C₂₃⋊C₁₁ #38760682

Order 25300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₅×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂₅×C₂₃⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	AGL(1,𝔽₅)×C₂₃⋊C₁₁	—	5	1	no	maximal
4	D₅×C₂₃⋊C₁₁	—	5	1	no	—
5	C₂₃×#1035	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
6	C₅×C₂₃⋊C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic
7	C₂₃×D₂₅	C₂×C₁₁	1	1	yes	characteristic
8	C₁₁×#1035	—	23	1	no	maximal, Hall
9	C₄×C₂₃⋊C₁₁	—	25	1	no	Hall
10	C₂₃×C₂₅	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×D₂₅	—	23	1	no	—
12	C₂×C₂₃⋊C₁₁	—	25	1	no	—
13	AGL(1,𝔽₅)×C₂₃	—	5	1	no	—
14	C₁₁×C₂₅	—	23	1	no	Hall
15	C₂₃⋊C₁₁	#1035	1	1	yes	characteristic, direct product factor, Hall
16	D₅×C₂₃	—	5	1	no	—
17	C₁₁×AGL(1,𝔽₅)	—	115	1	no	—
18	C₅×C₂₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
19	D₅×C₁₁	—	115	1	no	—
20	#1035	C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₂₃	—	25	1	no	Hall
22	C₅×C₁₁	—	23	1	no	—
23	D₂₅	C₂×C₂₃⋊C₁₁	1	1	yes	characteristic
24	C₂×C₂₃	—	25	1	no	—
25	C₄×C₁₁	—	575	1	no	Hall
26	C₂₅	C₄×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	C₁₁×#1035	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	—	575	1	no	—
29	AGL(1,𝔽₅)	—	5	1	no	—
30	C₁₁	—	23	1	no	Sylow
31	D₅	—	5	1	no	—
32	C₅	AGL(1,𝔽₅)×C₂₃⋊C₁₁	1	1	yes	characteristic
33	C₄	—	25	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₂₃×C₂₅	C₄×C₁₁
Frattini	C₅	AGL(1,𝔽₅)×C₂₃⋊C₁₁
socle	C₅×C₂₃	C₁₁×AGL(1,𝔽₅)
prime radical	D₂₅×C₂₃⋊C₁₁	C₂
cosocle	C₂₃×D₂₅	C₂×C₁₁
LCS	G ▷ C₂₃×C₂₅
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.