Subgroups — #36376971

Order 22550.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014765	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₄₅₁	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₁×C₄₁	C₂×C₅	1	1	yes	characteristic
4	D₄₁⋊C₂₅	—	11	1	no	maximal, Hall
5	C₄₁⋊C₂₅	—	11	1	no	Hall
6	D₄₅₁	C₂₅	1	1	yes	characteristic, complemented, Hall
7	D₁₁⋊C₂₅	—	41	1	no	maximal, Hall
8	C₁₁×C₄₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₅×D₄₁	—	55	1	no	—
10	C₁₁⋊C₂₅	—	41	1	no	Hall
11	C₅×C₄₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic
12	C₅×D₁₁	—	205	1	no	—
13	D₄₁	—	55	1	no	Hall
14	C₅×C₁₁	D₄₁⋊C₅	1	1	yes	characteristic
15	C₂×C₂₅	—	451	1	no	Hall
16	C₄₁	D₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₅	—	451	1	no	Sylow
18	D₁₁	—	205	1	no	Hall
19	C₁₁	D₄₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	2255	1	no	—
21	C₅	#17985250	1	1	yes	characteristic
22	C₂	—	2255	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	#17985250
commutator, hypocenter	C₁₁×C₄₁	C₂×C₂₅
Fitting, socle, cosocle	C₅×C₁₁×C₄₁	C₂×C₅
prime radical	C₅×D₄₅₁	C₅
LCS	G ▷ C₁₁×C₄₁
UCS	C₁ ◁ C₅

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.