Subgroups — #36348113

Order 22055.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₀₁⋊C₅	—	11	1	no	maximal, Hall
3	C₄₀₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
4	C₁₁⋊C₅	—	401	1	no	maximal, Hall
5	C₁₁	C₄₀₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
6	C₅	—	4411	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₄₀₁	C₅
LCS	G ▷ C₁₁×C₄₀₁
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.