Subgroups — C₁₁⋊C₅×C₄₅₇ #38737540

Order 25135.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄₅₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₄₅₇	—	11	1	no	maximal, Hall
3	C₄₅₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
4	C₁₁⋊C₅	C₄₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₁	C₅×C₄₅₇	1	1	yes	characteristic, complemented, Sylow
6	C₅	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₅₇	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₅×C₄₅₇
Frattini	C₁	G
Fitting, socle	C₁₁×C₄₅₇	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₄₅₇

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.