Subgroups — C₄₁×C₁₀₁⋊C₅ #35208463

Order 20705.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₁₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₀₁⋊C₅	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₄₁	—	101	1	no	maximal, Hall
4	C₁₀₁	C₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
5	C₄₁	C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	—	101	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	C₁₀₁⋊C₅
commutator, cosocle, hypocenter	C₁₀₁	C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₄₁×C₁₀₁	C₅
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₄₁

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.