Subgroups — C₄₁×C₁₅₁⋊C₅ #44526293

Order 30955.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₅₁⋊C₅	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₄₁	—	151	1	no	maximal, Hall
4	C₁₅₁	C₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
5	C₄₁	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	—	151	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₄₁	C₁₅₁⋊C₅
commutator, cosocle, hypocenter	C₁₅₁	C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₄₁×C₁₅₁	C₅
LCS	G ▷ C₁₅₁
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.