Subgroups — C₃₁×C₁₈₁⋊C₅ #43242582

Order 28055.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₁₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₈₁⋊C₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₈₁	C₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
4	C₅×C₃₁	—	181	1	no	maximal, Hall
5	C₃₁	C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	—	181	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	C₁₈₁⋊C₅
commutator, cosocle, hypocenter	C₁₈₁	C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₁₈₁	C₅
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₃₁

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.