Subgroups — C₅×C₁₅₃₁⋊C₃ #37525834

Order 22965.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₅₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₅₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₅₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₅	—	1531	1	no	maximal, Hall
5	C₅	C₁₅₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	1531	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₅₃₁⋊C₃
commutator, cosocle, hypocenter	C₁₅₃₁	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₅₃₁	C₃
LCS	G ▷ C₁₅₃₁
UCS	C₁ ◁ C₅

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.