Subgroups — (C₃₃₁⋊C₅)⋊C₉ #28415744

Order 14895.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic
2	C₃₃₁⋊C₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₃₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₃₁	C₃×C₅	1	1	yes	characteristic
5	C₃₃₁	C₅×C₉	1	1	yes	characteristic, complemented, Sylow
6	C₅×C₉	—	331	1	no	maximal, Hall
7	C₃×C₅	—	993	1	no	—
8	C₉	—	331	1	no	Sylow
9	C₅	—	993	1	no	Sylow
10	C₃	(C₃₃₁⋊C₃)⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	(C₃₃₁⋊C₃)⋊C₅
commutator, hypocenter	C₃₃₁	C₅×C₉
Fitting, socle, cosocle	C₃×C₃₃₁	C₃×C₅
prime radical	C₃×C₃₃₁⋊C₅	C₃
LCS	G ▷ C₃₃₁
UCS	C₁ ◁ C₃

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.