Subgroups — C₃⋊D₁₅ #782

Order 90.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅	—	3	4	no	maximal
3	C₃⋊D₃	—	5	1	no	maximal, Hall
4	C₃×C₅	D₃	1	4	yes	complemented
5	D₅	—	9	1	no	Hall
6	C₃²	D₅	1	1	yes	characteristic, complemented, Sylow
7	D₃	—	15	4	no	—
8	C₅	C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
9	C₃	D₁₅	1	4	yes	complemented
10	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁

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.