Subgroups — C₃⋊(C₃⋊D₁₅) #63211

Order 270.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊D₁₅	—	3	13	no	maximal
3	C₃⋊(C₃⋊D₃)	—	5	1	no	maximal, Hall
4	C₃²×C₅	D₃	1	13	yes	complemented
5	D₁₅	—	9	13	no	—
6	C₃³	D₅	1	1	yes	characteristic, complemented, Sylow
7	C₃⋊D₃	—	15	13	no	—
8	C₃×C₅	C₃⋊D₃	1	13	yes	complemented
9	D₅	—	27	1	no	Hall
10	C₃²	D₁₅	1	13	yes	complemented
11	D₃	—	45	13	no	—
12	C₅	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
13	C₃	C₃⋊D₁₅	1	13	yes	complemented
14	C₂	—	135	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃³×C₅	C₂
LCS	G ▷ C₃³×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.