Subgroups — D₁₃₅ #63185

Order 270.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₅	—	3	1	no	maximal
3	D₂₇	—	5	1	no	maximal, Hall
4	C₅×C₉	D₃	1	1	yes	characteristic
5	D₁₅	—	9	1	no	—
6	C₂₇	D₅	1	1	yes	characteristic, complemented, Sylow
7	D₉	—	15	1	no	—
8	C₃×C₅	D₉	1	1	yes	characteristic
9	D₅	—	27	1	no	Hall
10	C₉	D₁₅	1	1	yes	characteristic
11	D₃	—	45	1	no	—
12	C₅	D₂₇	1	1	yes	characteristic, complemented, Sylow
13	C₃	D₄₅	1	1	yes	characteristic
14	C₂	—	135	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₂₇	C₂
Frattini	C₉	D₁₅
socle	C₃×C₅	D₉
LCS	G ▷ C₅×C₂₇
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.