Subgroups — D₄₅ #776

Order 90.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉	C₂
Frattini	C₃	D₁₅
socle	C₃×C₅	D₃
LCS	G ▷ C₅×C₉
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.