Subgroups — C₅×D₉ #774

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	C₅×D₃	—	3	1	no	maximal
3	D₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅	D₃	1	1	yes	characteristic
5	C₂×C₅	—	9	1	no	Hall
6	C₉	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
7	D₃	—	3	1	no	—
8	C₅	D₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₃	C₅×D₃	1	1	yes	characteristic
10	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅
Frattini	C₃	C₅×D₃
Fitting	C₅×C₉	C₂
socle	C₃×C₅	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅

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.