Subgroups — C₅⋊D₄₅ #90653

Order 450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₅)	—	3	1	no	maximal
3	D₄₅	—	5	6	no	maximal
4	C₃×C₅²	D₃	1	1	yes	characteristic
5	C₅⋊D₅	—	9	1	no	Hall
6	C₅×C₉	D₅	1	6	yes	complemented
7	D₁₅	—	15	6	no	—
8	C₅²	D₉	1	1	yes	characteristic, complemented, Sylow
9	D₉	—	25	1	no	Hall
10	C₃×C₅	D₁₅	1	6	yes	—
11	D₅	—	45	6	no	—
12	C₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
13	D₃	—	75	1	no	—
14	C₅	D₄₅	1	6	yes	complemented
15	C₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
16	C₂	—	225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅²×C₉	C₂
Frattini	C₃	C₃⋊(C₅⋊D₅)
socle	C₃×C₅²	D₃
LCS	G ▷ C₅²×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.