Subgroups — C₅×D₄₅ #90652

Order 450.

30 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	C₅×D₁₅	—	3	1	no	maximal
3	D₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×D₉	—	5	1	no	maximal
5	C₃×C₅²	D₃	1	1	yes	characteristic
6	C₅×D₅	—	9	1	no	Hall
7	C₅×C₉	—	2	2	no	—
8	C₅×C₉	D₅	1	1	yes	characteristic, complemented
9	C₅×C₉	C₂×C₅	1	1	yes	characteristic, complemented
10	D₁₅	—	3	1	no	—
11	C₅×D₃	—	15	1	no	—
12	C₅²	D₉	1	1	yes	characteristic, complemented, Sylow
13	D₉	—	5	1	no	Hall
14	C₃×C₅	—	2	2	no	—
15	C₃×C₅	C₅×D₃	1	1	yes	characteristic
16	C₃×C₅	D₁₅	1	1	yes	characteristic
17	C₂×C₅	—	45	1	no	—
18	D₅	—	9	1	no	—
19	C₉	C₅×D₅	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	15	1	no	—
21	C₅	—	2	2	no	—
22	C₅	C₅×D₉	1	1	yes	characteristic, complemented
23	C₅	D₄₅	1	1	yes	characteristic, direct product factor
24	C₃	C₅×D₁₅	1	1	yes	characteristic
25	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₅
Frattini	C₃	C₅×D₁₅
Fitting	C₅²×C₉	C₂
socle	C₃×C₅²	D₃
LCS	G ▷ C₅×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.