Subgroups — C₃×C₃⋊(C₅⋊D₅) #90665

Order 450.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊D₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅⋊D₅	—	3	1	no	maximal
4	C₃×D₁₅	—	5	6	no	maximal
5	C₃×C₅²	—	2	1	no	—
6	C₃×C₅²	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅⋊D₅	—	3	1	no	Hall
9	C₃²×C₅	D₅	1	6	yes	complemented
10	D₁₅	—	5	6	no	—
11	C₃×D₅	—	15	6	no	—
12	C₅²	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₃	—	25	1	no	Hall
14	C₃×C₅	—	2	6	no	—
15	C₃×C₅	C₃×D₅	1	6	yes	complemented
16	C₃×C₅	D₁₅	1	6	yes	complemented
17	D₅	—	15	6	no	—
18	C₃²	C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	75	1	no	—
20	D₃	—	25	1	no	—
21	C₅	C₃×D₁₅	1	6	yes	complemented
22	C₃	—	2	1	no	—
23	C₃	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
24	C₃	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
25	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₃×C₅²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅²	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃

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.