Subgroups — C₃²×C₅×D₅ #90661

Order 450.

60 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	4	yes	maximal, direct product factor
3	C₂×C₃²×C₅	—	5	1	no	maximal
4	C₃²×D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅²	C₂×C₃	1	4	yes	complemented
6	C₅×D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅	—	2	2	no	—
8	C₃²×C₅	D₅	1	1	yes	characteristic, direct product factor
9	C₃²×C₅	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×C₃×C₅	—	5	4	no	—
11	C₃×D₅	C₃×C₅	1	4	yes	direct product factor
12	C₅²	C₂×C₃²	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃²	—	5	1	no	Hall
14	C₃×C₅	—	2	8	no	—
15	C₃×C₅	C₃×D₅	1	4	yes	direct product factor
16	C₃×C₅	C₂×C₃×C₅	1	4	yes	complemented
17	C₂×C₅	—	5	1	no	—
18	D₅	C₃²×C₅	1	1	yes	characteristic, direct product factor
19	C₃²	C₅×D₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	5	4	no	—
21	C₅	—	2	2	no	—
22	C₅	C₃²×D₅	1	1	yes	characteristic, direct product factor
23	C₅	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
24	C₃	C₃×C₅×D₅	1	4	yes	direct product factor
25	C₂	—	5	1	no	Sylow

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