Subgroups — C₃²×D₁₅ #63207

Order 270.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₅	—	3	1	no	maximal
4	C₃²×D₃	—	5	1	no	maximal, Hall
5	C₃²×C₅	—	2	4	no	—
6	C₃²×C₅	D₃	1	1	yes	characteristic, complemented
7	C₃²×C₅	C₂×C₃	1	4	yes	complemented
8	D₁₅	C₃²	1	1	yes	characteristic, direct product factor
9	C₃×D₅	—	3	4	no	—
10	C₃³	D₅	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃²	—	15	1	no	—
12	C₃×D₃	—	5	4	no	—
13	C₃×C₅	—	2	4	no	—
14	C₃×C₅	C₃×D₃	1	4	yes	complemented
15	C₃×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
16	D₅	—	3	1	no	Hall
17	C₃²	—	2	4	no	—
18	C₃²	C₃×D₅	1	4	yes	complemented
19	C₃²	D₁₅	1	1	yes	characteristic, direct product factor
20	C₂×C₃	—	15	4	no	—
21	D₃	—	5	1	no	—
22	C₅	C₃²×D₃	1	1	yes	characteristic, complemented, Sylow
23	C₃	—	2	4	no	—
24	C₃	C₃²×D₅	1	1	yes	characteristic, complemented
25	C₃	C₃×D₁₅	1	4	yes	direct product factor
26	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃³×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃²

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.