Subgroups — C₃×C₅×C₃⋊D₃ #63208

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	C₅×C₃⋊D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₃	—	3	4	no	maximal
4	C₃×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃²×C₅	—	2	4	no	—
6	C₃²×C₅	D₃	1	4	yes	complemented
7	C₃²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₅	—	9	1	no	—
9	C₅×D₃	—	3	4	no	—
10	C₃³	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
11	C₃⋊D₃	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₃×D₃	—	3	4	no	—
13	C₃×C₅	—	2	4	no	—
14	C₃×C₅	C₃×D₃	1	4	yes	complemented
15	C₃×C₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₅	—	9	1	no	Hall
17	C₃²	—	2	4	no	—
18	C₃²	C₅×D₃	1	4	yes	complemented
19	C₃²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	C₂×C₃	—	9	1	no	—
21	D₃	—	3	4	no	—
22	C₅	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃	—	2	4	no	—
24	C₃	C₃×C₅×D₃	1	4	yes	complemented
25	C₃	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
26	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃³×C₅	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃×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.