Subgroups — C₃×C₅×3₋¹⁺² #87953

Order 405.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅	C₃	1	1	yes	maximal, characteristic
2	C₅×3₋¹⁺²	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₅×C₉	C₃	1	3	yes	maximal, complemented
4	C₃×3₋¹⁺²	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃²×C₅	—	3	3	no	—
6	C₃²×C₅	C₃²	1	3	yes	—
7	C₃²×C₅	C₃²	1	1	yes	characteristic
8	C₅×C₉	C₃²	1	9	yes	complemented
9	C₃³	C₃×C₅	1	1	yes	characteristic
10	3₋¹⁺²	C₃×C₅	1	9	yes	direct product factor
11	C₃×C₉	C₃×C₅	1	3	yes	complemented
12	C₃×C₅	—	3	3	no	—
13	C₃×C₅	3₋¹⁺²	1	3	yes	direct product factor
14	C₃×C₅	C₃³	1	1	yes	characteristic
15	C₃²	—	3	3	no	—
16	C₃²	C₃²×C₅	1	3	yes	—
17	C₃²	C₃²×C₅	1	1	yes	characteristic
18	C₉	C₃²×C₅	1	9	yes	complemented
19	C₅	C₃×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
20	C₃	—	3	3	no	—
21	C₃	C₅×3₋¹⁺²	1	3	yes	direct product factor
22	C₃	C₃³×C₅	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₅	C₃²
commutator, Frattini, cosocle	C₃	C₃³×C₅
prime radical	C₃³×C₅	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₅ ◁ G

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.