Subgroups — C₅×3₋¹⁺⁴ #11925992

Order 1215.

460 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#737	C₃	1	27	yes	maximal, complemented
2	C₃×C₅×3₋¹⁺²	C₃	1	12	yes	maximal, complemented
3	C₃×C₅×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	3₋¹⁺⁴	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃³×C₅	C₃²	1	4	yes	—
6	C₅×3₋¹⁺²	C₃²	1	9	yes	—
7	C₅×3₋¹⁺²	C₃²	1	72	yes	complemented
8	C₅×H(3,𝔽₃)	C₃²	1	9	yes	—
9	C₃×C₅×C₉	C₃²	1	36	yes	complemented
10	#737	C₃×C₅	1	27	yes	complemented
11	C₃×3₋¹⁺²	C₃×C₅	1	12	yes	complemented
12	C₃×H(3,𝔽₃)	C₃×C₅	1	1	yes	characteristic
13	C₃²×C₅	—	9	4	no	—
14	C₃²×C₅	C₃³	1	12	yes	—
15	C₃²×C₅	C₃³	1	1	yes	characteristic
16	C₅×C₉	C₃³	1	27	yes	—
17	C₃³	C₃²×C₅	1	4	yes	—
18	3₋¹⁺²	C₃²×C₅	1	9	yes	—
19	3₋¹⁺²	C₃²×C₅	1	72	yes	complemented
20	H(3,𝔽₃)	C₃²×C₅	1	9	yes	—
21	C₃×C₉	C₃²×C₅	1	36	yes	complemented
22	C₃×C₅	—	3	1	no	—
23	C₃×C₅	—	3	12	no	—
24	C₃×C₅	C₃⁴	1	1	yes	characteristic
25	C₃²	—	9	4	no	—
26	C₃²	C₃³×C₅	1	12	yes	—
27	C₃²	C₃³×C₅	1	1	yes	characteristic
28	C₉	C₃³×C₅	1	27	yes	—
29	C₅	3₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
30	C₃	—	3	1	no	—
31	C₃	—	3	12	no	—
32	C₃	C₃⁴×C₅	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₅	C₃⁴
commutator, Frattini, cosocle	C₃	C₃⁴×C₅
prime radical	C₃×C₅×H(3,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×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.