Subgroups — C₃×S₅ #67189

Order 360.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×A₅	C₂	1	1	yes	maximal, characteristic, complemented
2	S₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×S₄	—	5	1	no	maximal, Hall
4	C₃×AGL(1,𝔽₅)	—	6	1	no	maximal
5	A₅	C₂×C₃	1	1	yes	characteristic, complemented
6	C₂×C₃×D₃	—	10	1	no	maximal
7	C₃×A₄	—	5	1	no	—
8	C₃×D₅	—	6	1	no	—
9	S₄	—	5	1	no	—
10	C₃×D₄	—	15	1	no	—
11	AGL(1,𝔽₅)	—	6	1	no	—
12	C₂×C₃²	—	10	1	no	—
13	C₃×D₃	—	10	1	no	—
14	C₃×D₃	—	10	1	no	—
15	C₃×C₅	—	6	1	no	—
16	C₂²×C₃	—	5	1	no	—
17	C₂²×C₃	—	15	1	no	—
18	C₂×D₃	—	10	1	no	—
19	A₄	—	5	1	no	—
20	A₄	—	10	1	no	—
21	C₃×C₄	—	15	1	no	—
22	D₅	—	6	1	no	—
23	C₃²	—	10	1	no	Sylow
24	D₄	—	15	1	no	Sylow
25	C₂×C₃	—	10	1	no	—
26	C₂×C₃	—	10	1	no	—
27	C₂×C₃	—	15	1	no	—
28	C₂×C₃	—	20	1	no	—
29	D₃	—	10	1	no	—
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	Sylow
32	C₂²	—	5	1	no	—
33	C₂²	—	15	1	no	—
34	C₄	—	15	1	no	—
35	C₃	—	10	1	no	—
36	C₃	—	20	1	no	—
37	C₃	S₅	1	1	yes	characteristic, direct product factor
38	C₂	—	10	1	no	—
39	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₃	S₅
commutator, cosocle, hypocenter	A₅	C₂×C₃
Frattini	C₁	G
socle	C₃×A₅	C₂
LCS	G ▷ A₅
UCS	C₁ ◁ C₃

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.