Subgroups — D₃×A₅ #67191

Order 360.

47 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	C₂×A₅	—	3	1	no	maximal
3	D₃×A₄	—	5	1	no	maximal, Hall
4	D₃×D₅	—	6	1	no	maximal
5	A₅	D₃	1	1	yes	characteristic, direct product factor
6	C₃×A₄	—	5	1	no	—
7	D₃²	—	10	1	no	maximal
8	D₁₅	—	6	1	no	—
9	C₃×D₅	—	6	1	no	—
10	C₅×D₃	—	6	1	no	—
11	C₂²×D₃	—	5	1	no	—
12	C₂×A₄	—	15	1	no	—
13	C₂×D₅	—	18	1	no	—
14	C₃⋊D₃	—	10	1	no	—
15	C₃×D₃	—	10	1	no	—
16	C₃×D₃	—	10	1	no	—
17	C₃×C₅	—	6	1	no	—
18	C₂²×C₃	—	5	1	no	—
19	C₂×D₃	—	15	1	no	—
20	C₂×D₃	—	15	1	no	—
21	C₂×D₃	—	30	1	no	—
22	A₄	—	5	1	no	—
23	A₄	—	10	1	no	—
24	C₂×C₅	—	18	1	no	—
25	D₅	—	6	1	no	—
26	D₅	—	18	1	no	—
27	C₃²	—	10	1	no	Sylow
28	C₂³	—	15	1	no	Sylow
29	C₂×C₃	—	15	1	no	—
30	C₂×C₃	—	30	1	no	—
31	D₃	—	10	1	no	—
32	D₃	—	15	1	no	—
33	D₃	—	30	1	no	—
34	D₃	—	60	1	no	—
35	D₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
36	C₅	—	6	1	no	Sylow
37	C₂²	—	5	1	no	—
38	C₂²	—	45	1	no	—
39	C₂²	—	45	1	no	—
40	C₃	—	10	1	no	—
41	C₃	—	20	1	no	—
42	C₃	C₂×A₅	1	1	yes	characteristic, complemented
43	C₂	—	3	1	no	—
44	C₂	—	15	1	no	—
45	C₂	—	45	1	no	—

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

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.