Subgroups — C₂×C₃×A₅ #67192

Order 360.

50 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, direct product factor
2	C₂×A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×A₄	—	5	1	no	maximal, Hall
4	C₂×C₃×D₅	—	6	1	no	maximal
5	A₅	C₂×C₃	1	1	yes	characteristic, direct product factor
6	C₂×C₃×D₃	—	10	1	no	maximal
7	C₃×A₄	—	5	1	no	—
8	C₂×C₃×C₅	—	6	1	no	—
9	C₃×D₅	—	6	1	no	—
10	C₃×D₅	—	6	1	no	—
11	C₂³×C₃	—	5	1	no	—
12	C₂×A₄	—	5	1	no	—
13	C₂×A₄	—	5	2	no	—
14	C₂×D₅	—	6	1	no	—
15	C₂×C₃²	—	10	1	no	—
16	C₃×D₃	—	10	1	no	—
17	C₃×D₃	—	10	1	no	—
18	C₃×C₅	—	6	1	no	—
19	C₂²×C₃	—	5	1	no	—
20	C₂²×C₃	—	15	1	no	—
21	C₂²×C₃	—	15	1	no	—
22	C₂×D₃	—	10	1	no	—
23	A₄	—	5	1	no	—
24	A₄	—	5	2	no	—
25	C₂×C₅	—	6	1	no	—
26	D₅	—	6	1	no	—
27	D₅	—	6	1	no	—
28	C₃²	—	10	1	no	Sylow
29	C₂³	—	5	1	no	Sylow
30	C₂×C₃	—	10	1	no	—
31	C₂×C₃	—	15	1	no	—
32	C₂×C₃	—	15	1	no	—
33	C₂×C₃	—	20	1	no	—
34	C₂×C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
35	D₃	—	10	1	no	—
36	D₃	—	10	1	no	—
37	C₅	—	6	1	no	Sylow
38	C₂²	—	5	1	no	—
39	C₂²	—	15	1	no	—
40	C₂²	—	15	1	no	—
41	C₃	—	10	1	no	—
42	C₃	—	20	1	no	—
43	C₃	C₂×A₅	1	1	yes	characteristic, direct product factor
44	C₂	—	15	1	no	—
45	C₂	—	15	1	no	—
46	C₂	C₃×A₅	1	1	yes	characteristic, direct product factor

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.