Subgroups — C₂³×A₅ #92111

Order 480.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×A₅	C₂	1	7	yes	maximal, direct product factor
2	C₂×A₅	C₂²	1	7	yes	direct product factor
3	C₂³×A₄	—	5	1	no	maximal, Hall
4	C₂³×D₅	—	6	1	no	maximal
5	A₅	C₂³	1	1	yes	characteristic, direct product factor
6	C₂³×D₃	—	10	1	no	maximal
7	C₂²×A₄	—	5	7	no	—
8	C₂³×C₅	—	6	1	no	—
9	C₂²×D₅	—	6	7	no	—
10	C₂²×D₅	—	6	7	no	—
11	C₂⁵	—	5	1	no	Sylow
12	C₂³×C₃	—	10	1	no	—
13	C₂²×D₃	—	10	7	no	—
14	C₂²×D₃	—	10	7	no	—
15	C₂×A₄	—	5	7	no	—
16	C₂²×C₅	—	6	7	no	—
17	C₂×D₅	—	6	21	no	—
18	C₂×D₅	—	6	7	no	—
19	C₂⁴	—	5	7	no	—
20	C₂⁴	—	15	7	no	—
21	C₂⁴	—	15	1	no	—
22	C₂²×C₃	—	10	7	no	—
23	C₂×D₃	—	10	21	no	—
24	C₂×D₃	—	10	7	no	—
25	A₄	—	5	1	no	—
26	C₂×C₅	—	6	7	no	—
27	D₅	—	6	1	no	—
28	D₅	—	6	7	no	—
29	C₂³	—	5	7	no	—
30	C₂³	—	15	21	no	—
31	C₂³	—	15	14	no	—
32	C₂³	—	15	7	no	—
33	C₂³	—	15	7	no	—
34	C₂³	A₅	1	1	yes	maximal normal, characteristic, direct product factor
35	C₂×C₃	—	10	7	no	—
36	D₃	—	10	7	no	—
37	D₃	—	10	1	no	—
38	C₅	—	6	1	no	Sylow
39	C₂²	—	5	1	no	—
40	C₂²	—	15	7	no	—
41	C₂²	—	15	14	no	—
42	C₂²	—	15	7	no	—
43	C₂²	—	15	21	no	—
44	C₂²	C₂×A₅	1	7	yes	direct product factor
45	C₃	—	10	1	no	Sylow
46	C₂	—	15	1	no	—
47	C₂	—	15	7	no	—
48	C₂	C₂²×A₅	1	7	yes	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.