Subgroups — C₄×A₅ #6731

Order 240.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₅	C₂	1	1	yes	maximal, characteristic
2	A₅	C₄	1	1	yes	characteristic, direct product factor
3	C₄×A₄	—	5	1	no	maximal, Hall
4	C₄×D₅	—	6	1	no	maximal
5	C₂×A₄	—	5	1	no	—
6	C₄×D₃	—	10	1	no	maximal
7	C₂×D₅	—	6	1	no	—
8	C₄×C₅	—	6	1	no	—
9	Dic₅	—	6	1	no	—
10	C₂²×C₄	—	5	1	no	Sylow
11	C₂×D₃	—	10	1	no	—
12	A₄	—	5	1	no	—
13	C₃×C₄	—	10	1	no	—
14	Dic₃	—	10	1	no	—
15	C₂×C₅	—	6	1	no	—
16	D₅	—	6	1	no	—
17	D₅	—	6	1	no	—
18	C₂³	—	5	1	no	—
19	C₂×C₄	—	15	1	no	—
20	C₂×C₄	—	15	1	no	—
21	C₂×C₃	—	10	1	no	—
22	D₃	—	10	1	no	—
23	D₃	—	10	1	no	—
24	C₅	—	6	1	no	Sylow
25	C₂²	—	5	1	no	—
26	C₂²	—	15	1	no	—
27	C₂²	—	15	1	no	—
28	C₄	—	15	1	no	—
29	C₄	A₅	1	1	yes	maximal normal, characteristic, direct product factor
30	C₃	—	10	1	no	Sylow
31	C₂	—	15	1	no	—
32	C₂	—	15	1	no	—
33	C₂	C₂×A₅	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. A₅	C₄	direct (N × H)
29. C₄	A₅	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.