Subgroups — C₂²×A₅ #6829

Order 240.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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