Subgroups — C₅×A₅ #64479

Order 300.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₄	—	5	1	no	maximal
2	A₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₅	—	6	1	no	maximal
4	C₅×D₃	—	10	1	no	maximal
5	C₅²	—	6	1	no	Sylow
6	C₂²×C₅	—	5	1	no	—
7	C₃×C₅	—	10	1	no	—
8	A₄	—	5	1	no	Hall
9	C₂×C₅	—	15	1	no	—
10	D₅	—	6	1	no	—
11	D₃	—	10	1	no	—
12	C₅	—	6	1	no	—
13	C₅	—	12	2	no	—
14	C₅	A₅	1	1	yes	maximal normal, characteristic, direct product factor
15	C₂²	—	5	1	no	Sylow
16	C₃	—	10	1	no	Sylow
17	C₂	—	15	1	no	—

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

N	H ≅ G/N	type
2. A₅	C₅	direct (N × H)
14. C₅	A₅	direct (N × H)

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