Subgroups — C₇×A₅ #88288

Order 420.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×A₄	—	5	1	no	maximal, Hall
2	C₇×D₅	—	6	1	no	maximal
3	A₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	D₃×C₇	—	10	1	no	maximal
5	C₅×C₇	—	6	1	no	Hall
6	C₂²×C₇	—	5	1	no	Hall
7	C₃×C₇	—	10	1	no	Hall
8	C₂×C₇	—	15	1	no	—
9	A₄	—	5	1	no	Hall
10	D₅	—	6	1	no	—
11	C₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Sylow
12	D₃	—	10	1	no	—
13	C₅	—	6	1	no	Sylow
14	C₂²	—	5	1	no	Sylow
15	C₃	—	10	1	no	Sylow
16	C₂	—	15	1	no	—

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

N	H ≅ G/N	type
3. A₅	C₇	direct (N × H)
11. C₇	A₅	direct (N × H)

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