Subgroups — C₇×D₅ #599

Order 70.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇	—	5	1	no	maximal, Hall
3	D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇	D₅	1	1	yes	characteristic, direct product factor, Sylow
5	C₅	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₇

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.