Subgroups — C₇×C₅⋊D₅ #66842

Order 350.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅	—	5	6	no	maximal
3	C₅⋊D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇	D₅	1	6	yes	complemented
5	C₅²	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₇	—	25	1	no	Hall
7	D₅	—	5	6	no	—
8	C₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
9	C₅	C₇×D₅	1	6	yes	complemented
10	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇	C₂
LCS	G ▷ C₅²
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.