Subgroups — C₅²×D₇ #66839

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	C₅×D₇	C₅	1	6	yes	maximal, direct product factor
3	C₂×C₅²	—	7	1	no	maximal, Hall
4	C₅×C₇	C₂×C₅	1	6	yes	complemented
5	C₅²	D₇	1	1	yes	characteristic, direct product factor, Sylow
6	D₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅	—	7	6	no	—
8	C₇	C₂×C₅²	1	1	yes	characteristic, complemented, Sylow
9	C₅	C₅×D₇	1	6	yes	direct product factor
10	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅²

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.