Subgroups — C₅⋊D₃₅ #66843

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	D₃₅	—	5	6	no	maximal
3	C₅⋊D₅	—	7	1	no	maximal, Hall
4	C₅×C₇	D₅	1	6	yes	complemented
5	C₅²	D₇	1	1	yes	characteristic, complemented, Sylow
6	D₇	—	25	1	no	Hall
7	D₅	—	35	6	no	—
8	C₇	C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
9	C₅	D₃₅	1	6	yes	complemented
10	C₂	—	175	1	no	Sylow

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

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.