Subgroups — C₅×C₇⋊D₇ #92439

Order 490.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₇	—	7	8	no	maximal
4	C₇²	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
5	C₅×C₇	D₇	1	8	yes	complemented
6	D₇	—	7	8	no	—
7	C₂×C₅	—	49	1	no	Hall
8	C₇	C₅×D₇	1	8	yes	complemented
9	C₅	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₅

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.