Subgroups — C₇⋊AGL(1,𝔽₅) #3648

Order 140.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇	—	5	1	no	maximal, Hall
4	AGL(1,𝔽₅)	—	7	1	no	maximal, Hall
5	C₂×C₇	—	5	1	no	—
6	D₅	D₇	1	1	yes	characteristic
7	C₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
8	C₅	Dic₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	35	1	no	Sylow
10	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇	C₄
prime radical, cosocle	C₇×D₅	C₂
LCS	G ▷ C₅×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.