Subgroups — C₁₅₆₇⋊AGL(1,𝔽₅) #44531360

Order 31340.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₅₆₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₅₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₅₆₇	—	5	1	no	maximal, Hall
4	C₂×C₁₅₆₇	—	5	1	no	—
5	C₁₅₆₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
6	AGL(1,𝔽₅)	—	1567	1	no	maximal, Hall
7	D₅	D₁₅₆₇	1	1	yes	characteristic
8	C₅	Dic₁₅₆₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	7835	1	no	Sylow
10	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₅₆₇	C₄
prime radical, cosocle	D₅×C₁₅₆₇	C₂
LCS	G ▷ C₅×C₁₅₆₇
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.