Subgroups — C₁₇₂₃⋊AGL(1,𝔽₅) #46828049

Order 34460.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₇₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₇₂₃	—	5	1	no	maximal, Hall
4	C₂×C₁₇₂₃	—	5	1	no	—
5	C₁₇₂₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
6	AGL(1,𝔽₅)	—	1723	1	no	maximal, Hall
7	D₅	D₁₇₂₃	1	1	yes	characteristic
8	C₅	Dic₁₇₂₃	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	8615	1	no	Sylow
10	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇₂₃	C₄
prime radical, cosocle	D₅×C₁₇₂₃	C₂
LCS	G ▷ C₅×C₁₇₂₃
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.