Subgroups — AGL(1,𝔽₁₆) #6830

Order 240.

14 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂²⋊A₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂⁴	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₅	—	16	1	no	maximal, Hall
5	A₄	—	20	1	no	—
6	C₂³	—	15	1	no	—
7	C₅	—	16	1	no	Sylow
8	C₂²	—	5	1	no	—
9	C₂²	—	15	2	no	—
10	C₃	—	16	1	no	Sylow
11	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁴	C₃×C₅
LCS	G ▷ C₂⁴
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.