AGL(1,𝔽₅)×#4181 #72247184

order	3240
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₃	AGL(1,𝔽₅)×C₃⋊D₉
commutator, Fitting, hypocenter	C₅×C₃²⋊C₉	C₂×C₄
Frattini	C₃²	C₃⋊D₃×AGL(1,𝔽₅)
socle	C₃²×C₅	C₄×C₃⋊D₃
prime radical	D₅×#4181	C₂
cosocle	D₅×C₃²⋊C₉	C₂²
LCS	G ▷ C₅×C₃²⋊C₉
UCS	C₁ ◁ C₃

316 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 90

maximal subgroup of	AGL(1,𝔽₅)×#92302, AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₉)⋊C₂
maximal normal subgroup of	AGL(1,𝔽₅)×#92302, AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₉)⋊C₂

Past the SmallGroups library coverage — no SmallGroups id.