AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂ #72213725

order	2160
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×H(3,𝔽₃)	C₂²×C₄
Frattini	C₃	D₃²×AGL(1,𝔽₅)
socle	C₃×C₅	C₄×D₃²
prime radical	D₅×((C₃⋊D₃)⋊C₃)⋊C₂	C₂
cosocle	D₅×H(3,𝔽₃)	C₂³
LCS	G ▷ C₅×H(3,𝔽₃)
UCS	C₁

410 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

maximal subgroup of	AGL(1,𝔽₅)×AGL(2,𝔽₃), C₃×AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂, C₂×AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂, …
maximal normal subgroup of	C₃×AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂, C₂×AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂
maximal quotient of	C₃×AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂, C₂×AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₃)⋊C₂, AGL(1,𝔽₅)×((C₃⋊D₃)⋊C₉)⋊C₂, …

Past the SmallGroups library coverage — no SmallGroups id.