AGL(1,𝔽₅)×PSU(3,𝔽₂)⋊C₃ #72213680

order	4320
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₅×PSU(3,𝔽₂)	C₃×C₄
Fitting, socle	C₃²×C₅	C₄×SL(2,𝔽₃)
prime radical	D₅×PSU(3,𝔽₂)⋊C₃	C₂
cosocle	D₅×PSU(3,𝔽₂)	C₂×C₃
LCS	G ▷ C₅×PSU(3,𝔽₂)
UCS	C₁

164 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 22 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)×PSU(3,𝔽₂)⋊C₃, C₂×AGL(1,𝔽₅)×PSU(3,𝔽₂)⋊C₃
maximal normal subgroup of	AGL(1,𝔽₅)×AGL(2,𝔽₃), C₃×AGL(1,𝔽₅)×PSU(3,𝔽₂)⋊C₃, C₂×AGL(1,𝔽₅)×PSU(3,𝔽₂)⋊C₃
maximal quotient of	C₃×AGL(1,𝔽₅)×PSU(3,𝔽₂)⋊C₃, C₂×AGL(1,𝔽₅)×PSU(3,𝔽₂)⋊C₃

Past the SmallGroups library coverage — no SmallGroups id.