C₃×D₅×#226 #13088505

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅×S₄
commutator, cosocle, hypocenter	C₅×SL(2,𝔽₃)	C₂²×C₃
Frattini	C₂	C₃×D₅×S₄
Fitting	C₃×C₅×Q₈	C₂×D₃
socle	C₂×C₃×C₅	C₂×S₄
prime radical	C₃×D₅×SL(2,𝔽₃)	C₂
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

170 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

μ_t(G) = 240

maximal subgroup of	D₅×#226⋊A₄, C₃×D₅×#983
maximal normal subgroup of	C₃×D₅×#983

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4822);