C₅×D₇×GL(2,𝔽₃) #72218659

order	3360
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇×S₄
commutator, cosocle, hypocenter	C₇×SL(2,𝔽₃)	C₂²×C₅
Frattini	C₂	C₅×D₇×S₄
Fitting	C₅×C₇×Q₈	C₂×D₃
socle	C₂×C₅×C₇	C₂×S₄
LCS	G ▷ C₇×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅

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

normal subgroups only

This group has 204 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.

maximal subgroup of	C₅×AGL(1,𝔽₇)×GL(2,𝔽₃), D₅×D₇×GL(2,𝔽₃)
maximal normal subgroup of	C₅×AGL(1,𝔽₇)×GL(2,𝔽₃), D₅×D₇×GL(2,𝔽₃)

Past the SmallGroups library coverage — no SmallGroups id.