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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C3×F5

Direct product G=N×Q with N=C2×C4 and Q=C3×F5
dρLabelID
F5×C2×C12120F5xC2xC12480,1050

Semidirect products G=N:Q with N=C2×C4 and Q=C3×F5
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C3×F5) = C3×D10.D4φ: C3×F5/C15 → C4 ⊆ Aut C2×C41204(C2xC4):(C3xF5)480,279
(C2×C4)⋊2(C3×F5) = C3×D10.3Q8φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4120(C2xC4):2(C3xF5)480,286
(C2×C4)⋊3(C3×F5) = C6×C4⋊F5φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4120(C2xC4):3(C3xF5)480,1051
(C2×C4)⋊4(C3×F5) = C3×D10.C23φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C41204(C2xC4):4(C3xF5)480,1052

Non-split extensions G=N.Q with N=C2×C4 and Q=C3×F5
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C3×F5) = C3×Dic5.D4φ: C3×F5/C15 → C4 ⊆ Aut C2×C42404(C2xC4).(C3xF5)480,285
(C2×C4).2(C3×F5) = C3×C10.C42φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4480(C2xC4).2(C3xF5)480,282
(C2×C4).3(C3×F5) = C3×D10⋊C8φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4240(C2xC4).3(C3xF5)480,283
(C2×C4).4(C3×F5) = C3×Dic5⋊C8φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4480(C2xC4).4(C3xF5)480,284
(C2×C4).5(C3×F5) = C3×C20.C8φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C42404(C2xC4).5(C3xF5)480,278
(C2×C4).6(C3×F5) = C3×C20⋊C8φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4480(C2xC4).6(C3xF5)480,281
(C2×C4).7(C3×F5) = C6×C4.F5φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C4240(C2xC4).7(C3xF5)480,1048
(C2×C4).8(C3×F5) = C3×D5⋊M4(2)φ: C3×F5/C3×D5 → C2 ⊆ Aut C2×C41204(C2xC4).8(C3xF5)480,1049
(C2×C4).9(C3×F5) = C6×C5⋊C16central extension (φ=1)480(C2xC4).9(C3xF5)480,277
(C2×C4).10(C3×F5) = C12×C5⋊C8central extension (φ=1)480(C2xC4).10(C3xF5)480,280
(C2×C4).11(C3×F5) = C6×D5⋊C8central extension (φ=1)240(C2xC4).11(C3xF5)480,1047

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