# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×A4

Direct product G=N×Q with N=C2×C10 and Q=C2×A4
dρLabelID
A4×C22×C10120A4xC2^2xC10480,1208

Semidirect products G=N:Q with N=C2×C10 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C2×A4) = D5×C22⋊A4φ: C2×A4/C22C6 ⊆ Aut C2×C1060(C2xC10):(C2xA4)480,1203
(C2×C10)⋊2(C2×A4) = C10×C22⋊A4φ: C2×A4/C23C3 ⊆ Aut C2×C1060(C2xC10):2(C2xA4)480,1209
(C2×C10)⋊3(C2×A4) = C5×D4×A4φ: C2×A4/A4C2 ⊆ Aut C2×C10606(C2xC10):3(C2xA4)480,1127
(C2×C10)⋊4(C2×A4) = A4×C5⋊D4φ: C2×A4/A4C2 ⊆ Aut C2×C10606(C2xC10):4(C2xA4)480,1045
(C2×C10)⋊5(C2×A4) = C22×D5×A4φ: C2×A4/A4C2 ⊆ Aut C2×C1060(C2xC10):5(C2xA4)480,1202

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C2×A4) = C204D4⋊C3φ: C2×A4/C22C6 ⊆ Aut C2×C10606+(C2xC10).1(C2xA4)480,262
(C2×C10).2(C2×A4) = (C4×C20)⋊C6φ: C2×A4/C22C6 ⊆ Aut C2×C10806(C2xC10).2(C2xA4)480,263
(C2×C10).3(C2×A4) = D5×C42⋊C3φ: C2×A4/C22C6 ⊆ Aut C2×C10606(C2xC10).3(C2xA4)480,264
(C2×C10).4(C2×A4) = (C22×D5)⋊A4φ: C2×A4/C22C6 ⊆ Aut C2×C10406(C2xC10).4(C2xA4)480,268
(C2×C10).5(C2×A4) = C10×C42⋊C3φ: C2×A4/C23C3 ⊆ Aut C2×C10603(C2xC10).5(C2xA4)480,654
(C2×C10).6(C2×A4) = C5×C24⋊C6φ: C2×A4/C23C3 ⊆ Aut C2×C10406(C2xC10).6(C2xA4)480,656
(C2×C10).7(C2×A4) = C5×C42⋊C6φ: C2×A4/C23C3 ⊆ Aut C2×C10806(C2xC10).7(C2xA4)480,657
(C2×C10).8(C2×A4) = C5×C23.A4φ: C2×A4/C23C3 ⊆ Aut C2×C10606(C2xC10).8(C2xA4)480,658
(C2×C10).9(C2×A4) = C5×D4.A4φ: C2×A4/A4C2 ⊆ Aut C2×C10804(C2xC10).9(C2xA4)480,1132
(C2×C10).10(C2×A4) = Dic5×SL2(𝔽3)φ: C2×A4/A4C2 ⊆ Aut C2×C10160(C2xC10).10(C2xA4)480,266
(C2×C10).11(C2×A4) = C2×Dic5.A4φ: C2×A4/A4C2 ⊆ Aut C2×C10160(C2xC10).11(C2xA4)480,1038
(C2×C10).12(C2×A4) = C2×D5×SL2(𝔽3)φ: C2×A4/A4C2 ⊆ Aut C2×C1080(C2xC10).12(C2xA4)480,1039
(C2×C10).13(C2×A4) = SL2(𝔽3).11D10φ: C2×A4/A4C2 ⊆ Aut C2×C10804(C2xC10).13(C2xA4)480,1040
(C2×C10).14(C2×A4) = C2×A4×Dic5φ: C2×A4/A4C2 ⊆ Aut C2×C10120(C2xC10).14(C2xA4)480,1044
(C2×C10).15(C2×A4) = C20×SL2(𝔽3)central extension (φ=1)160(C2xC10).15(C2xA4)480,655
(C2×C10).16(C2×A4) = A4×C2×C20central extension (φ=1)120(C2xC10).16(C2xA4)480,1126
(C2×C10).17(C2×A4) = C2×C10×SL2(𝔽3)central extension (φ=1)160(C2xC10).17(C2xA4)480,1128
(C2×C10).18(C2×A4) = C10×C4.A4central extension (φ=1)160(C2xC10).18(C2xA4)480,1130

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