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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C10

Direct product G=N×Q with N=C2×C4 and Q=C2×C10
dρLabelID
C23×C20160C2^3xC20160,228

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C10) = C5×C22≀C2φ: C2×C10/C5 → C22 ⊆ Aut C2×C440(C2xC4):1(C2xC10)160,181
(C2×C4)⋊2(C2×C10) = C5×2+ 1+4φ: C2×C10/C5 → C22 ⊆ Aut C2×C4404(C2xC4):2(C2xC10)160,232
(C2×C4)⋊3(C2×C10) = C10×C22⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4):3(C2xC10)160,176
(C2×C4)⋊4(C2×C10) = D4×C2×C10φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4):4(C2xC10)160,229
(C2×C4)⋊5(C2×C10) = C10×C4○D4φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4):5(C2xC10)160,231

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C10) = C5×C4.D4φ: C2×C10/C5 → C22 ⊆ Aut C2×C4404(C2xC4).1(C2xC10)160,50
(C2×C4).2(C2×C10) = C5×C4.10D4φ: C2×C10/C5 → C22 ⊆ Aut C2×C4804(C2xC4).2(C2xC10)160,51
(C2×C4).3(C2×C10) = C5×C4⋊D4φ: C2×C10/C5 → C22 ⊆ Aut C2×C480(C2xC4).3(C2xC10)160,182
(C2×C4).4(C2×C10) = C5×C22⋊Q8φ: C2×C10/C5 → C22 ⊆ Aut C2×C480(C2xC4).4(C2xC10)160,183
(C2×C4).5(C2×C10) = C5×C22.D4φ: C2×C10/C5 → C22 ⊆ Aut C2×C480(C2xC4).5(C2xC10)160,184
(C2×C4).6(C2×C10) = C5×C4.4D4φ: C2×C10/C5 → C22 ⊆ Aut C2×C480(C2xC4).6(C2xC10)160,185
(C2×C4).7(C2×C10) = C5×C42.C2φ: C2×C10/C5 → C22 ⊆ Aut C2×C4160(C2xC4).7(C2xC10)160,186
(C2×C4).8(C2×C10) = C5×C42⋊2C2φ: C2×C10/C5 → C22 ⊆ Aut C2×C480(C2xC4).8(C2xC10)160,187
(C2×C4).9(C2×C10) = C5×C4⋊Q8φ: C2×C10/C5 → C22 ⊆ Aut C2×C4160(C2xC4).9(C2xC10)160,189
(C2×C4).10(C2×C10) = C5×C8⋊C22φ: C2×C10/C5 → C22 ⊆ Aut C2×C4404(C2xC4).10(C2xC10)160,197
(C2×C4).11(C2×C10) = C5×C8.C22φ: C2×C10/C5 → C22 ⊆ Aut C2×C4804(C2xC4).11(C2xC10)160,198
(C2×C4).12(C2×C10) = C5×2- 1+4φ: C2×C10/C5 → C22 ⊆ Aut C2×C4804(C2xC4).12(C2xC10)160,233
(C2×C4).13(C2×C10) = C10×C4⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).13(C2xC10)160,177
(C2×C4).14(C2×C10) = C5×C42⋊C2φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4).14(C2xC10)160,178
(C2×C4).15(C2×C10) = D4×C20φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4).15(C2xC10)160,179
(C2×C4).16(C2×C10) = Q8×C20φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).16(C2xC10)160,180
(C2×C4).17(C2×C10) = C5×D4⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4).17(C2xC10)160,52
(C2×C4).18(C2×C10) = C5×Q8⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).18(C2xC10)160,53
(C2×C4).19(C2×C10) = C5×C4≀C2φ: C2×C10/C10 → C2 ⊆ Aut C2×C4402(C2xC4).19(C2xC10)160,54
(C2×C4).20(C2×C10) = C5×C4.Q8φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).20(C2xC10)160,56
(C2×C4).21(C2×C10) = C5×C2.D8φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).21(C2xC10)160,57
(C2×C4).22(C2×C10) = C5×C8.C4φ: C2×C10/C10 → C2 ⊆ Aut C2×C4802(C2xC4).22(C2xC10)160,58
(C2×C4).23(C2×C10) = C5×C4⋊1D4φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4).23(C2xC10)160,188
(C2×C4).24(C2×C10) = C5×C8○D4φ: C2×C10/C10 → C2 ⊆ Aut C2×C4802(C2xC4).24(C2xC10)160,192
(C2×C4).25(C2×C10) = C10×D8φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4).25(C2xC10)160,193
(C2×C4).26(C2×C10) = C10×SD16φ: C2×C10/C10 → C2 ⊆ Aut C2×C480(C2xC4).26(C2xC10)160,194
(C2×C4).27(C2×C10) = C10×Q16φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).27(C2xC10)160,195
(C2×C4).28(C2×C10) = C5×C4○D8φ: C2×C10/C10 → C2 ⊆ Aut C2×C4802(C2xC4).28(C2xC10)160,196
(C2×C4).29(C2×C10) = Q8×C2×C10φ: C2×C10/C10 → C2 ⊆ Aut C2×C4160(C2xC4).29(C2xC10)160,230
(C2×C4).30(C2×C10) = C5×C8⋊C4central extension (φ=1)160(C2xC4).30(C2xC10)160,47
(C2×C4).31(C2×C10) = C5×C22⋊C8central extension (φ=1)80(C2xC4).31(C2xC10)160,48
(C2×C4).32(C2×C10) = C5×C4⋊C8central extension (φ=1)160(C2xC4).32(C2xC10)160,55
(C2×C4).33(C2×C10) = C10×M4(2)central extension (φ=1)80(C2xC4).33(C2xC10)160,191

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