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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C3×D4

Direct product G=N×Q with N=C2×C10 and Q=C3×D4
dρLabelID
D4×C2×C30240D4xC2xC30480,1181

Semidirect products G=N:Q with N=C2×C10 and Q=C3×D4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1(C3×D4) = A4×D20φ: C3×D4/C4 → C6 ⊆ Aut C2×C10606+(C2xC10):1(C3xD4)480,1037
(C2×C10)⋊2(C3×D4) = A4×C5⋊D4φ: C3×D4/C22 → C6 ⊆ Aut C2×C10606(C2xC10):2(C3xD4)480,1045
(C2×C10)⋊3(C3×D4) = C3×C22⋊D20φ: C3×D4/C6 → C22 ⊆ Aut C2×C10120(C2xC10):3(C3xD4)480,675
(C2×C10)⋊4(C3×D4) = C3×C23⋊D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C10120(C2xC10):4(C3xD4)480,730
(C2×C10)⋊5(C3×D4) = C3×Dic5⋊D4φ: C3×D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10):5(C3xD4)480,732
(C2×C10)⋊6(C3×D4) = C5×D4×A4φ: C3×D4/D4 → C3 ⊆ Aut C2×C10606(C2xC10):6(C3xD4)480,1127
(C2×C10)⋊7(C3×D4) = C15×C4⋊D4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10):7(C3xD4)480,926
(C2×C10)⋊8(C3×D4) = C3×C20⋊7D4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10):8(C3xD4)480,723
(C2×C10)⋊9(C3×D4) = C2×C6×D20φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10):9(C3xD4)480,1137
(C2×C10)⋊10(C3×D4) = C15×C22≀C2φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10120(C2xC10):10(C3xD4)480,925
(C2×C10)⋊11(C3×D4) = C3×C24⋊2D5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10120(C2xC10):11(C3xD4)480,746
(C2×C10)⋊12(C3×D4) = C2×C6×C5⋊D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10):12(C3xD4)480,1149

Non-split extensions G=N.Q with N=C2×C10 and Q=C3×D4
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C3×D4) = C3×D20⋊7C4φ: C3×D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).1(C3xD4)480,103
(C2×C10).2(C3×D4) = C3×C23⋊Dic5φ: C3×D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).2(C3xD4)480,112
(C2×C10).3(C3×D4) = C3×D4⋊2Dic5φ: C3×D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).3(C3xD4)480,115
(C2×C10).4(C3×D4) = C3×C22.D20φ: C3×D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10).4(C3xD4)480,679
(C2×C10).5(C3×D4) = C3×C8⋊D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).5(C3xD4)480,701
(C2×C10).6(C3×D4) = C3×C8.D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).6(C3xD4)480,702
(C2×C10).7(C3×D4) = C3×C23.18D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10).7(C3xD4)480,728
(C2×C10).8(C3×D4) = C3×D4⋊D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).8(C3xD4)480,742
(C2×C10).9(C3×D4) = C3×D4.8D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).9(C3xD4)480,743
(C2×C10).10(C3×D4) = C3×D4.9D10φ: C3×D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).10(C3xD4)480,744
(C2×C10).11(C3×D4) = C15×C4○D8φ: C3×D4/C12 → C2 ⊆ Aut C2×C102402(C2xC10).11(C3xD4)480,940
(C2×C10).12(C3×D4) = C3×C20.44D4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10480(C2xC10).12(C3xD4)480,94
(C2×C10).13(C3×D4) = C3×C40⋊6C4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10480(C2xC10).13(C3xD4)480,95
(C2×C10).14(C3×D4) = C3×C40⋊5C4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10480(C2xC10).14(C3xD4)480,96
(C2×C10).15(C3×D4) = C3×D20⋊5C4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10).15(C3xD4)480,99
(C2×C10).16(C3×D4) = C6×C40⋊C2φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10).16(C3xD4)480,695
(C2×C10).17(C3×D4) = C6×D40φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10).17(C3xD4)480,696
(C2×C10).18(C3×D4) = C3×D40⋊7C2φ: C3×D4/C12 → C2 ⊆ Aut C2×C102402(C2xC10).18(C3xD4)480,697
(C2×C10).19(C3×D4) = C6×Dic20φ: C3×D4/C12 → C2 ⊆ Aut C2×C10480(C2xC10).19(C3xD4)480,698
(C2×C10).20(C3×D4) = C6×C4⋊Dic5φ: C3×D4/C12 → C2 ⊆ Aut C2×C10480(C2xC10).20(C3xD4)480,718
(C2×C10).21(C3×D4) = C6×D10⋊C4φ: C3×D4/C12 → C2 ⊆ Aut C2×C10240(C2xC10).21(C3xD4)480,720
(C2×C10).22(C3×D4) = C15×C23⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).22(C3xD4)480,202
(C2×C10).23(C3×D4) = C15×C4≀C2φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C101202(C2xC10).23(C3xD4)480,207
(C2×C10).24(C3×D4) = C15×C22.D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).24(C3xD4)480,928
(C2×C10).25(C3×D4) = C15×C8⋊C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).25(C3xD4)480,941
(C2×C10).26(C3×D4) = C15×C8.C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C102404(C2xC10).26(C3xD4)480,942
(C2×C10).27(C3×D4) = C3×D20⋊4C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C101202(C2xC10).27(C3xD4)480,83
(C2×C10).28(C3×D4) = C3×C23.1D10φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).28(C3xD4)480,84
(C2×C10).29(C3×D4) = C3×C10.D8φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).29(C3xD4)480,85
(C2×C10).30(C3×D4) = C3×C20.Q8φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).30(C3xD4)480,86
(C2×C10).31(C3×D4) = C3×D20⋊6C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).31(C3xD4)480,87
(C2×C10).32(C3×D4) = C3×C10.Q16φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).32(C3xD4)480,88
(C2×C10).33(C3×D4) = C3×C10.10C42φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).33(C3xD4)480,109
(C2×C10).34(C3×D4) = C3×D4⋊Dic5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).34(C3xD4)480,110
(C2×C10).35(C3×D4) = C3×Q8⋊Dic5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).35(C3xD4)480,113
(C2×C10).36(C3×D4) = C6×C10.D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).36(C3xD4)480,716
(C2×C10).37(C3×D4) = C3×C23.23D10φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).37(C3xD4)480,722
(C2×C10).38(C3×D4) = C6×D4⋊D5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).38(C3xD4)480,724
(C2×C10).39(C3×D4) = C3×D4.D10φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).39(C3xD4)480,725
(C2×C10).40(C3×D4) = C6×D4.D5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).40(C3xD4)480,726
(C2×C10).41(C3×D4) = C6×Q8⋊D5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).41(C3xD4)480,734
(C2×C10).42(C3×D4) = C3×C20.C23φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C102404(C2xC10).42(C3xD4)480,735
(C2×C10).43(C3×D4) = C6×C5⋊Q16φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).43(C3xD4)480,736
(C2×C10).44(C3×D4) = C6×C23.D5φ: C3×D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).44(C3xD4)480,745
(C2×C10).45(C3×D4) = C15×C2.C42central extension (φ=1)480(C2xC10).45(C3xD4)480,198
(C2×C10).46(C3×D4) = C15×D4⋊C4central extension (φ=1)240(C2xC10).46(C3xD4)480,205
(C2×C10).47(C3×D4) = C15×Q8⋊C4central extension (φ=1)480(C2xC10).47(C3xD4)480,206
(C2×C10).48(C3×D4) = C15×C4.Q8central extension (φ=1)480(C2xC10).48(C3xD4)480,209
(C2×C10).49(C3×D4) = C15×C2.D8central extension (φ=1)480(C2xC10).49(C3xD4)480,210
(C2×C10).50(C3×D4) = C22⋊C4×C30central extension (φ=1)240(C2xC10).50(C3xD4)480,920
(C2×C10).51(C3×D4) = C4⋊C4×C30central extension (φ=1)480(C2xC10).51(C3xD4)480,921
(C2×C10).52(C3×D4) = D8×C30central extension (φ=1)240(C2xC10).52(C3xD4)480,937
(C2×C10).53(C3×D4) = SD16×C30central extension (φ=1)240(C2xC10).53(C3xD4)480,938
(C2×C10).54(C3×D4) = Q16×C30central extension (φ=1)480(C2xC10).54(C3xD4)480,939

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