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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=S3×C10

Direct product G=N×Q with N=C2×C4 and Q=S3×C10
dρLabelID
S3×C22×C20240S3xC2^2xC20480,1151

Semidirect products G=N:Q with N=C2×C4 and Q=S3×C10
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(S3×C10) = C5×D6⋊D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C4120(C2xC4):1(S3xC10)480,761
(C2×C4)⋊2(S3×C10) = C5×C23⋊2D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C4120(C2xC4):2(S3xC10)480,816
(C2×C4)⋊3(S3×C10) = C5×D4⋊6D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4):3(S3xC10)480,1156
(C2×C4)⋊4(S3×C10) = C5×D4○D12φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4):4(S3xC10)480,1161
(C2×C4)⋊5(S3×C10) = C5×S3×C22⋊C4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4120(C2xC4):5(S3xC10)480,759
(C2×C4)⋊6(S3×C10) = S3×D4×C10φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4120(C2xC4):6(S3xC10)480,1154
(C2×C4)⋊7(S3×C10) = C5×S3×C4○D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C41204(C2xC4):7(S3xC10)480,1160
(C2×C4)⋊8(S3×C10) = C10×D6⋊C4φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4):8(S3xC10)480,806
(C2×C4)⋊9(S3×C10) = C2×C10×D12φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4):9(S3xC10)480,1152
(C2×C4)⋊10(S3×C10) = C10×C4○D12φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4):10(S3xC10)480,1153

Non-split extensions G=N.Q with N=C2×C4 and Q=S3×C10
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(S3×C10) = C5×C12.46D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4).1(S3xC10)480,142
(C2×C4).2(S3×C10) = C5×C12.47D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).2(S3xC10)480,143
(C2×C4).3(S3×C10) = C5×C12.D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4).3(S3xC10)480,152
(C2×C4).4(S3×C10) = C5×C12.10D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).4(S3xC10)480,155
(C2×C4).5(S3×C10) = C5×Dic3.D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).5(S3xC10)480,757
(C2×C4).6(S3×C10) = C5×C23.9D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).6(S3xC10)480,762
(C2×C4).7(S3×C10) = C5×C23.11D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).7(S3xC10)480,764
(C2×C4).8(S3×C10) = C5×C23.21D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).8(S3xC10)480,765
(C2×C4).9(S3×C10) = C5×Dic3.Q8φ: S3×C10/C15 → C22 ⊆ Aut C2×C4480(C2xC4).9(S3xC10)480,768
(C2×C4).10(S3×C10) = C5×D6.D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).10(S3xC10)480,773
(C2×C4).11(S3×C10) = C5×C12⋊D4φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).11(S3xC10)480,774
(C2×C4).12(S3×C10) = C5×C4.D12φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).12(S3xC10)480,776
(C2×C4).13(S3×C10) = C5×C8⋊D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4).13(S3xC10)480,787
(C2×C4).14(S3×C10) = C5×C8.D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).14(S3xC10)480,788
(C2×C4).15(S3×C10) = C5×D12⋊6C22φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4).15(S3xC10)480,811
(C2×C4).16(S3×C10) = C5×C23.23D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).16(S3xC10)480,814
(C2×C4).17(S3×C10) = C5×C23.14D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).17(S3xC10)480,818
(C2×C4).18(S3×C10) = C5×Q8.11D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).18(S3xC10)480,821
(C2×C4).19(S3×C10) = C5×D6⋊3Q8φ: S3×C10/C15 → C22 ⊆ Aut C2×C4240(C2xC4).19(S3xC10)480,825
(C2×C4).20(S3×C10) = C5×D4⋊D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C41204(C2xC4).20(S3xC10)480,828
(C2×C4).21(S3×C10) = C5×Q8.14D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).21(S3xC10)480,830
(C2×C4).22(S3×C10) = C5×Q8.15D6φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).22(S3xC10)480,1159
(C2×C4).23(S3×C10) = C5×Q8○D12φ: S3×C10/C15 → C22 ⊆ Aut C2×C42404(C2xC4).23(S3xC10)480,1162
(C2×C4).24(S3×C10) = C5×C23.16D6φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).24(S3xC10)480,756
(C2×C4).25(S3×C10) = C5×C23.8D6φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).25(S3xC10)480,758
(C2×C4).26(S3×C10) = C5×Dic3⋊4D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).26(S3xC10)480,760
(C2×C4).27(S3×C10) = C5×Dic3⋊D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).27(S3xC10)480,763
(C2×C4).28(S3×C10) = C5×S3×C4⋊C4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).28(S3xC10)480,770
(C2×C4).29(S3×C10) = C5×C4⋊C4⋊7S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).29(S3xC10)480,771
(C2×C4).30(S3×C10) = C5×D6⋊Q8φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).30(S3xC10)480,775
(C2×C4).31(S3×C10) = C5×C4⋊C4⋊S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).31(S3xC10)480,777
(C2×C4).32(S3×C10) = C5×C6.Q16φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).32(S3xC10)480,126
(C2×C4).33(S3×C10) = C5×C12.Q8φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).33(S3xC10)480,127
(C2×C4).34(S3×C10) = C5×C6.D8φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).34(S3xC10)480,128
(C2×C4).35(S3×C10) = C5×C6.SD16φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).35(S3xC10)480,129
(C2×C4).36(S3×C10) = C5×C12.53D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C42404(C2xC4).36(S3xC10)480,141
(C2×C4).37(S3×C10) = C5×D12⋊C4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C41204(C2xC4).37(S3xC10)480,144
(C2×C4).38(S3×C10) = C5×D4⋊Dic3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).38(S3xC10)480,151
(C2×C4).39(S3×C10) = C5×Q8⋊2Dic3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).39(S3xC10)480,154
(C2×C4).40(S3×C10) = C5×Q8⋊3Dic3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C41204(C2xC4).40(S3xC10)480,156
(C2×C4).41(S3×C10) = C5×Dic6⋊C4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).41(S3xC10)480,766
(C2×C4).42(S3×C10) = C5×C12⋊Q8φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).42(S3xC10)480,767
(C2×C4).43(S3×C10) = C5×C4.Dic6φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).43(S3xC10)480,769
(C2×C4).44(S3×C10) = C5×Dic3⋊5D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).44(S3xC10)480,772
(C2×C4).45(S3×C10) = C5×S3×M4(2)φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C41204(C2xC4).45(S3xC10)480,785
(C2×C4).46(S3×C10) = C5×D12.C4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C42404(C2xC4).46(S3xC10)480,786
(C2×C4).47(S3×C10) = C10×D4⋊S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).47(S3xC10)480,810
(C2×C4).48(S3×C10) = C10×D4.S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).48(S3xC10)480,812
(C2×C4).49(S3×C10) = C5×D4×Dic3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).49(S3xC10)480,813
(C2×C4).50(S3×C10) = C5×C23.12D6φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).50(S3xC10)480,815
(C2×C4).51(S3×C10) = C5×D6⋊3D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).51(S3xC10)480,817
(C2×C4).52(S3×C10) = C5×C12⋊3D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).52(S3xC10)480,819
(C2×C4).53(S3×C10) = C10×Q8⋊2S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).53(S3xC10)480,820
(C2×C4).54(S3×C10) = C10×C3⋊Q16φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).54(S3xC10)480,822
(C2×C4).55(S3×C10) = C5×Dic3⋊Q8φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).55(S3xC10)480,823
(C2×C4).56(S3×C10) = C5×Q8×Dic3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4480(C2xC4).56(S3xC10)480,824
(C2×C4).57(S3×C10) = C5×C12.23D4φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).57(S3xC10)480,826
(C2×C4).58(S3×C10) = C5×D4.Dic3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C42404(C2xC4).58(S3xC10)480,827
(C2×C4).59(S3×C10) = C5×Q8.13D6φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C42404(C2xC4).59(S3xC10)480,829
(C2×C4).60(S3×C10) = C10×D4⋊2S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).60(S3xC10)480,1155
(C2×C4).61(S3×C10) = S3×Q8×C10φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).61(S3xC10)480,1157
(C2×C4).62(S3×C10) = C10×Q8⋊3S3φ: S3×C10/C5×S3 → C2 ⊆ Aut C2×C4240(C2xC4).62(S3xC10)480,1158
(C2×C4).63(S3×C10) = C5×C12.6Q8φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).63(S3xC10)480,749
(C2×C4).64(S3×C10) = C5×C42⋊2S3φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).64(S3xC10)480,751
(C2×C4).65(S3×C10) = C5×C42⋊7S3φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).65(S3xC10)480,754
(C2×C4).66(S3×C10) = C5×C42⋊3S3φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).66(S3xC10)480,755
(C2×C4).67(S3×C10) = C10×Dic3⋊C4φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).67(S3xC10)480,802
(C2×C4).68(S3×C10) = C5×C23.28D6φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).68(S3xC10)480,808
(C2×C4).69(S3×C10) = C5×C42⋊4S3φ: S3×C10/C30 → C2 ⊆ Aut C2×C41202(C2xC4).69(S3xC10)480,124
(C2×C4).70(S3×C10) = C5×C2.Dic12φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).70(S3xC10)480,135
(C2×C4).71(S3×C10) = C5×C8⋊Dic3φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).71(S3xC10)480,136
(C2×C4).72(S3×C10) = C5×C24⋊1C4φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).72(S3xC10)480,137
(C2×C4).73(S3×C10) = C5×C24.C4φ: S3×C10/C30 → C2 ⊆ Aut C2×C42402(C2xC4).73(S3xC10)480,138
(C2×C4).74(S3×C10) = C5×C2.D24φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).74(S3xC10)480,140
(C2×C4).75(S3×C10) = C20×Dic6φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).75(S3xC10)480,747
(C2×C4).76(S3×C10) = C5×C12⋊2Q8φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).76(S3xC10)480,748
(C2×C4).77(S3×C10) = C20×D12φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).77(S3xC10)480,752
(C2×C4).78(S3×C10) = C5×C4⋊D12φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).78(S3xC10)480,753
(C2×C4).79(S3×C10) = C5×C8○D12φ: S3×C10/C30 → C2 ⊆ Aut C2×C42402(C2xC4).79(S3xC10)480,780
(C2×C4).80(S3×C10) = C10×C24⋊C2φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).80(S3xC10)480,781
(C2×C4).81(S3×C10) = C10×D24φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).81(S3xC10)480,782
(C2×C4).82(S3×C10) = C5×C4○D24φ: S3×C10/C30 → C2 ⊆ Aut C2×C42402(C2xC4).82(S3xC10)480,783
(C2×C4).83(S3×C10) = C10×Dic12φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).83(S3xC10)480,784
(C2×C4).84(S3×C10) = C10×C4.Dic3φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).84(S3xC10)480,800
(C2×C4).85(S3×C10) = C5×C12.48D4φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).85(S3xC10)480,803
(C2×C4).86(S3×C10) = C10×C4⋊Dic3φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).86(S3xC10)480,804
(C2×C4).87(S3×C10) = C5×C12⋊7D4φ: S3×C10/C30 → C2 ⊆ Aut C2×C4240(C2xC4).87(S3xC10)480,809
(C2×C4).88(S3×C10) = C2×C10×Dic6φ: S3×C10/C30 → C2 ⊆ Aut C2×C4480(C2xC4).88(S3xC10)480,1150
(C2×C4).89(S3×C10) = C20×C3⋊C8central extension (φ=1)480(C2xC4).89(S3xC10)480,121
(C2×C4).90(S3×C10) = C5×C42.S3central extension (φ=1)480(C2xC4).90(S3xC10)480,122
(C2×C4).91(S3×C10) = C5×C12⋊C8central extension (φ=1)480(C2xC4).91(S3xC10)480,123
(C2×C4).92(S3×C10) = Dic3×C40central extension (φ=1)480(C2xC4).92(S3xC10)480,132
(C2×C4).93(S3×C10) = C5×Dic3⋊C8central extension (φ=1)480(C2xC4).93(S3xC10)480,133
(C2×C4).94(S3×C10) = C5×C24⋊C4central extension (φ=1)480(C2xC4).94(S3xC10)480,134
(C2×C4).95(S3×C10) = C5×D6⋊C8central extension (φ=1)240(C2xC4).95(S3xC10)480,139
(C2×C4).96(S3×C10) = C5×C12.55D4central extension (φ=1)240(C2xC4).96(S3xC10)480,149
(C2×C4).97(S3×C10) = S3×C4×C20central extension (φ=1)240(C2xC4).97(S3xC10)480,750
(C2×C4).98(S3×C10) = S3×C2×C40central extension (φ=1)240(C2xC4).98(S3xC10)480,778
(C2×C4).99(S3×C10) = C10×C8⋊S3central extension (φ=1)240(C2xC4).99(S3xC10)480,779
(C2×C4).100(S3×C10) = C2×C10×C3⋊C8central extension (φ=1)480(C2xC4).100(S3xC10)480,799
(C2×C4).101(S3×C10) = Dic3×C2×C20central extension (φ=1)480(C2xC4).101(S3xC10)480,801
(C2×C4).102(S3×C10) = C5×C23.26D6central extension (φ=1)240(C2xC4).102(S3xC10)480,805
(C2×C4).103(S3×C10) = C20×C3⋊D4central extension (φ=1)240(C2xC4).103(S3xC10)480,807

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