# Extensions 1→N→G→Q→1 with N=C5×C10 and Q=C2×C4

Direct product G=N×Q with N=C5×C10 and Q=C2×C4
dρLabelID
C2×C10×C20400C2xC10xC20400,201

Semidirect products G=N:Q with N=C5×C10 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C5×C10)⋊1(C2×C4) = C2×D5×F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10408+(C5xC10):1(C2xC4)400,209
(C5×C10)⋊2(C2×C4) = C2×D5⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10208+(C5xC10):2(C2xC4)400,210
(C5×C10)⋊3(C2×C4) = F5×C2×C10φ: C2×C4/C2C4 ⊆ Aut C5×C1080(C5xC10):3(C2xC4)400,214
(C5×C10)⋊4(C2×C4) = C22×D5.D5φ: C2×C4/C2C4 ⊆ Aut C5×C1080(C5xC10):4(C2xC4)400,215
(C5×C10)⋊5(C2×C4) = C22×C5⋊F5φ: C2×C4/C2C4 ⊆ Aut C5×C10100(C5xC10):5(C2xC4)400,216
(C5×C10)⋊6(C2×C4) = C22×C52⋊C4φ: C2×C4/C2C4 ⊆ Aut C5×C1040(C5xC10):6(C2xC4)400,217
(C5×C10)⋊7(C2×C4) = C2×D5×Dic5φ: C2×C4/C2C22 ⊆ Aut C5×C1080(C5xC10):7(C2xC4)400,172
(C5×C10)⋊8(C2×C4) = C2×Dic52D5φ: C2×C4/C2C22 ⊆ Aut C5×C1040(C5xC10):8(C2xC4)400,175
(C5×C10)⋊9(C2×C4) = D5×C2×C20φ: C2×C4/C4C2 ⊆ Aut C5×C1080(C5xC10):9(C2xC4)400,182
(C5×C10)⋊10(C2×C4) = C2×C4×C5⋊D5φ: C2×C4/C4C2 ⊆ Aut C5×C10200(C5xC10):10(C2xC4)400,192
(C5×C10)⋊11(C2×C4) = Dic5×C2×C10φ: C2×C4/C22C2 ⊆ Aut C5×C1080(C5xC10):11(C2xC4)400,189
(C5×C10)⋊12(C2×C4) = C22×C526C4φ: C2×C4/C22C2 ⊆ Aut C5×C10400(C5xC10):12(C2xC4)400,199

Non-split extensions G=N.Q with N=C5×C10 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C5×C10).1(C2×C4) = Dic5×F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10808-(C5xC10).1(C2xC4)400,117
(C5×C10).2(C2×C4) = D5.D20φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10408+(C5xC10).2(C2xC4)400,118
(C5×C10).3(C2×C4) = D5.Dic10φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10808-(C5xC10).3(C2xC4)400,119
(C5×C10).4(C2×C4) = D5×C5⋊C8φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10808-(C5xC10).4(C2xC4)400,120
(C5×C10).5(C2×C4) = Dic5.4F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10408+(C5xC10).5(C2xC4)400,121
(C5×C10).6(C2×C4) = D10.F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10808-(C5xC10).6(C2xC4)400,122
(C5×C10).7(C2×C4) = Dic5.F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10408+(C5xC10).7(C2xC4)400,123
(C5×C10).8(C2×C4) = C523C42φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10208+(C5xC10).8(C2xC4)400,124
(C5×C10).9(C2×C4) = D10⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10208+(C5xC10).9(C2xC4)400,125
(C5×C10).10(C2×C4) = Dic5⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10208+(C5xC10).10(C2xC4)400,126
(C5×C10).11(C2×C4) = D10.2F5φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10808-(C5xC10).11(C2xC4)400,127
(C5×C10).12(C2×C4) = C524M4(2)φ: C2×C4/C1C2×C4 ⊆ Aut C5×C10808-(C5xC10).12(C2xC4)400,128
(C5×C10).13(C2×C4) = C5×D5⋊C8φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).13(C2xC4)400,135
(C5×C10).14(C2×C4) = C5×C4.F5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).14(C2xC4)400,136
(C5×C10).15(C2×C4) = C20×F5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).15(C2xC4)400,137
(C5×C10).16(C2×C4) = C5×C4⋊F5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).16(C2xC4)400,138
(C5×C10).17(C2×C4) = C10×C5⋊C8φ: C2×C4/C2C4 ⊆ Aut C5×C1080(C5xC10).17(C2xC4)400,139
(C5×C10).18(C2×C4) = C5×C22.F5φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).18(C2xC4)400,140
(C5×C10).19(C2×C4) = C5×C22⋊F5φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).19(C2xC4)400,141
(C5×C10).20(C2×C4) = C20.14F5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).20(C2xC4)400,142
(C5×C10).21(C2×C4) = C20.12F5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).21(C2xC4)400,143
(C5×C10).22(C2×C4) = C4×D5.D5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).22(C2xC4)400,144
(C5×C10).23(C2×C4) = C205F5φ: C2×C4/C2C4 ⊆ Aut C5×C10804(C5xC10).23(C2xC4)400,145
(C5×C10).24(C2×C4) = C2×C523C8φ: C2×C4/C2C4 ⊆ Aut C5×C1080(C5xC10).24(C2xC4)400,146
(C5×C10).25(C2×C4) = C102.C4φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).25(C2xC4)400,147
(C5×C10).26(C2×C4) = D10.D10φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).26(C2xC4)400,148
(C5×C10).27(C2×C4) = C20.F5φ: C2×C4/C2C4 ⊆ Aut C5×C10200(C5xC10).27(C2xC4)400,149
(C5×C10).28(C2×C4) = C527M4(2)φ: C2×C4/C2C4 ⊆ Aut C5×C10200(C5xC10).28(C2xC4)400,150
(C5×C10).29(C2×C4) = C4×C5⋊F5φ: C2×C4/C2C4 ⊆ Aut C5×C10100(C5xC10).29(C2xC4)400,151
(C5×C10).30(C2×C4) = C20⋊F5φ: C2×C4/C2C4 ⊆ Aut C5×C10100(C5xC10).30(C2xC4)400,152
(C5×C10).31(C2×C4) = C2×C524C8φ: C2×C4/C2C4 ⊆ Aut C5×C10400(C5xC10).31(C2xC4)400,153
(C5×C10).32(C2×C4) = C5213M4(2)φ: C2×C4/C2C4 ⊆ Aut C5×C10200(C5xC10).32(C2xC4)400,154
(C5×C10).33(C2×C4) = C102⋊C4φ: C2×C4/C2C4 ⊆ Aut C5×C10100(C5xC10).33(C2xC4)400,155
(C5×C10).34(C2×C4) = C20.11F5φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).34(C2xC4)400,156
(C5×C10).35(C2×C4) = C528M4(2)φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).35(C2xC4)400,157
(C5×C10).36(C2×C4) = C4×C52⋊C4φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).36(C2xC4)400,158
(C5×C10).37(C2×C4) = C202F5φ: C2×C4/C2C4 ⊆ Aut C5×C10404(C5xC10).37(C2xC4)400,159
(C5×C10).38(C2×C4) = C2×C525C8φ: C2×C4/C2C4 ⊆ Aut C5×C1080(C5xC10).38(C2xC4)400,160
(C5×C10).39(C2×C4) = C5214M4(2)φ: C2×C4/C2C4 ⊆ Aut C5×C10404-(C5xC10).39(C2xC4)400,161
(C5×C10).40(C2×C4) = C1024C4φ: C2×C4/C2C4 ⊆ Aut C5×C10204+(C5xC10).40(C2xC4)400,162
(C5×C10).41(C2×C4) = D5×C52C8φ: C2×C4/C2C22 ⊆ Aut C5×C10804(C5xC10).41(C2xC4)400,60
(C5×C10).42(C2×C4) = C20.29D10φ: C2×C4/C2C22 ⊆ Aut C5×C10404(C5xC10).42(C2xC4)400,61
(C5×C10).43(C2×C4) = C20.30D10φ: C2×C4/C2C22 ⊆ Aut C5×C10804(C5xC10).43(C2xC4)400,62
(C5×C10).44(C2×C4) = C20.31D10φ: C2×C4/C2C22 ⊆ Aut C5×C10404(C5xC10).44(C2xC4)400,63
(C5×C10).45(C2×C4) = Dic52φ: C2×C4/C2C22 ⊆ Aut C5×C1080(C5xC10).45(C2xC4)400,71
(C5×C10).46(C2×C4) = D10⋊Dic5φ: C2×C4/C2C22 ⊆ Aut C5×C1080(C5xC10).46(C2xC4)400,72
(C5×C10).47(C2×C4) = C10.D20φ: C2×C4/C2C22 ⊆ Aut C5×C1040(C5xC10).47(C2xC4)400,73
(C5×C10).48(C2×C4) = Dic5⋊Dic5φ: C2×C4/C2C22 ⊆ Aut C5×C1080(C5xC10).48(C2xC4)400,74
(C5×C10).49(C2×C4) = C10.Dic10φ: C2×C4/C2C22 ⊆ Aut C5×C1080(C5xC10).49(C2xC4)400,75
(C5×C10).50(C2×C4) = D5×C40φ: C2×C4/C4C2 ⊆ Aut C5×C10802(C5xC10).50(C2xC4)400,76
(C5×C10).51(C2×C4) = C5×C8⋊D5φ: C2×C4/C4C2 ⊆ Aut C5×C10802(C5xC10).51(C2xC4)400,77
(C5×C10).52(C2×C4) = Dic5×C20φ: C2×C4/C4C2 ⊆ Aut C5×C1080(C5xC10).52(C2xC4)400,83
(C5×C10).53(C2×C4) = C5×C10.D4φ: C2×C4/C4C2 ⊆ Aut C5×C1080(C5xC10).53(C2xC4)400,84
(C5×C10).54(C2×C4) = C5×D10⋊C4φ: C2×C4/C4C2 ⊆ Aut C5×C1080(C5xC10).54(C2xC4)400,86
(C5×C10).55(C2×C4) = C8×C5⋊D5φ: C2×C4/C4C2 ⊆ Aut C5×C10200(C5xC10).55(C2xC4)400,92
(C5×C10).56(C2×C4) = C40⋊D5φ: C2×C4/C4C2 ⊆ Aut C5×C10200(C5xC10).56(C2xC4)400,93
(C5×C10).57(C2×C4) = C4×C526C4φ: C2×C4/C4C2 ⊆ Aut C5×C10400(C5xC10).57(C2xC4)400,99
(C5×C10).58(C2×C4) = C102.22C22φ: C2×C4/C4C2 ⊆ Aut C5×C10400(C5xC10).58(C2xC4)400,100
(C5×C10).59(C2×C4) = C10.11D20φ: C2×C4/C4C2 ⊆ Aut C5×C10200(C5xC10).59(C2xC4)400,102
(C5×C10).60(C2×C4) = C10×C52C8φ: C2×C4/C22C2 ⊆ Aut C5×C1080(C5xC10).60(C2xC4)400,81
(C5×C10).61(C2×C4) = C5×C4.Dic5φ: C2×C4/C22C2 ⊆ Aut C5×C10402(C5xC10).61(C2xC4)400,82
(C5×C10).62(C2×C4) = C5×C4⋊Dic5φ: C2×C4/C22C2 ⊆ Aut C5×C1080(C5xC10).62(C2xC4)400,85
(C5×C10).63(C2×C4) = C5×C23.D5φ: C2×C4/C22C2 ⊆ Aut C5×C1040(C5xC10).63(C2xC4)400,91
(C5×C10).64(C2×C4) = C2×C527C8φ: C2×C4/C22C2 ⊆ Aut C5×C10400(C5xC10).64(C2xC4)400,97
(C5×C10).65(C2×C4) = C20.59D10φ: C2×C4/C22C2 ⊆ Aut C5×C10200(C5xC10).65(C2xC4)400,98
(C5×C10).66(C2×C4) = C203Dic5φ: C2×C4/C22C2 ⊆ Aut C5×C10400(C5xC10).66(C2xC4)400,101
(C5×C10).67(C2×C4) = C10211C4φ: C2×C4/C22C2 ⊆ Aut C5×C10200(C5xC10).67(C2xC4)400,107
(C5×C10).68(C2×C4) = C22⋊C4×C52central extension (φ=1)200(C5xC10).68(C2xC4)400,109
(C5×C10).69(C2×C4) = C4⋊C4×C52central extension (φ=1)400(C5xC10).69(C2xC4)400,110
(C5×C10).70(C2×C4) = M4(2)×C52central extension (φ=1)200(C5xC10).70(C2xC4)400,112

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