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

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

Semidirect products G=N:Q with N=C2×C10 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C2×C4) = D4×F5φ: C2×C4/C1C2×C4 ⊆ Aut C2×C10208+(C2xC10):(C2xC4)160,207
(C2×C10)⋊2(C2×C4) = C2×C22⋊F5φ: C2×C4/C2C4 ⊆ Aut C2×C1040(C2xC10):2(C2xC4)160,212
(C2×C10)⋊3(C2×C4) = C23×F5φ: C2×C4/C2C4 ⊆ Aut C2×C1040(C2xC10):3(C2xC4)160,236
(C2×C10)⋊4(C2×C4) = D5×C22⋊C4φ: C2×C4/C2C22 ⊆ Aut C2×C1040(C2xC10):4(C2xC4)160,101
(C2×C10)⋊5(C2×C4) = Dic54D4φ: C2×C4/C2C22 ⊆ Aut C2×C1080(C2xC10):5(C2xC4)160,102
(C2×C10)⋊6(C2×C4) = D4×Dic5φ: C2×C4/C2C22 ⊆ Aut C2×C1080(C2xC10):6(C2xC4)160,155
(C2×C10)⋊7(C2×C4) = D4×C20φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10):7(C2xC4)160,179
(C2×C10)⋊8(C2×C4) = C4×C5⋊D4φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10):8(C2xC4)160,149
(C2×C10)⋊9(C2×C4) = D5×C22×C4φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10):9(C2xC4)160,214
(C2×C10)⋊10(C2×C4) = C10×C22⋊C4φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10):10(C2xC4)160,176
(C2×C10)⋊11(C2×C4) = C2×C23.D5φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10):11(C2xC4)160,173
(C2×C10)⋊12(C2×C4) = C23×Dic5φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10):12(C2xC4)160,226

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C2×C10).(C2×C4) = D4.F5φ: C2×C4/C1C2×C4 ⊆ Aut C2×C10808-(C2xC10).(C2xC4)160,206
(C2×C10).2(C2×C4) = D10.D4φ: C2×C4/C2C4 ⊆ Aut C2×C10404+(C2xC10).2(C2xC4)160,74
(C2×C10).3(C2×C4) = C4×C5⋊C8φ: C2×C4/C2C4 ⊆ Aut C2×C10160(C2xC10).3(C2xC4)160,75
(C2×C10).4(C2×C4) = C20⋊C8φ: C2×C4/C2C4 ⊆ Aut C2×C10160(C2xC10).4(C2xC4)160,76
(C2×C10).5(C2×C4) = C10.C42φ: C2×C4/C2C4 ⊆ Aut C2×C10160(C2xC10).5(C2xC4)160,77
(C2×C10).6(C2×C4) = D10⋊C8φ: C2×C4/C2C4 ⊆ Aut C2×C1080(C2xC10).6(C2xC4)160,78
(C2×C10).7(C2×C4) = Dic5⋊C8φ: C2×C4/C2C4 ⊆ Aut C2×C10160(C2xC10).7(C2xC4)160,79
(C2×C10).8(C2×C4) = Dic5.D4φ: C2×C4/C2C4 ⊆ Aut C2×C10804-(C2xC10).8(C2xC4)160,80
(C2×C10).9(C2×C4) = D10.3Q8φ: C2×C4/C2C4 ⊆ Aut C2×C1040(C2xC10).9(C2xC4)160,81
(C2×C10).10(C2×C4) = C23⋊F5φ: C2×C4/C2C4 ⊆ Aut C2×C10404(C2xC10).10(C2xC4)160,86
(C2×C10).11(C2×C4) = C23.2F5φ: C2×C4/C2C4 ⊆ Aut C2×C1080(C2xC10).11(C2xC4)160,87
(C2×C10).12(C2×C4) = C23.F5φ: C2×C4/C2C4 ⊆ Aut C2×C10404(C2xC10).12(C2xC4)160,88
(C2×C10).13(C2×C4) = C2×D5⋊C8φ: C2×C4/C2C4 ⊆ Aut C2×C1080(C2xC10).13(C2xC4)160,200
(C2×C10).14(C2×C4) = C2×C4.F5φ: C2×C4/C2C4 ⊆ Aut C2×C1080(C2xC10).14(C2xC4)160,201
(C2×C10).15(C2×C4) = D5⋊M4(2)φ: C2×C4/C2C4 ⊆ Aut C2×C10404(C2xC10).15(C2xC4)160,202
(C2×C10).16(C2×C4) = C2×C4×F5φ: C2×C4/C2C4 ⊆ Aut C2×C1040(C2xC10).16(C2xC4)160,203
(C2×C10).17(C2×C4) = C2×C4⋊F5φ: C2×C4/C2C4 ⊆ Aut C2×C1040(C2xC10).17(C2xC4)160,204
(C2×C10).18(C2×C4) = D10.C23φ: C2×C4/C2C4 ⊆ Aut C2×C10404(C2xC10).18(C2xC4)160,205
(C2×C10).19(C2×C4) = C22×C5⋊C8φ: C2×C4/C2C4 ⊆ Aut C2×C10160(C2xC10).19(C2xC4)160,210
(C2×C10).20(C2×C4) = C2×C22.F5φ: C2×C4/C2C4 ⊆ Aut C2×C1080(C2xC10).20(C2xC4)160,211
(C2×C10).21(C2×C4) = C23.1D10φ: C2×C4/C2C22 ⊆ Aut C2×C10404(C2xC10).21(C2xC4)160,13
(C2×C10).22(C2×C4) = C20.46D4φ: C2×C4/C2C22 ⊆ Aut C2×C10404+(C2xC10).22(C2xC4)160,30
(C2×C10).23(C2×C4) = C4.12D20φ: C2×C4/C2C22 ⊆ Aut C2×C10804-(C2xC10).23(C2xC4)160,31
(C2×C10).24(C2×C4) = C23.11D10φ: C2×C4/C2C22 ⊆ Aut C2×C1080(C2xC10).24(C2xC4)160,98
(C2×C10).25(C2×C4) = D5×M4(2)φ: C2×C4/C2C22 ⊆ Aut C2×C10404(C2xC10).25(C2xC4)160,127
(C2×C10).26(C2×C4) = D20.2C4φ: C2×C4/C2C22 ⊆ Aut C2×C10804(C2xC10).26(C2xC4)160,128
(C2×C10).27(C2×C4) = D4.Dic5φ: C2×C4/C2C22 ⊆ Aut C2×C10804(C2xC10).27(C2xC4)160,169
(C2×C10).28(C2×C4) = C5×C8○D4φ: C2×C4/C4C2 ⊆ Aut C2×C10802(C2xC10).28(C2xC4)160,192
(C2×C10).29(C2×C4) = C8×Dic5φ: C2×C4/C4C2 ⊆ Aut C2×C10160(C2xC10).29(C2xC4)160,20
(C2×C10).30(C2×C4) = C20.8Q8φ: C2×C4/C4C2 ⊆ Aut C2×C10160(C2xC10).30(C2xC4)160,21
(C2×C10).31(C2×C4) = C408C4φ: C2×C4/C4C2 ⊆ Aut C2×C10160(C2xC10).31(C2xC4)160,22
(C2×C10).32(C2×C4) = D101C8φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10).32(C2xC4)160,27
(C2×C10).33(C2×C4) = C10.10C42φ: C2×C4/C4C2 ⊆ Aut C2×C10160(C2xC10).33(C2xC4)160,38
(C2×C10).34(C2×C4) = D5×C2×C8φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10).34(C2xC4)160,120
(C2×C10).35(C2×C4) = C2×C8⋊D5φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10).35(C2xC4)160,121
(C2×C10).36(C2×C4) = D20.3C4φ: C2×C4/C4C2 ⊆ Aut C2×C10802(C2xC10).36(C2xC4)160,122
(C2×C10).37(C2×C4) = C2×C10.D4φ: C2×C4/C4C2 ⊆ Aut C2×C10160(C2xC10).37(C2xC4)160,144
(C2×C10).38(C2×C4) = C2×D10⋊C4φ: C2×C4/C4C2 ⊆ Aut C2×C1080(C2xC10).38(C2xC4)160,148
(C2×C10).39(C2×C4) = C5×C23⋊C4φ: C2×C4/C22C2 ⊆ Aut C2×C10404(C2xC10).39(C2xC4)160,49
(C2×C10).40(C2×C4) = C5×C4.D4φ: C2×C4/C22C2 ⊆ Aut C2×C10404(C2xC10).40(C2xC4)160,50
(C2×C10).41(C2×C4) = C5×C4.10D4φ: C2×C4/C22C2 ⊆ Aut C2×C10804(C2xC10).41(C2xC4)160,51
(C2×C10).42(C2×C4) = C5×C42⋊C2φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10).42(C2xC4)160,178
(C2×C10).43(C2×C4) = C10×M4(2)φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10).43(C2xC4)160,191
(C2×C10).44(C2×C4) = C4×C52C8φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10).44(C2xC4)160,9
(C2×C10).45(C2×C4) = C42.D5φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10).45(C2xC4)160,10
(C2×C10).46(C2×C4) = C203C8φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10).46(C2xC4)160,11
(C2×C10).47(C2×C4) = C20.55D4φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10).47(C2xC4)160,37
(C2×C10).48(C2×C4) = C20.D4φ: C2×C4/C22C2 ⊆ Aut C2×C10404(C2xC10).48(C2xC4)160,40
(C2×C10).49(C2×C4) = C23⋊Dic5φ: C2×C4/C22C2 ⊆ Aut C2×C10404(C2xC10).49(C2xC4)160,41
(C2×C10).50(C2×C4) = C20.10D4φ: C2×C4/C22C2 ⊆ Aut C2×C10804(C2xC10).50(C2xC4)160,43
(C2×C10).51(C2×C4) = C22×C52C8φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10).51(C2xC4)160,141
(C2×C10).52(C2×C4) = C2×C4.Dic5φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10).52(C2xC4)160,142
(C2×C10).53(C2×C4) = C2×C4×Dic5φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10).53(C2xC4)160,143
(C2×C10).54(C2×C4) = C2×C4⋊Dic5φ: C2×C4/C22C2 ⊆ Aut C2×C10160(C2xC10).54(C2xC4)160,146
(C2×C10).55(C2×C4) = C23.21D10φ: C2×C4/C22C2 ⊆ Aut C2×C1080(C2xC10).55(C2xC4)160,147
(C2×C10).56(C2×C4) = C5×C2.C42central extension (φ=1)160(C2xC10).56(C2xC4)160,45
(C2×C10).57(C2×C4) = C5×C8⋊C4central extension (φ=1)160(C2xC10).57(C2xC4)160,47
(C2×C10).58(C2×C4) = C5×C22⋊C8central extension (φ=1)80(C2xC10).58(C2xC4)160,48
(C2×C10).59(C2×C4) = C5×C4⋊C8central extension (φ=1)160(C2xC10).59(C2xC4)160,55
(C2×C10).60(C2×C4) = C10×C4⋊C4central extension (φ=1)160(C2xC10).60(C2xC4)160,177

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