# Extensions 1→N→G→Q→1 with N=C20 and Q=C2×C4

Direct product G=N×Q with N=C20 and Q=C2×C4
dρLabelID
C2×C4×C20160C2xC4xC20160,175

Semidirect products G=N:Q with N=C20 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C20⋊(C2×C4) = D4×F5φ: C2×C4/C1C2×C4 ⊆ Aut C20208+C20:(C2xC4)160,207
C202(C2×C4) = C2×C4⋊F5φ: C2×C4/C2C4 ⊆ Aut C2040C20:2(C2xC4)160,204
C203(C2×C4) = C2×C4×F5φ: C2×C4/C2C4 ⊆ Aut C2040C20:3(C2xC4)160,203
C204(C2×C4) = D5×C4⋊C4φ: C2×C4/C2C22 ⊆ Aut C2080C20:4(C2xC4)160,112
C205(C2×C4) = D208C4φ: C2×C4/C2C22 ⊆ Aut C2080C20:5(C2xC4)160,114
C206(C2×C4) = D4×Dic5φ: C2×C4/C2C22 ⊆ Aut C2080C20:6(C2xC4)160,155
C207(C2×C4) = C4×D20φ: C2×C4/C4C2 ⊆ Aut C2080C20:7(C2xC4)160,94
C208(C2×C4) = D5×C42φ: C2×C4/C4C2 ⊆ Aut C2080C20:8(C2xC4)160,92
C209(C2×C4) = D4×C20φ: C2×C4/C4C2 ⊆ Aut C2080C20:9(C2xC4)160,179
C2010(C2×C4) = C2×C4⋊Dic5φ: C2×C4/C22C2 ⊆ Aut C20160C20:10(C2xC4)160,146
C2011(C2×C4) = C2×C4×Dic5φ: C2×C4/C22C2 ⊆ Aut C20160C20:11(C2xC4)160,143
C2012(C2×C4) = C10×C4⋊C4φ: C2×C4/C22C2 ⊆ Aut C20160C20:12(C2xC4)160,177

Non-split extensions G=N.Q with N=C20 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C20.1(C2×C4) = D20⋊C4φ: C2×C4/C1C2×C4 ⊆ Aut C20408+C20.1(C2xC4)160,82
C20.2(C2×C4) = D4⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C20408-C20.2(C2xC4)160,83
C20.3(C2×C4) = Q8⋊F5φ: C2×C4/C1C2×C4 ⊆ Aut C20408-C20.3(C2xC4)160,84
C20.4(C2×C4) = Q82F5φ: C2×C4/C1C2×C4 ⊆ Aut C20408+C20.4(C2xC4)160,85
C20.5(C2×C4) = D4.F5φ: C2×C4/C1C2×C4 ⊆ Aut C20808-C20.5(C2xC4)160,206
C20.6(C2×C4) = Q8.F5φ: C2×C4/C1C2×C4 ⊆ Aut C20808+C20.6(C2xC4)160,208
C20.7(C2×C4) = Q8×F5φ: C2×C4/C1C2×C4 ⊆ Aut C20408-C20.7(C2xC4)160,209
C20.8(C2×C4) = C40⋊C4φ: C2×C4/C2C4 ⊆ Aut C20404C20.8(C2xC4)160,68
C20.9(C2×C4) = D5.D8φ: C2×C4/C2C4 ⊆ Aut C20404C20.9(C2xC4)160,69
C20.10(C2×C4) = C40.C4φ: C2×C4/C2C4 ⊆ Aut C20804C20.10(C2xC4)160,70
C20.11(C2×C4) = D10.Q8φ: C2×C4/C2C4 ⊆ Aut C20804C20.11(C2xC4)160,71
C20.12(C2×C4) = C2×C4.F5φ: C2×C4/C2C4 ⊆ Aut C2080C20.12(C2xC4)160,201
C20.13(C2×C4) = D5⋊C16φ: C2×C4/C2C4 ⊆ Aut C20804C20.13(C2xC4)160,64
C20.14(C2×C4) = C8.F5φ: C2×C4/C2C4 ⊆ Aut C20804C20.14(C2xC4)160,65
C20.15(C2×C4) = C8×F5φ: C2×C4/C2C4 ⊆ Aut C20404C20.15(C2xC4)160,66
C20.16(C2×C4) = C8⋊F5φ: C2×C4/C2C4 ⊆ Aut C20404C20.16(C2xC4)160,67
C20.17(C2×C4) = C2×C5⋊C16φ: C2×C4/C2C4 ⊆ Aut C20160C20.17(C2xC4)160,72
C20.18(C2×C4) = C20.C8φ: C2×C4/C2C4 ⊆ Aut C20804C20.18(C2xC4)160,73
C20.19(C2×C4) = C2×D5⋊C8φ: C2×C4/C2C4 ⊆ Aut C2080C20.19(C2xC4)160,200
C20.20(C2×C4) = D5⋊M4(2)φ: C2×C4/C2C4 ⊆ Aut C20404C20.20(C2xC4)160,202
C20.21(C2×C4) = D10.C23φ: C2×C4/C2C4 ⊆ Aut C20404C20.21(C2xC4)160,205
C20.22(C2×C4) = C10.D8φ: C2×C4/C2C22 ⊆ Aut C20160C20.22(C2xC4)160,14
C20.23(C2×C4) = C20.Q8φ: C2×C4/C2C22 ⊆ Aut C20160C20.23(C2xC4)160,15
C20.24(C2×C4) = D206C4φ: C2×C4/C2C22 ⊆ Aut C2080C20.24(C2xC4)160,16
C20.25(C2×C4) = C10.Q16φ: C2×C4/C2C22 ⊆ Aut C20160C20.25(C2xC4)160,17
C20.26(C2×C4) = C20.53D4φ: C2×C4/C2C22 ⊆ Aut C20804C20.26(C2xC4)160,29
C20.27(C2×C4) = D207C4φ: C2×C4/C2C22 ⊆ Aut C20404C20.27(C2xC4)160,32
C20.28(C2×C4) = D4⋊Dic5φ: C2×C4/C2C22 ⊆ Aut C2080C20.28(C2xC4)160,39
C20.29(C2×C4) = Q8⋊Dic5φ: C2×C4/C2C22 ⊆ Aut C20160C20.29(C2xC4)160,42
C20.30(C2×C4) = D42Dic5φ: C2×C4/C2C22 ⊆ Aut C20404C20.30(C2xC4)160,44
C20.31(C2×C4) = Dic53Q8φ: C2×C4/C2C22 ⊆ Aut C20160C20.31(C2xC4)160,108
C20.32(C2×C4) = C4⋊C47D5φ: C2×C4/C2C22 ⊆ Aut C2080C20.32(C2xC4)160,113
C20.33(C2×C4) = D5×M4(2)φ: C2×C4/C2C22 ⊆ Aut C20404C20.33(C2xC4)160,127
C20.34(C2×C4) = D20.2C4φ: C2×C4/C2C22 ⊆ Aut C20804C20.34(C2xC4)160,128
C20.35(C2×C4) = Q8×Dic5φ: C2×C4/C2C22 ⊆ Aut C20160C20.35(C2xC4)160,166
C20.36(C2×C4) = D4.Dic5φ: C2×C4/C2C22 ⊆ Aut C20804C20.36(C2xC4)160,169
C20.37(C2×C4) = D204C4φ: C2×C4/C4C2 ⊆ Aut C20402C20.37(C2xC4)160,12
C20.38(C2×C4) = C20.44D4φ: C2×C4/C4C2 ⊆ Aut C20160C20.38(C2xC4)160,23
C20.39(C2×C4) = D205C4φ: C2×C4/C4C2 ⊆ Aut C2080C20.39(C2xC4)160,28
C20.40(C2×C4) = C4×Dic10φ: C2×C4/C4C2 ⊆ Aut C20160C20.40(C2xC4)160,89
C20.41(C2×C4) = D20.3C4φ: C2×C4/C4C2 ⊆ Aut C20802C20.41(C2xC4)160,122
C20.42(C2×C4) = D5×C16φ: C2×C4/C4C2 ⊆ Aut C20802C20.42(C2xC4)160,4
C20.43(C2×C4) = C80⋊C2φ: C2×C4/C4C2 ⊆ Aut C20802C20.43(C2xC4)160,5
C20.44(C2×C4) = C4×C52C8φ: C2×C4/C4C2 ⊆ Aut C20160C20.44(C2xC4)160,9
C20.45(C2×C4) = C42.D5φ: C2×C4/C4C2 ⊆ Aut C20160C20.45(C2xC4)160,10
C20.46(C2×C4) = C42⋊D5φ: C2×C4/C4C2 ⊆ Aut C2080C20.46(C2xC4)160,93
C20.47(C2×C4) = D5×C2×C8φ: C2×C4/C4C2 ⊆ Aut C2080C20.47(C2xC4)160,120
C20.48(C2×C4) = C2×C8⋊D5φ: C2×C4/C4C2 ⊆ Aut C2080C20.48(C2xC4)160,121
C20.49(C2×C4) = C5×D4⋊C4φ: C2×C4/C4C2 ⊆ Aut C2080C20.49(C2xC4)160,52
C20.50(C2×C4) = C5×Q8⋊C4φ: C2×C4/C4C2 ⊆ Aut C20160C20.50(C2xC4)160,53
C20.51(C2×C4) = C5×C4≀C2φ: C2×C4/C4C2 ⊆ Aut C20402C20.51(C2xC4)160,54
C20.52(C2×C4) = Q8×C20φ: C2×C4/C4C2 ⊆ Aut C20160C20.52(C2xC4)160,180
C20.53(C2×C4) = C5×C8○D4φ: C2×C4/C4C2 ⊆ Aut C20802C20.53(C2xC4)160,192
C20.54(C2×C4) = C406C4φ: C2×C4/C22C2 ⊆ Aut C20160C20.54(C2xC4)160,24
C20.55(C2×C4) = C405C4φ: C2×C4/C22C2 ⊆ Aut C20160C20.55(C2xC4)160,25
C20.56(C2×C4) = C40.6C4φ: C2×C4/C22C2 ⊆ Aut C20802C20.56(C2xC4)160,26
C20.57(C2×C4) = C2×C4.Dic5φ: C2×C4/C22C2 ⊆ Aut C2080C20.57(C2xC4)160,142
C20.58(C2×C4) = C23.21D10φ: C2×C4/C22C2 ⊆ Aut C2080C20.58(C2xC4)160,147
C20.59(C2×C4) = C2×C52C16φ: C2×C4/C22C2 ⊆ Aut C20160C20.59(C2xC4)160,18
C20.60(C2×C4) = C20.4C8φ: C2×C4/C22C2 ⊆ Aut C20802C20.60(C2xC4)160,19
C20.61(C2×C4) = C8×Dic5φ: C2×C4/C22C2 ⊆ Aut C20160C20.61(C2xC4)160,20
C20.62(C2×C4) = C408C4φ: C2×C4/C22C2 ⊆ Aut C20160C20.62(C2xC4)160,22
C20.63(C2×C4) = C22×C52C8φ: C2×C4/C22C2 ⊆ Aut C20160C20.63(C2xC4)160,141
C20.64(C2×C4) = C5×C4.Q8φ: C2×C4/C22C2 ⊆ Aut C20160C20.64(C2xC4)160,56
C20.65(C2×C4) = C5×C2.D8φ: C2×C4/C22C2 ⊆ Aut C20160C20.65(C2xC4)160,57
C20.66(C2×C4) = C5×C8.C4φ: C2×C4/C22C2 ⊆ Aut C20802C20.66(C2xC4)160,58
C20.67(C2×C4) = C5×C42⋊C2φ: C2×C4/C22C2 ⊆ Aut C2080C20.67(C2xC4)160,178
C20.68(C2×C4) = C10×M4(2)φ: C2×C4/C22C2 ⊆ Aut C2080C20.68(C2xC4)160,191
C20.69(C2×C4) = C5×C8⋊C4central extension (φ=1)160C20.69(C2xC4)160,47
C20.70(C2×C4) = C5×M5(2)central extension (φ=1)802C20.70(C2xC4)160,60

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