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Extensions 1→N→G→Q→1 with N=C20 and Q=C2×C8

Direct product G=N×Q with N=C20 and Q=C2×C8
dρLabelID
C2×C4×C40320C2xC4xC40320,903

Semidirect products G=N:Q with N=C20 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
C20⋊1(C2×C8) = D20⋊2C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20160C20:1(C2xC8)320,1040
C20⋊2(C2×C8) = D4×C5⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20160C20:2(C2xC8)320,1110
C20⋊3(C2×C8) = C42.11F5φ: C2×C8/C4 → C4 ⊆ Aut C20160C20:3(C2xC8)320,1017
C20⋊4(C2×C8) = C4×D5⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C20160C20:4(C2xC8)320,1013
C20⋊5(C2×C8) = D5×C4⋊C8φ: C2×C8/C4 → C22 ⊆ Aut C20160C20:5(C2xC8)320,459
C20⋊6(C2×C8) = D20⋊5C8φ: C2×C8/C4 → C22 ⊆ Aut C20160C20:6(C2xC8)320,461
C20⋊7(C2×C8) = D4×C5⋊2C8φ: C2×C8/C4 → C22 ⊆ Aut C20160C20:7(C2xC8)320,637
C20⋊8(C2×C8) = C2×C20⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C20320C20:8(C2xC8)320,1085
C20⋊9(C2×C8) = C2×C4×C5⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C20320C20:9(C2xC8)320,1084
C20⋊10(C2×C8) = C8×D20φ: C2×C8/C8 → C2 ⊆ Aut C20160C20:10(C2xC8)320,313
C20⋊11(C2×C8) = D5×C4×C8φ: C2×C8/C8 → C2 ⊆ Aut C20160C20:11(C2xC8)320,311
C20⋊12(C2×C8) = D4×C40φ: C2×C8/C8 → C2 ⊆ Aut C20160C20:12(C2xC8)320,935
C20⋊13(C2×C8) = C2×C20⋊3C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20:13(C2xC8)320,550
C20⋊14(C2×C8) = C2×C4×C5⋊2C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20:14(C2xC8)320,547
C20⋊15(C2×C8) = C10×C4⋊C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20:15(C2xC8)320,923

Non-split extensions G=N.Q with N=C20 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
C20.1(C2×C8) = D20⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20160C20.1(C2xC8)320,209
C20.2(C2×C8) = Dic10⋊1C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20320C20.2(C2xC8)320,210
C20.3(C2×C8) = D20.C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C201608C20.3(C2xC8)320,236
C20.4(C2×C8) = Dic5.23D8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20160C20.4(C2xC8)320,262
C20.5(C2×C8) = Dic5.12Q16φ: C2×C8/C2 → C2×C4 ⊆ Aut C20320C20.5(C2xC8)320,268
C20.6(C2×C8) = D4.(C5⋊C8)φ: C2×C8/C2 → C2×C4 ⊆ Aut C201608C20.6(C2xC8)320,270
C20.7(C2×C8) = Dic10⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20320C20.7(C2xC8)320,1041
C20.8(C2×C8) = Dic10.C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C201608C20.8(C2xC8)320,1063
C20.9(C2×C8) = Q8×C5⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C20320C20.9(C2xC8)320,1124
C20.10(C2×C8) = C5⋊C16.C22φ: C2×C8/C2 → C2×C4 ⊆ Aut C201608C20.10(C2xC8)320,1129
C20.11(C2×C8) = C42.9F5φ: C2×C8/C4 → C4 ⊆ Aut C20804C20.11(C2xC8)320,199
C20.12(C2×C8) = C20.26M4(2)φ: C2×C8/C4 → C4 ⊆ Aut C20320C20.12(C2xC8)320,221
C20.13(C2×C8) = Dic5.13D8φ: C2×C8/C4 → C4 ⊆ Aut C20320C20.13(C2xC8)320,222
C20.14(C2×C8) = C42.12F5φ: C2×C8/C4 → C4 ⊆ Aut C20160C20.14(C2xC8)320,1018
C20.15(C2×C8) = D5⋊M5(2)φ: C2×C8/C4 → C4 ⊆ Aut C20804C20.15(C2xC8)320,1053
C20.16(C2×C8) = D5⋊C32φ: C2×C8/C4 → C4 ⊆ Aut C201604C20.16(C2xC8)320,179
C20.17(C2×C8) = C80.C4φ: C2×C8/C4 → C4 ⊆ Aut C201604C20.17(C2xC8)320,180
C20.18(C2×C8) = C4×C5⋊C16φ: C2×C8/C4 → C4 ⊆ Aut C20320C20.18(C2xC8)320,195
C20.19(C2×C8) = C42.4F5φ: C2×C8/C4 → C4 ⊆ Aut C20320C20.19(C2xC8)320,197
C20.20(C2×C8) = C8×C5⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C20320C20.20(C2xC8)320,216
C20.21(C2×C8) = C40⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C20320C20.21(C2xC8)320,217
C20.22(C2×C8) = C42.6F5φ: C2×C8/C4 → C4 ⊆ Aut C20160C20.22(C2xC8)320,1016
C20.23(C2×C8) = C2×D5⋊C16φ: C2×C8/C4 → C4 ⊆ Aut C20160C20.23(C2xC8)320,1051
C20.24(C2×C8) = C2×C8.F5φ: C2×C8/C4 → C4 ⊆ Aut C20160C20.24(C2xC8)320,1052
C20.25(C2×C8) = C20.53D8φ: C2×C8/C4 → C22 ⊆ Aut C20320C20.25(C2xC8)320,37
C20.26(C2×C8) = C20.39SD16φ: C2×C8/C4 → C22 ⊆ Aut C20320C20.26(C2xC8)320,38
C20.27(C2×C8) = D20⋊4C8φ: C2×C8/C4 → C22 ⊆ Aut C20160C20.27(C2xC8)320,41
C20.28(C2×C8) = Dic10⋊4C8φ: C2×C8/C4 → C22 ⊆ Aut C20320C20.28(C2xC8)320,42
C20.29(C2×C8) = C40.9Q8φ: C2×C8/C4 → C22 ⊆ Aut C20804C20.29(C2xC8)320,69
C20.30(C2×C8) = D20.4C8φ: C2×C8/C4 → C22 ⊆ Aut C201604C20.30(C2xC8)320,73
C20.31(C2×C8) = C20.57D8φ: C2×C8/C4 → C22 ⊆ Aut C20160C20.31(C2xC8)320,92
C20.32(C2×C8) = C20.26Q16φ: C2×C8/C4 → C22 ⊆ Aut C20320C20.32(C2xC8)320,93
C20.33(C2×C8) = C40.92D4φ: C2×C8/C4 → C22 ⊆ Aut C201604C20.33(C2xC8)320,119
C20.34(C2×C8) = Dic10⋊5C8φ: C2×C8/C4 → C22 ⊆ Aut C20320C20.34(C2xC8)320,457
C20.35(C2×C8) = C42.200D10φ: C2×C8/C4 → C22 ⊆ Aut C20160C20.35(C2xC8)320,460
C20.36(C2×C8) = D5×M5(2)φ: C2×C8/C4 → C22 ⊆ Aut C20804C20.36(C2xC8)320,533
C20.37(C2×C8) = D20.5C8φ: C2×C8/C4 → C22 ⊆ Aut C201604C20.37(C2xC8)320,534
C20.38(C2×C8) = Q8×C5⋊2C8φ: C2×C8/C4 → C22 ⊆ Aut C20320C20.38(C2xC8)320,650
C20.39(C2×C8) = C40.70C23φ: C2×C8/C4 → C22 ⊆ Aut C201604C20.39(C2xC8)320,767
C20.40(C2×C8) = C40⋊2C8φ: C2×C8/C22 → C4 ⊆ Aut C20320C20.40(C2xC8)320,219
C20.41(C2×C8) = C40⋊1C8φ: C2×C8/C22 → C4 ⊆ Aut C20320C20.41(C2xC8)320,220
C20.42(C2×C8) = C40.1C8φ: C2×C8/C22 → C4 ⊆ Aut C20804C20.42(C2xC8)320,227
C20.43(C2×C8) = C2×C20.C8φ: C2×C8/C22 → C4 ⊆ Aut C20160C20.43(C2xC8)320,1081
C20.44(C2×C8) = Dic5.12M4(2)φ: C2×C8/C22 → C4 ⊆ Aut C20160C20.44(C2xC8)320,1086
C20.45(C2×C8) = C2×C5⋊C32φ: C2×C8/C22 → C4 ⊆ Aut C20320C20.45(C2xC8)320,214
C20.46(C2×C8) = C5⋊M6(2)φ: C2×C8/C22 → C4 ⊆ Aut C201604C20.46(C2xC8)320,215
C20.47(C2×C8) = Dic5⋊C16φ: C2×C8/C22 → C4 ⊆ Aut C20320C20.47(C2xC8)320,223
C20.48(C2×C8) = C40.C8φ: C2×C8/C22 → C4 ⊆ Aut C20320C20.48(C2xC8)320,224
C20.49(C2×C8) = C22×C5⋊C16φ: C2×C8/C22 → C4 ⊆ Aut C20320C20.49(C2xC8)320,1080
C20.50(C2×C8) = Dic10⋊3C8φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.50(C2xC8)320,14
C20.51(C2×C8) = D20⋊3C8φ: C2×C8/C8 → C2 ⊆ Aut C20160C20.51(C2xC8)320,17
C20.52(C2×C8) = D20.3C8φ: C2×C8/C8 → C2 ⊆ Aut C201602C20.52(C2xC8)320,66
C20.53(C2×C8) = C8×Dic10φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.53(C2xC8)320,305
C20.54(C2×C8) = D20.6C8φ: C2×C8/C8 → C2 ⊆ Aut C201602C20.54(C2xC8)320,528
C20.55(C2×C8) = D5×C32φ: C2×C8/C8 → C2 ⊆ Aut C201602C20.55(C2xC8)320,4
C20.56(C2×C8) = C32⋊D5φ: C2×C8/C8 → C2 ⊆ Aut C201602C20.56(C2xC8)320,5
C20.57(C2×C8) = C8×C5⋊2C8φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.57(C2xC8)320,11
C20.58(C2×C8) = C42.279D10φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.58(C2xC8)320,12
C20.59(C2×C8) = C16×Dic5φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.59(C2xC8)320,58
C20.60(C2×C8) = C80⋊17C4φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.60(C2xC8)320,60
C20.61(C2×C8) = C42.282D10φ: C2×C8/C8 → C2 ⊆ Aut C20160C20.61(C2xC8)320,312
C20.62(C2×C8) = D5×C2×C16φ: C2×C8/C8 → C2 ⊆ Aut C20160C20.62(C2xC8)320,526
C20.63(C2×C8) = C2×C80⋊C2φ: C2×C8/C8 → C2 ⊆ Aut C20160C20.63(C2xC8)320,527
C20.64(C2×C8) = C5×D4⋊C8φ: C2×C8/C8 → C2 ⊆ Aut C20160C20.64(C2xC8)320,130
C20.65(C2×C8) = C5×Q8⋊C8φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.65(C2xC8)320,131
C20.66(C2×C8) = C5×D4.C8φ: C2×C8/C8 → C2 ⊆ Aut C201602C20.66(C2xC8)320,155
C20.67(C2×C8) = Q8×C40φ: C2×C8/C8 → C2 ⊆ Aut C20320C20.67(C2xC8)320,946
C20.68(C2×C8) = C5×D4○C16φ: C2×C8/C8 → C2 ⊆ Aut C201602C20.68(C2xC8)320,1005
C20.69(C2×C8) = C40⋊6C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.69(C2xC8)320,15
C20.70(C2×C8) = C40⋊5C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.70(C2xC8)320,16
C20.71(C2×C8) = C40.7C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20802C20.71(C2xC8)320,21
C20.72(C2×C8) = C42.6Dic5φ: C2×C8/C2×C4 → C2 ⊆ Aut C20160C20.72(C2xC8)320,552
C20.73(C2×C8) = C40⋊8C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.73(C2xC8)320,13
C20.74(C2×C8) = C4×C5⋊2C16φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.74(C2xC8)320,18
C20.75(C2×C8) = C40.10C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.75(C2xC8)320,19
C20.76(C2×C8) = C2×C5⋊2C32φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.76(C2xC8)320,56
C20.77(C2×C8) = C80.9C4φ: C2×C8/C2×C4 → C2 ⊆ Aut C201602C20.77(C2xC8)320,57
C20.78(C2×C8) = C22×C5⋊2C16φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.78(C2xC8)320,723
C20.79(C2×C8) = C2×C20.4C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20160C20.79(C2xC8)320,724
C20.80(C2×C8) = C5×C8⋊2C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.80(C2xC8)320,139
C20.81(C2×C8) = C5×C8⋊1C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20320C20.81(C2xC8)320,140
C20.82(C2×C8) = C5×C8.C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C20802C20.82(C2xC8)320,169
C20.83(C2×C8) = C5×C42.12C4φ: C2×C8/C2×C4 → C2 ⊆ Aut C20160C20.83(C2xC8)320,932
C20.84(C2×C8) = C10×M5(2)φ: C2×C8/C2×C4 → C2 ⊆ Aut C20160C20.84(C2xC8)320,1004
C20.85(C2×C8) = C5×C8⋊C8central extension (φ=1)320C20.85(C2xC8)320,127
C20.86(C2×C8) = C5×C16⋊5C4central extension (φ=1)320C20.86(C2xC8)320,151
C20.87(C2×C8) = C5×M6(2)central extension (φ=1)1602C20.87(C2xC8)320,175

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