# Extensions 1→N→G→Q→1 with N=C20 and Q=C42

Direct product G=N×Q with N=C20 and Q=C42
dρLabelID
C42×C20320C4^2xC20320,875

Semidirect products G=N:Q with N=C20 and Q=C42
extensionφ:Q→Aut NdρLabelID
C20⋊C42 = C4⋊C4×F5φ: C42/C2C2×C4 ⊆ Aut C2080C20:C4^2320,1048
C202C42 = C4×C4⋊F5φ: C42/C4C4 ⊆ Aut C2080C20:2C4^2320,1025
C203C42 = C42×F5φ: C42/C4C4 ⊆ Aut C2080C20:3C4^2320,1023
C204C42 = C4⋊C4×Dic5φ: C42/C22C22 ⊆ Aut C20320C20:4C4^2320,602
C205C42 = C4×C4⋊Dic5φ: C42/C2×C4C2 ⊆ Aut C20320C20:5C4^2320,561
C206C42 = C42×Dic5φ: C42/C2×C4C2 ⊆ Aut C20320C20:6C4^2320,557
C207C42 = C4⋊C4×C20φ: C42/C2×C4C2 ⊆ Aut C20320C20:7C4^2320,879

Non-split extensions G=N.Q with N=C20 and Q=C42
extensionφ:Q→Aut NdρLabelID
C20.1C42 = D10.18D8φ: C42/C2C2×C4 ⊆ Aut C2080C20.1C4^2320,212
C20.2C42 = C20.C42φ: C42/C2C2×C4 ⊆ Aut C2080C20.2C4^2320,213
C20.3C42 = M4(2)⋊3F5φ: C42/C2C2×C4 ⊆ Aut C20408C20.3C4^2320,238
C20.4C42 = M4(2).F5φ: C42/C2C2×C4 ⊆ Aut C20808C20.4C4^2320,239
C20.5C42 = D10.C42φ: C42/C2C2×C4 ⊆ Aut C20160C20.5C4^2320,1039
C20.6C42 = M4(2)×F5φ: C42/C2C2×C4 ⊆ Aut C20408C20.6C4^2320,1064
C20.7C42 = M4(2)⋊5F5φ: C42/C2C2×C4 ⊆ Aut C20808C20.7C4^2320,1066
C20.8C42 = C426F5φ: C42/C4C4 ⊆ Aut C20404C20.8C4^2320,200
C20.9C42 = D10.10D8φ: C42/C4C4 ⊆ Aut C2080C20.9C4^2320,231
C20.10C42 = C20.10C42φ: C42/C4C4 ⊆ Aut C20160C20.10C4^2320,234
C20.11C42 = C4×C4.F5φ: C42/C4C4 ⊆ Aut C20160C20.11C4^2320,1015
C20.12C42 = C20.12C42φ: C42/C4C4 ⊆ Aut C20804C20.12C4^2320,1056
C20.13C42 = C16×F5φ: C42/C4C4 ⊆ Aut C20804C20.13C4^2320,181
C20.14C42 = C167F5φ: C42/C4C4 ⊆ Aut C20804C20.14C4^2320,182
C20.15C42 = C16⋊F5φ: C42/C4C4 ⊆ Aut C20804C20.15C4^2320,183
C20.16C42 = C164F5φ: C42/C4C4 ⊆ Aut C20804C20.16C4^2320,184
C20.17C42 = C4×C5⋊C16φ: C42/C4C4 ⊆ Aut C20320C20.17C4^2320,195
C20.18C42 = C42.4F5φ: C42/C4C4 ⊆ Aut C20320C20.18C4^2320,197
C20.19C42 = C42.3F5φ: C42/C4C4 ⊆ Aut C20804C20.19C4^2320,198
C20.20C42 = C423F5φ: C42/C4C4 ⊆ Aut C20804C20.20C4^2320,201
C20.21C42 = Dic5⋊C16φ: C42/C4C4 ⊆ Aut C20320C20.21C4^2320,223
C20.22C42 = C40.C8φ: C42/C4C4 ⊆ Aut C20320C20.22C4^2320,224
C20.23C42 = C20.23C42φ: C42/C4C4 ⊆ Aut C20804C20.23C4^2320,228
C20.24C42 = C20.24C42φ: C42/C4C4 ⊆ Aut C20804C20.24C4^2320,233
C20.25C42 = C20.25C42φ: C42/C4C4 ⊆ Aut C20804C20.25C4^2320,235
C20.26C42 = C4×D5⋊C8φ: C42/C4C4 ⊆ Aut C20160C20.26C4^2320,1013
C20.27C42 = C42.5F5φ: C42/C4C4 ⊆ Aut C20160C20.27C4^2320,1014
C20.28C42 = C424F5φ: C42/C4C4 ⊆ Aut C2080C20.28C4^2320,1024
C20.29C42 = C2×C8×F5φ: C42/C4C4 ⊆ Aut C2080C20.29C4^2320,1054
C20.30C42 = C2×C8⋊F5φ: C42/C4C4 ⊆ Aut C2080C20.30C4^2320,1055
C20.31C42 = C20.31C42φ: C42/C22C22 ⊆ Aut C20320C20.31C4^2320,87
C20.32C42 = C20.32C42φ: C42/C22C22 ⊆ Aut C2080C20.32C4^2320,90
C20.33C42 = C20.33C42φ: C42/C22C22 ⊆ Aut C2080C20.33C4^2320,113
C20.34C42 = C20.34C42φ: C42/C22C22 ⊆ Aut C20160C20.34C4^2320,116
C20.35C42 = C20.35C42φ: C42/C22C22 ⊆ Aut C20160C20.35C4^2320,624
C20.36C42 = M4(2)×Dic5φ: C42/C22C22 ⊆ Aut C20160C20.36C4^2320,744
C20.37C42 = C20.37C42φ: C42/C22C22 ⊆ Aut C20160C20.37C4^2320,749
C20.38C42 = C426Dic5φ: C42/C2×C4C2 ⊆ Aut C2080C20.38C4^2320,81
C20.39C42 = C20.39C42φ: C42/C2×C4C2 ⊆ Aut C20320C20.39C4^2320,109
C20.40C42 = C20.40C42φ: C42/C2×C4C2 ⊆ Aut C20160C20.40C4^2320,110
C20.41C42 = C4×C4.Dic5φ: C42/C2×C4C2 ⊆ Aut C20160C20.41C4^2320,549
C20.42C42 = C20.42C42φ: C42/C2×C4C2 ⊆ Aut C20160C20.42C4^2320,728
C20.43C42 = C4×C52C16φ: C42/C2×C4C2 ⊆ Aut C20320C20.43C4^2320,18
C20.44C42 = C40.10C8φ: C42/C2×C4C2 ⊆ Aut C20320C20.44C4^2320,19
C20.45C42 = C20.45C42φ: C42/C2×C4C2 ⊆ Aut C20804C20.45C4^2320,24
C20.46C42 = C16×Dic5φ: C42/C2×C4C2 ⊆ Aut C20320C20.46C4^2320,58
C20.47C42 = C8017C4φ: C42/C2×C4C2 ⊆ Aut C20320C20.47C4^2320,60
C20.48C42 = C80⋊C4φ: C42/C2×C4C2 ⊆ Aut C20804C20.48C4^2320,70
C20.49C42 = C421Dic5φ: C42/C2×C4C2 ⊆ Aut C20804C20.49C4^2320,89
C20.50C42 = C23.9D20φ: C42/C2×C4C2 ⊆ Aut C20804C20.50C4^2320,115
C20.51C42 = C20.51C42φ: C42/C2×C4C2 ⊆ Aut C20804C20.51C4^2320,118
C20.52C42 = C2×C4×C52C8φ: C42/C2×C4C2 ⊆ Aut C20320C20.52C4^2320,547
C20.53C42 = C2×C42.D5φ: C42/C2×C4C2 ⊆ Aut C20320C20.53C4^2320,548
C20.54C42 = C424Dic5φ: C42/C2×C4C2 ⊆ Aut C20320C20.54C4^2320,559
C20.55C42 = C2×C8×Dic5φ: C42/C2×C4C2 ⊆ Aut C20320C20.55C4^2320,725
C20.56C42 = C2×C408C4φ: C42/C2×C4C2 ⊆ Aut C20320C20.56C4^2320,727
C20.57C42 = C5×C426C4φ: C42/C2×C4C2 ⊆ Aut C2080C20.57C4^2320,144
C20.58C42 = C5×C22.4Q16φ: C42/C2×C4C2 ⊆ Aut C20320C20.58C4^2320,145
C20.59C42 = C5×C4.C42φ: C42/C2×C4C2 ⊆ Aut C20160C20.59C4^2320,146
C20.60C42 = M4(2)×C20φ: C42/C2×C4C2 ⊆ Aut C20160C20.60C4^2320,905
C20.61C42 = C5×C82M4(2)φ: C42/C2×C4C2 ⊆ Aut C20160C20.61C4^2320,906
C20.62C42 = C5×C4.9C42central extension (φ=1)804C20.62C4^2320,142
C20.63C42 = C5×C4.10C42central extension (φ=1)804C20.63C4^2320,143
C20.64C42 = C5×C165C4central extension (φ=1)320C20.64C4^2320,151
C20.65C42 = C5×C16⋊C4central extension (φ=1)804C20.65C4^2320,152
C20.66C42 = C5×C424C4central extension (φ=1)320C20.66C4^2320,877
C20.67C42 = C10×C8⋊C4central extension (φ=1)320C20.67C4^2320,904

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