# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C42

Direct product G=N×Q with N=C2×C10 and Q=C42
dρLabelID
C22×C4×C20320C2^2xC4xC20320,1513

Semidirect products G=N:Q with N=C2×C10 and Q=C42
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊C42 = C22⋊C4×F5φ: C42/C2C2×C4 ⊆ Aut C2×C1040(C2xC10):C4^2320,1036
(C2×C10)⋊2C42 = C4×C22⋊F5φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10):2C4^2320,1101
(C2×C10)⋊3C42 = C22×C4×F5φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10):3C4^2320,1590
(C2×C10)⋊4C42 = C22⋊C4×Dic5φ: C42/C22C22 ⊆ Aut C2×C10160(C2xC10):4C4^2320,568
(C2×C10)⋊5C42 = C22⋊C4×C20φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10):5C4^2320,878
(C2×C10)⋊6C42 = C4×C23.D5φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10):6C4^2320,836
(C2×C10)⋊7C42 = C22×C4×Dic5φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10):7C4^2320,1454

Non-split extensions G=N.Q with N=C2×C10 and Q=C42
extensionφ:Q→Aut NdρLabelID
(C2×C10).1C42 = (C22×F5)⋊C4φ: C42/C2C2×C4 ⊆ Aut C2×C10408+(C2xC10).1C4^2320,204
(C2×C10).2C42 = C22⋊C4.F5φ: C42/C2C2×C4 ⊆ Aut C2×C10808-(C2xC10).2C4^2320,205
(C2×C10).3C42 = M4(2)⋊F5φ: C42/C2C2×C4 ⊆ Aut C2×C10408(C2xC10).3C4^2320,237
(C2×C10).4C42 = M4(2)⋊4F5φ: C42/C2C2×C4 ⊆ Aut C2×C10808(C2xC10).4C4^2320,240
(C2×C10).5C42 = Dic5.C42φ: C42/C2C2×C4 ⊆ Aut C2×C10160(C2xC10).5C4^2320,1029
(C2×C10).6C42 = M4(2)×F5φ: C42/C2C2×C4 ⊆ Aut C2×C10408(C2xC10).6C4^2320,1064
(C2×C10).7C42 = M4(2)⋊5F5φ: C42/C2C2×C4 ⊆ Aut C2×C10808(C2xC10).7C4^2320,1066
(C2×C10).8C42 = C8×C5⋊C8φ: C42/C4C4 ⊆ Aut C2×C10320(C2xC10).8C4^2320,216
(C2×C10).9C42 = C40⋊C8φ: C42/C4C4 ⊆ Aut C2×C10320(C2xC10).9C4^2320,217
(C2×C10).10C42 = C20.31M4(2)φ: C42/C4C4 ⊆ Aut C2×C10320(C2xC10).10C4^2320,218
(C2×C10).11C42 = D10.3M4(2)φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10).11C4^2320,230
(C2×C10).12C42 = (C2×C8)⋊F5φ: C42/C4C4 ⊆ Aut C2×C10804(C2xC10).12C4^2320,232
(C2×C10).13C42 = C22⋊F5⋊C4φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10).13C4^2320,255
(C2×C10).14C42 = C10.(C4⋊C8)φ: C42/C4C4 ⊆ Aut C2×C10320(C2xC10).14C4^2320,256
(C2×C10).15C42 = C22.F5⋊C4φ: C42/C4C4 ⊆ Aut C2×C10160(C2xC10).15C4^2320,257
(C2×C10).16C42 = C2×C8×F5φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10).16C4^2320,1054
(C2×C10).17C42 = C2×C8⋊F5φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10).17C4^2320,1055
(C2×C10).18C42 = C20.12C42φ: C42/C4C4 ⊆ Aut C2×C10804(C2xC10).18C4^2320,1056
(C2×C10).19C42 = C2×C4×C5⋊C8φ: C42/C4C4 ⊆ Aut C2×C10320(C2xC10).19C4^2320,1084
(C2×C10).20C42 = C2×C10.C42φ: C42/C4C4 ⊆ Aut C2×C10320(C2xC10).20C4^2320,1087
(C2×C10).21C42 = C4×C22.F5φ: C42/C4C4 ⊆ Aut C2×C10160(C2xC10).21C4^2320,1088
(C2×C10).22C42 = C2×D10.3Q8φ: C42/C4C4 ⊆ Aut C2×C1080(C2xC10).22C4^2320,1100
(C2×C10).23C42 = C24.2D10φ: C42/C22C22 ⊆ Aut C2×C1080(C2xC10).23C4^2320,85
(C2×C10).24C42 = C20.60(C4⋊C4)φ: C42/C22C22 ⊆ Aut C2×C10804(C2xC10).24C4^2320,91
(C2×C10).25C42 = M4(2)⋊Dic5φ: C42/C22C22 ⊆ Aut C2×C10160(C2xC10).25C4^2320,112
(C2×C10).26C42 = M4(2)⋊4Dic5φ: C42/C22C22 ⊆ Aut C2×C10804(C2xC10).26C4^2320,117
(C2×C10).27C42 = C20.35C42φ: C42/C22C22 ⊆ Aut C2×C10160(C2xC10).27C4^2320,624
(C2×C10).28C42 = M4(2)×Dic5φ: C42/C22C22 ⊆ Aut C2×C10160(C2xC10).28C4^2320,744
(C2×C10).29C42 = C20.37C42φ: C42/C22C22 ⊆ Aut C2×C10160(C2xC10).29C4^2320,749
(C2×C10).30C42 = C5×C23.9D4φ: C42/C2×C4C2 ⊆ Aut C2×C1080(C2xC10).30C4^2320,147
(C2×C10).31C42 = C5×C22.C42φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).31C4^2320,148
(C2×C10).32C42 = C5×M4(2)⋊4C4φ: C42/C2×C4C2 ⊆ Aut C2×C10804(C2xC10).32C4^2320,149
(C2×C10).33C42 = M4(2)×C20φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).33C4^2320,905
(C2×C10).34C42 = C5×C82M4(2)φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).34C4^2320,906
(C2×C10).35C42 = C8×C52C8φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).35C4^2320,11
(C2×C10).36C42 = C42.279D10φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).36C4^2320,12
(C2×C10).37C42 = C408C8φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).37C4^2320,13
(C2×C10).38C42 = (C2×C20)⋊8C8φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).38C4^2320,82
(C2×C10).39C42 = C24.D10φ: C42/C2×C4C2 ⊆ Aut C2×C1080(C2xC10).39C4^2320,84
(C2×C10).40C42 = (C2×C20).Q8φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).40C4^2320,88
(C2×C10).41C42 = (C2×C40)⋊15C4φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).41C4^2320,108
(C2×C10).42C42 = (C2×C40)⋊C4φ: C42/C2×C4C2 ⊆ Aut C2×C10804(C2xC10).42C4^2320,114
(C2×C10).43C42 = C2×C4×C52C8φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).43C4^2320,547
(C2×C10).44C42 = C2×C42.D5φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).44C4^2320,548
(C2×C10).45C42 = C4×C4.Dic5φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).45C4^2320,549
(C2×C10).46C42 = C2×C8×Dic5φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).46C4^2320,725
(C2×C10).47C42 = C2×C408C4φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).47C4^2320,727
(C2×C10).48C42 = C20.42C42φ: C42/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).48C4^2320,728
(C2×C10).49C42 = C2×C10.10C42φ: C42/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).49C4^2320,835
(C2×C10).50C42 = C5×C8⋊C8central extension (φ=1)320(C2xC10).50C4^2320,127
(C2×C10).51C42 = C5×C22.7C42central extension (φ=1)320(C2xC10).51C4^2320,141
(C2×C10).52C42 = C10×C2.C42central extension (φ=1)320(C2xC10).52C4^2320,876
(C2×C10).53C42 = C10×C8⋊C4central extension (φ=1)320(C2xC10).53C4^2320,904

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