# Extensions 1→N→G→Q→1 with N=C22×C4 and Q=F5

Direct product G=N×Q with N=C22×C4 and Q=F5
dρLabelID
C22×C4×F580C2^2xC4xF5320,1590

Semidirect products G=N:Q with N=C22×C4 and Q=F5
extensionφ:Q→Aut NdρLabelID
(C22×C4)⋊1F5 = (C22×C4)⋊F5φ: F5/C5C4 ⊆ Aut C22×C4804(C2^2xC4):1F5320,254
(C22×C4)⋊2F5 = C22⋊F5⋊C4φ: F5/C5C4 ⊆ Aut C22×C480(C2^2xC4):2F5320,255
(C22×C4)⋊3F5 = C2×D10.D4φ: F5/C5C4 ⊆ Aut C22×C480(C2^2xC4):3F5320,1082
(C22×C4)⋊4F5 = C23⋊F55C2φ: F5/C5C4 ⊆ Aut C22×C4804(C2^2xC4):4F5320,1083
(C22×C4)⋊5F5 = C2×D10.3Q8φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4):5F5320,1100
(C22×C4)⋊6F5 = C4×C22⋊F5φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4):6F5320,1101
(C22×C4)⋊7F5 = (C22×C4)⋊7F5φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4):7F5320,1102
(C22×C4)⋊8F5 = D106(C4⋊C4)φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4):8F5320,1103
(C22×C4)⋊9F5 = C22×C4⋊F5φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4):9F5320,1591
(C22×C4)⋊10F5 = C2×D10.C23φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4):10F5320,1592

Non-split extensions G=N.Q with N=C22×C4 and Q=F5
extensionφ:Q→Aut NdρLabelID
(C22×C4).1F5 = (C22×C4).F5φ: F5/C5C4 ⊆ Aut C22×C4160(C2^2xC4).1F5320,252
(C22×C4).2F5 = C5⋊(C23⋊C8)φ: F5/C5C4 ⊆ Aut C22×C480(C2^2xC4).2F5320,253
(C22×C4).3F5 = C22.F5⋊C4φ: F5/C5C4 ⊆ Aut C22×C4160(C2^2xC4).3F5320,257
(C22×C4).4F5 = C20.29M4(2)φ: F5/C5C4 ⊆ Aut C22×C4804(C2^2xC4).4F5320,250
(C22×C4).5F5 = (C2×C20)⋊1C8φ: F5/C5C4 ⊆ Aut C22×C4160(C2^2xC4).5F5320,251
(C22×C4).6F5 = C2×Dic5.D4φ: F5/C5C4 ⊆ Aut C22×C4160(C2^2xC4).6F5320,1098
(C22×C4).7F5 = (C4×D5).D4φ: F5/C5C4 ⊆ Aut C22×C4804(C2^2xC4).7F5320,1099
(C22×C4).8F5 = C10.6M5(2)φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).8F5320,249
(C22×C4).9F5 = C10.(C4⋊C8)φ: F5/D5C2 ⊆ Aut C22×C4320(C2^2xC4).9F5320,256
(C22×C4).10F5 = C2×C10.C42φ: F5/D5C2 ⊆ Aut C22×C4320(C2^2xC4).10F5320,1087
(C22×C4).11F5 = C4×C22.F5φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).11F5320,1088
(C22×C4).12F5 = C2×D10⋊C8φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).12F5320,1089
(C22×C4).13F5 = C2×Dic5⋊C8φ: F5/D5C2 ⊆ Aut C22×C4320(C2^2xC4).13F5320,1090
(C22×C4).14F5 = D10.11M4(2)φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4).14F5320,1091
(C22×C4).15F5 = C20.34M4(2)φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).15F5320,1092
(C22×C4).16F5 = D109M4(2)φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4).16F5320,1093
(C22×C4).17F5 = Dic5.13M4(2)φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).17F5320,1095
(C22×C4).18F5 = C2×C20.C8φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).18F5320,1081
(C22×C4).19F5 = C2×C20⋊C8φ: F5/D5C2 ⊆ Aut C22×C4320(C2^2xC4).19F5320,1085
(C22×C4).20F5 = Dic5.12M4(2)φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).20F5320,1086
(C22×C4).21F5 = D1010M4(2)φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4).21F5320,1094
(C22×C4).22F5 = C208M4(2)φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).22F5320,1096
(C22×C4).23F5 = C20.30M4(2)φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).23F5320,1097
(C22×C4).24F5 = C22×C4.F5φ: F5/D5C2 ⊆ Aut C22×C4160(C2^2xC4).24F5320,1588
(C22×C4).25F5 = C2×D5⋊M4(2)φ: F5/D5C2 ⊆ Aut C22×C480(C2^2xC4).25F5320,1589
(C22×C4).26F5 = C22×C5⋊C16central extension (φ=1)320(C2^2xC4).26F5320,1080
(C22×C4).27F5 = C2×C4×C5⋊C8central extension (φ=1)320(C2^2xC4).27F5320,1084
(C22×C4).28F5 = C22×D5⋊C8central extension (φ=1)160(C2^2xC4).28F5320,1587

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