# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×C8

Direct product G=N×Q with N=C2×C10 and Q=C2×C8
dρLabelID
C23×C40320C2^3xC40320,1567

Semidirect products G=N:Q with N=C2×C10 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1(C2×C8) = C5⋊C88D4φ: C2×C8/C2C2×C4 ⊆ Aut C2×C10160(C2xC10):1(C2xC8)320,1030
(C2×C10)⋊2(C2×C8) = D4×C5⋊C8φ: C2×C8/C2C2×C4 ⊆ Aut C2×C10160(C2xC10):2(C2xC8)320,1110
(C2×C10)⋊3(C2×C8) = D10.11M4(2)φ: C2×C8/C4C4 ⊆ Aut C2×C1080(C2xC10):3(C2xC8)320,1091
(C2×C10)⋊4(C2×C8) = C22×D5⋊C8φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10):4(C2xC8)320,1587
(C2×C10)⋊5(C2×C8) = D5×C22⋊C8φ: C2×C8/C4C22 ⊆ Aut C2×C1080(C2xC10):5(C2xC8)320,351
(C2×C10)⋊6(C2×C8) = C55(C8×D4)φ: C2×C8/C4C22 ⊆ Aut C2×C10160(C2xC10):6(C2xC8)320,352
(C2×C10)⋊7(C2×C8) = D4×C52C8φ: C2×C8/C4C22 ⊆ Aut C2×C10160(C2xC10):7(C2xC8)320,637
(C2×C10)⋊8(C2×C8) = C2×C23.2F5φ: C2×C8/C22C4 ⊆ Aut C2×C10160(C2xC10):8(C2xC8)320,1135
(C2×C10)⋊9(C2×C8) = C23×C5⋊C8φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10):9(C2xC8)320,1605
(C2×C10)⋊10(C2×C8) = D4×C40φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10):10(C2xC8)320,935
(C2×C10)⋊11(C2×C8) = C8×C5⋊D4φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10):11(C2xC8)320,736
(C2×C10)⋊12(C2×C8) = D5×C22×C8φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10):12(C2xC8)320,1408
(C2×C10)⋊13(C2×C8) = C10×C22⋊C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10):13(C2xC8)320,907
(C2×C10)⋊14(C2×C8) = C2×C20.55D4φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10):14(C2xC8)320,833
(C2×C10)⋊15(C2×C8) = C23×C52C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10):15(C2xC8)320,1452

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C2×C8) = Dic10.C8φ: C2×C8/C2C2×C4 ⊆ Aut C2×C101608(C2xC10).1(C2xC8)320,1063
(C2×C10).2(C2×C8) = C5⋊C16.C22φ: C2×C8/C2C2×C4 ⊆ Aut C2×C101608(C2xC10).2(C2xC8)320,1129
(C2×C10).3(C2×C8) = Dic5⋊C16φ: C2×C8/C4C4 ⊆ Aut C2×C10320(C2xC10).3(C2xC8)320,223
(C2×C10).4(C2×C8) = C40.C8φ: C2×C8/C4C4 ⊆ Aut C2×C10320(C2xC10).4(C2xC8)320,224
(C2×C10).5(C2×C8) = D10⋊C16φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10).5(C2xC8)320,225
(C2×C10).6(C2×C8) = C10.M5(2)φ: C2×C8/C4C4 ⊆ Aut C2×C10320(C2xC10).6(C2xC8)320,226
(C2×C10).7(C2×C8) = C20.10M4(2)φ: C2×C8/C4C4 ⊆ Aut C2×C10804(C2xC10).7(C2xC8)320,229
(C2×C10).8(C2×C8) = (C22×C4).F5φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10).8(C2xC8)320,252
(C2×C10).9(C2×C8) = C5⋊(C23⋊C8)φ: C2×C8/C4C4 ⊆ Aut C2×C1080(C2xC10).9(C2xC8)320,253
(C2×C10).10(C2×C8) = C2×D5⋊C16φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10).10(C2xC8)320,1051
(C2×C10).11(C2×C8) = C2×C8.F5φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10).11(C2xC8)320,1052
(C2×C10).12(C2×C8) = D5⋊M5(2)φ: C2×C8/C4C4 ⊆ Aut C2×C10804(C2xC10).12(C2xC8)320,1053
(C2×C10).13(C2×C8) = C2×D10⋊C8φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10).13(C2xC8)320,1089
(C2×C10).14(C2×C8) = C2×Dic5⋊C8φ: C2×C8/C4C4 ⊆ Aut C2×C10320(C2xC10).14(C2xC8)320,1090
(C2×C10).15(C2×C8) = C20.34M4(2)φ: C2×C8/C4C4 ⊆ Aut C2×C10160(C2xC10).15(C2xC8)320,1092
(C2×C10).16(C2×C8) = C53(C23⋊C8)φ: C2×C8/C4C22 ⊆ Aut C2×C1080(C2xC10).16(C2xC8)320,26
(C2×C10).17(C2×C8) = (C2×Dic5)⋊C8φ: C2×C8/C4C22 ⊆ Aut C2×C10160(C2xC10).17(C2xC8)320,27
(C2×C10).18(C2×C8) = C8.25D20φ: C2×C8/C4C22 ⊆ Aut C2×C10804(C2xC10).18(C2xC8)320,72
(C2×C10).19(C2×C8) = Dic5.14M4(2)φ: C2×C8/C4C22 ⊆ Aut C2×C10160(C2xC10).19(C2xC8)320,345
(C2×C10).20(C2×C8) = D5×M5(2)φ: C2×C8/C4C22 ⊆ Aut C2×C10804(C2xC10).20(C2xC8)320,533
(C2×C10).21(C2×C8) = D20.5C8φ: C2×C8/C4C22 ⊆ Aut C2×C101604(C2xC10).21(C2xC8)320,534
(C2×C10).22(C2×C8) = C40.70C23φ: C2×C8/C4C22 ⊆ Aut C2×C101604(C2xC10).22(C2xC8)320,767
(C2×C10).23(C2×C8) = C4×C5⋊C16φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).23(C2xC8)320,195
(C2×C10).24(C2×C8) = C20⋊C16φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).24(C2xC8)320,196
(C2×C10).25(C2×C8) = C42.4F5φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).25(C2xC8)320,197
(C2×C10).26(C2×C8) = C10.6M5(2)φ: C2×C8/C22C4 ⊆ Aut C2×C10160(C2xC10).26(C2xC8)320,249
(C2×C10).27(C2×C8) = C20.29M4(2)φ: C2×C8/C22C4 ⊆ Aut C2×C10804(C2xC10).27(C2xC8)320,250
(C2×C10).28(C2×C8) = (C2×C20)⋊1C8φ: C2×C8/C22C4 ⊆ Aut C2×C10160(C2xC10).28(C2xC8)320,251
(C2×C10).29(C2×C8) = C10.(C4⋊C8)φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).29(C2xC8)320,256
(C2×C10).30(C2×C8) = C24.F5φ: C2×C8/C22C4 ⊆ Aut C2×C1080(C2xC10).30(C2xC8)320,271
(C2×C10).31(C2×C8) = C22×C5⋊C16φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).31(C2xC8)320,1080
(C2×C10).32(C2×C8) = C2×C20.C8φ: C2×C8/C22C4 ⊆ Aut C2×C10160(C2xC10).32(C2xC8)320,1081
(C2×C10).33(C2×C8) = C2×C4×C5⋊C8φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).33(C2xC8)320,1084
(C2×C10).34(C2×C8) = C2×C20⋊C8φ: C2×C8/C22C4 ⊆ Aut C2×C10320(C2xC10).34(C2xC8)320,1085
(C2×C10).35(C2×C8) = Dic5.12M4(2)φ: C2×C8/C22C4 ⊆ Aut C2×C10160(C2xC10).35(C2xC8)320,1086
(C2×C10).36(C2×C8) = C5×D4○C16φ: C2×C8/C8C2 ⊆ Aut C2×C101602(C2xC10).36(C2xC8)320,1005
(C2×C10).37(C2×C8) = C16×Dic5φ: C2×C8/C8C2 ⊆ Aut C2×C10320(C2xC10).37(C2xC8)320,58
(C2×C10).38(C2×C8) = C40.88D4φ: C2×C8/C8C2 ⊆ Aut C2×C10320(C2xC10).38(C2xC8)320,59
(C2×C10).39(C2×C8) = C8017C4φ: C2×C8/C8C2 ⊆ Aut C2×C10320(C2xC10).39(C2xC8)320,60
(C2×C10).40(C2×C8) = D101C16φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10).40(C2xC8)320,65
(C2×C10).41(C2×C8) = (C2×C40)⋊15C4φ: C2×C8/C8C2 ⊆ Aut C2×C10320(C2xC10).41(C2xC8)320,108
(C2×C10).42(C2×C8) = D5×C2×C16φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10).42(C2xC8)320,526
(C2×C10).43(C2×C8) = C2×C80⋊C2φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10).43(C2xC8)320,527
(C2×C10).44(C2×C8) = D20.6C8φ: C2×C8/C8C2 ⊆ Aut C2×C101602(C2xC10).44(C2xC8)320,528
(C2×C10).45(C2×C8) = C2×C8×Dic5φ: C2×C8/C8C2 ⊆ Aut C2×C10320(C2xC10).45(C2xC8)320,725
(C2×C10).46(C2×C8) = C2×C20.8Q8φ: C2×C8/C8C2 ⊆ Aut C2×C10320(C2xC10).46(C2xC8)320,726
(C2×C10).47(C2×C8) = C2×D101C8φ: C2×C8/C8C2 ⊆ Aut C2×C10160(C2xC10).47(C2xC8)320,735
(C2×C10).48(C2×C8) = C5×C23⋊C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C1080(C2xC10).48(C2xC8)320,128
(C2×C10).49(C2×C8) = C5×C22.M4(2)φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).49(C2xC8)320,129
(C2×C10).50(C2×C8) = C5×C23.C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10804(C2xC10).50(C2xC8)320,154
(C2×C10).51(C2×C8) = C5×C42.12C4φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).51(C2xC8)320,932
(C2×C10).52(C2×C8) = C10×M5(2)φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).52(C2xC8)320,1004
(C2×C10).53(C2×C8) = C4×C52C16φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).53(C2xC8)320,18
(C2×C10).54(C2×C8) = C40.10C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).54(C2xC8)320,19
(C2×C10).55(C2×C8) = C203C16φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).55(C2xC8)320,20
(C2×C10).56(C2×C8) = (C2×C20)⋊8C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).56(C2xC8)320,82
(C2×C10).57(C2×C8) = C24.Dic5φ: C2×C8/C2×C4C2 ⊆ Aut C2×C1080(C2xC10).57(C2xC8)320,83
(C2×C10).58(C2×C8) = (C2×C20)⋊C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).58(C2xC8)320,86
(C2×C10).59(C2×C8) = C40.91D4φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).59(C2xC8)320,107
(C2×C10).60(C2×C8) = C40.D4φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10804(C2xC10).60(C2xC8)320,111
(C2×C10).61(C2×C8) = C2×C4×C52C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).61(C2xC8)320,547
(C2×C10).62(C2×C8) = C2×C203C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).62(C2xC8)320,550
(C2×C10).63(C2×C8) = C42.6Dic5φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).63(C2xC8)320,552
(C2×C10).64(C2×C8) = C22×C52C16φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10320(C2xC10).64(C2xC8)320,723
(C2×C10).65(C2×C8) = C2×C20.4C8φ: C2×C8/C2×C4C2 ⊆ Aut C2×C10160(C2xC10).65(C2xC8)320,724
(C2×C10).66(C2×C8) = C5×C22.7C42central extension (φ=1)320(C2xC10).66(C2xC8)320,141
(C2×C10).67(C2×C8) = C5×C165C4central extension (φ=1)320(C2xC10).67(C2xC8)320,151
(C2×C10).68(C2×C8) = C5×C22⋊C16central extension (φ=1)160(C2xC10).68(C2xC8)320,153
(C2×C10).69(C2×C8) = C5×C4⋊C16central extension (φ=1)320(C2xC10).69(C2xC8)320,168
(C2×C10).70(C2×C8) = C10×C4⋊C8central extension (φ=1)320(C2xC10).70(C2xC8)320,923

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