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Extensions 1→N→G→Q→1 with N=C2xC10 and Q=C2xC12

Direct product G=NxQ with N=C2xC10 and Q=C2xC12
dρLabelID
C23xC60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C2xC10 and Q=C2xC12
extensionφ:Q→Aut NdρLabelID
(C2xC10):(C2xC12) = C2xA4xF5φ: C2xC12/C2 → C12 ⊆ Aut C2xC103012+(C2xC10):(C2xC12)480,1192
(C2xC10):2(C2xC12) = C3xD4xF5φ: C2xC12/C3 → C2xC4 ⊆ Aut C2xC10608(C2xC10):2(C2xC12)480,1054
(C2xC10):3(C2xC12) = C4xD5xA4φ: C2xC12/C4 → C6 ⊆ Aut C2xC10606(C2xC10):3(C2xC12)480,1036
(C2xC10):4(C2xC12) = C2xA4xDic5φ: C2xC12/C22 → C6 ⊆ Aut C2xC10120(C2xC10):4(C2xC12)480,1044
(C2xC10):5(C2xC12) = C6xC22:F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC10120(C2xC10):5(C2xC12)480,1059
(C2xC10):6(C2xC12) = F5xC22xC6φ: C2xC12/C6 → C4 ⊆ Aut C2xC10120(C2xC10):6(C2xC12)480,1205
(C2xC10):7(C2xC12) = C3xD5xC22:C4φ: C2xC12/C6 → C22 ⊆ Aut C2xC10120(C2xC10):7(C2xC12)480,673
(C2xC10):8(C2xC12) = C3xDic5:4D4φ: C2xC12/C6 → C22 ⊆ Aut C2xC10240(C2xC10):8(C2xC12)480,674
(C2xC10):9(C2xC12) = C3xD4xDic5φ: C2xC12/C6 → C22 ⊆ Aut C2xC10240(C2xC10):9(C2xC12)480,727
(C2xC10):10(C2xC12) = A4xC2xC20φ: C2xC12/C2xC4 → C3 ⊆ Aut C2xC10120(C2xC10):10(C2xC12)480,1126
(C2xC10):11(C2xC12) = D4xC60φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10):11(C2xC12)480,923
(C2xC10):12(C2xC12) = C12xC5:D4φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10):12(C2xC12)480,721
(C2xC10):13(C2xC12) = D5xC22xC12φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10):13(C2xC12)480,1136
(C2xC10):14(C2xC12) = C22:C4xC30φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10):14(C2xC12)480,920
(C2xC10):15(C2xC12) = C6xC23.D5φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10):15(C2xC12)480,745
(C2xC10):16(C2xC12) = Dic5xC22xC6φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10):16(C2xC12)480,1148

Non-split extensions G=N.Q with N=C2xC10 and Q=C2xC12
extensionφ:Q→Aut NdρLabelID
(C2xC10).(C2xC12) = C3xD4.F5φ: C2xC12/C3 → C2xC4 ⊆ Aut C2xC102408(C2xC10).(C2xC12)480,1053
(C2xC10).2(C2xC12) = C3xD10.D4φ: C2xC12/C6 → C4 ⊆ Aut C2xC101204(C2xC10).2(C2xC12)480,279
(C2xC10).3(C2xC12) = C12xC5:C8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10480(C2xC10).3(C2xC12)480,280
(C2xC10).4(C2xC12) = C3xC20:C8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10480(C2xC10).4(C2xC12)480,281
(C2xC10).5(C2xC12) = C3xC10.C42φ: C2xC12/C6 → C4 ⊆ Aut C2xC10480(C2xC10).5(C2xC12)480,282
(C2xC10).6(C2xC12) = C3xD10:C8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10240(C2xC10).6(C2xC12)480,283
(C2xC10).7(C2xC12) = C3xDic5:C8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10480(C2xC10).7(C2xC12)480,284
(C2xC10).8(C2xC12) = C3xDic5.D4φ: C2xC12/C6 → C4 ⊆ Aut C2xC102404(C2xC10).8(C2xC12)480,285
(C2xC10).9(C2xC12) = C3xD10.3Q8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10120(C2xC10).9(C2xC12)480,286
(C2xC10).10(C2xC12) = C3xC23:F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC101204(C2xC10).10(C2xC12)480,291
(C2xC10).11(C2xC12) = C3xC23.2F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC10240(C2xC10).11(C2xC12)480,292
(C2xC10).12(C2xC12) = C3xC23.F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC101204(C2xC10).12(C2xC12)480,293
(C2xC10).13(C2xC12) = C6xD5:C8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10240(C2xC10).13(C2xC12)480,1047
(C2xC10).14(C2xC12) = C6xC4.F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC10240(C2xC10).14(C2xC12)480,1048
(C2xC10).15(C2xC12) = C3xD5:M4(2)φ: C2xC12/C6 → C4 ⊆ Aut C2xC101204(C2xC10).15(C2xC12)480,1049
(C2xC10).16(C2xC12) = F5xC2xC12φ: C2xC12/C6 → C4 ⊆ Aut C2xC10120(C2xC10).16(C2xC12)480,1050
(C2xC10).17(C2xC12) = C6xC4:F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC10120(C2xC10).17(C2xC12)480,1051
(C2xC10).18(C2xC12) = C3xD10.C23φ: C2xC12/C6 → C4 ⊆ Aut C2xC101204(C2xC10).18(C2xC12)480,1052
(C2xC10).19(C2xC12) = C2xC6xC5:C8φ: C2xC12/C6 → C4 ⊆ Aut C2xC10480(C2xC10).19(C2xC12)480,1057
(C2xC10).20(C2xC12) = C6xC22.F5φ: C2xC12/C6 → C4 ⊆ Aut C2xC10240(C2xC10).20(C2xC12)480,1058
(C2xC10).21(C2xC12) = C3xC23.1D10φ: C2xC12/C6 → C22 ⊆ Aut C2xC101204(C2xC10).21(C2xC12)480,84
(C2xC10).22(C2xC12) = C3xC20.46D4φ: C2xC12/C6 → C22 ⊆ Aut C2xC101204(C2xC10).22(C2xC12)480,101
(C2xC10).23(C2xC12) = C3xC4.12D20φ: C2xC12/C6 → C22 ⊆ Aut C2xC102404(C2xC10).23(C2xC12)480,102
(C2xC10).24(C2xC12) = C3xC23.11D10φ: C2xC12/C6 → C22 ⊆ Aut C2xC10240(C2xC10).24(C2xC12)480,670
(C2xC10).25(C2xC12) = C3xD5xM4(2)φ: C2xC12/C6 → C22 ⊆ Aut C2xC101204(C2xC10).25(C2xC12)480,699
(C2xC10).26(C2xC12) = C3xD20.2C4φ: C2xC12/C6 → C22 ⊆ Aut C2xC102404(C2xC10).26(C2xC12)480,700
(C2xC10).27(C2xC12) = C3xD4.Dic5φ: C2xC12/C6 → C22 ⊆ Aut C2xC102404(C2xC10).27(C2xC12)480,741
(C2xC10).28(C2xC12) = C15xC8oD4φ: C2xC12/C12 → C2 ⊆ Aut C2xC102402(C2xC10).28(C2xC12)480,936
(C2xC10).29(C2xC12) = Dic5xC24φ: C2xC12/C12 → C2 ⊆ Aut C2xC10480(C2xC10).29(C2xC12)480,91
(C2xC10).30(C2xC12) = C3xC20.8Q8φ: C2xC12/C12 → C2 ⊆ Aut C2xC10480(C2xC10).30(C2xC12)480,92
(C2xC10).31(C2xC12) = C3xC40:8C4φ: C2xC12/C12 → C2 ⊆ Aut C2xC10480(C2xC10).31(C2xC12)480,93
(C2xC10).32(C2xC12) = C3xD10:1C8φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10).32(C2xC12)480,98
(C2xC10).33(C2xC12) = D5xC2xC24φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10).33(C2xC12)480,692
(C2xC10).34(C2xC12) = C6xC8:D5φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10).34(C2xC12)480,693
(C2xC10).35(C2xC12) = C3xD20.3C4φ: C2xC12/C12 → C2 ⊆ Aut C2xC102402(C2xC10).35(C2xC12)480,694
(C2xC10).36(C2xC12) = Dic5xC2xC12φ: C2xC12/C12 → C2 ⊆ Aut C2xC10480(C2xC10).36(C2xC12)480,715
(C2xC10).37(C2xC12) = C6xC10.D4φ: C2xC12/C12 → C2 ⊆ Aut C2xC10480(C2xC10).37(C2xC12)480,716
(C2xC10).38(C2xC12) = C6xD10:C4φ: C2xC12/C12 → C2 ⊆ Aut C2xC10240(C2xC10).38(C2xC12)480,720
(C2xC10).39(C2xC12) = C15xC23:C4φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC101204(C2xC10).39(C2xC12)480,202
(C2xC10).40(C2xC12) = C15xC4.D4φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC101204(C2xC10).40(C2xC12)480,203
(C2xC10).41(C2xC12) = C15xC4.10D4φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC102404(C2xC10).41(C2xC12)480,204
(C2xC10).42(C2xC12) = C15xC42:C2φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10).42(C2xC12)480,922
(C2xC10).43(C2xC12) = M4(2)xC30φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10).43(C2xC12)480,935
(C2xC10).44(C2xC12) = C12xC5:2C8φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10).44(C2xC12)480,80
(C2xC10).45(C2xC12) = C3xC42.D5φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10).45(C2xC12)480,81
(C2xC10).46(C2xC12) = C3xC20:3C8φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10).46(C2xC12)480,82
(C2xC10).47(C2xC12) = C3xC20.55D4φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10).47(C2xC12)480,108
(C2xC10).48(C2xC12) = C3xC10.10C42φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10).48(C2xC12)480,109
(C2xC10).49(C2xC12) = C3xC20.D4φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC101204(C2xC10).49(C2xC12)480,111
(C2xC10).50(C2xC12) = C3xC23:Dic5φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC101204(C2xC10).50(C2xC12)480,112
(C2xC10).51(C2xC12) = C3xC20.10D4φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC102404(C2xC10).51(C2xC12)480,114
(C2xC10).52(C2xC12) = C2xC6xC5:2C8φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10).52(C2xC12)480,713
(C2xC10).53(C2xC12) = C6xC4.Dic5φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10).53(C2xC12)480,714
(C2xC10).54(C2xC12) = C6xC4:Dic5φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10480(C2xC10).54(C2xC12)480,718
(C2xC10).55(C2xC12) = C3xC23.21D10φ: C2xC12/C2xC6 → C2 ⊆ Aut C2xC10240(C2xC10).55(C2xC12)480,719
(C2xC10).56(C2xC12) = C15xC2.C42central extension (φ=1)480(C2xC10).56(C2xC12)480,198
(C2xC10).57(C2xC12) = C15xC8:C4central extension (φ=1)480(C2xC10).57(C2xC12)480,200
(C2xC10).58(C2xC12) = C15xC22:C8central extension (φ=1)240(C2xC10).58(C2xC12)480,201
(C2xC10).59(C2xC12) = C15xC4:C8central extension (φ=1)480(C2xC10).59(C2xC12)480,208
(C2xC10).60(C2xC12) = C4:C4xC30central extension (φ=1)480(C2xC10).60(C2xC12)480,921

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