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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×C12

Direct product G=N×Q with N=C2×C10 and Q=C2×C12
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C2×C10 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C2×C12) = C2×A4×F5φ: C2×C12/C2 → C12 ⊆ Aut C2×C103012+(C2xC10):(C2xC12)480,1192
(C2×C10)⋊2(C2×C12) = C3×D4×F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C2×C10608(C2xC10):2(C2xC12)480,1054
(C2×C10)⋊3(C2×C12) = C4×D5×A4φ: C2×C12/C4 → C6 ⊆ Aut C2×C10606(C2xC10):3(C2xC12)480,1036
(C2×C10)⋊4(C2×C12) = C2×A4×Dic5φ: C2×C12/C22 → C6 ⊆ Aut C2×C10120(C2xC10):4(C2xC12)480,1044
(C2×C10)⋊5(C2×C12) = C6×C22⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C10120(C2xC10):5(C2xC12)480,1059
(C2×C10)⋊6(C2×C12) = F5×C22×C6φ: C2×C12/C6 → C4 ⊆ Aut C2×C10120(C2xC10):6(C2xC12)480,1205
(C2×C10)⋊7(C2×C12) = C3×D5×C22⋊C4φ: C2×C12/C6 → C22 ⊆ Aut C2×C10120(C2xC10):7(C2xC12)480,673
(C2×C10)⋊8(C2×C12) = C3×Dic5⋊4D4φ: C2×C12/C6 → C22 ⊆ Aut C2×C10240(C2xC10):8(C2xC12)480,674
(C2×C10)⋊9(C2×C12) = C3×D4×Dic5φ: C2×C12/C6 → C22 ⊆ Aut C2×C10240(C2xC10):9(C2xC12)480,727
(C2×C10)⋊10(C2×C12) = A4×C2×C20φ: C2×C12/C2×C4 → C3 ⊆ Aut C2×C10120(C2xC10):10(C2xC12)480,1126
(C2×C10)⋊11(C2×C12) = D4×C60φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10):11(C2xC12)480,923
(C2×C10)⋊12(C2×C12) = C12×C5⋊D4φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10):12(C2xC12)480,721
(C2×C10)⋊13(C2×C12) = D5×C22×C12φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10):13(C2xC12)480,1136
(C2×C10)⋊14(C2×C12) = C22⋊C4×C30φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10):14(C2xC12)480,920
(C2×C10)⋊15(C2×C12) = C6×C23.D5φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10):15(C2xC12)480,745
(C2×C10)⋊16(C2×C12) = Dic5×C22×C6φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10):16(C2xC12)480,1148

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
(C2×C10).(C2×C12) = C3×D4.F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C2×C102408(C2xC10).(C2xC12)480,1053
(C2×C10).2(C2×C12) = C3×D10.D4φ: C2×C12/C6 → C4 ⊆ Aut C2×C101204(C2xC10).2(C2xC12)480,279
(C2×C10).3(C2×C12) = C12×C5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10480(C2xC10).3(C2xC12)480,280
(C2×C10).4(C2×C12) = C3×C20⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10480(C2xC10).4(C2xC12)480,281
(C2×C10).5(C2×C12) = C3×C10.C42φ: C2×C12/C6 → C4 ⊆ Aut C2×C10480(C2xC10).5(C2xC12)480,282
(C2×C10).6(C2×C12) = C3×D10⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10240(C2xC10).6(C2xC12)480,283
(C2×C10).7(C2×C12) = C3×Dic5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10480(C2xC10).7(C2xC12)480,284
(C2×C10).8(C2×C12) = C3×Dic5.D4φ: C2×C12/C6 → C4 ⊆ Aut C2×C102404(C2xC10).8(C2xC12)480,285
(C2×C10).9(C2×C12) = C3×D10.3Q8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10120(C2xC10).9(C2xC12)480,286
(C2×C10).10(C2×C12) = C3×C23⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C101204(C2xC10).10(C2xC12)480,291
(C2×C10).11(C2×C12) = C3×C23.2F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C10240(C2xC10).11(C2xC12)480,292
(C2×C10).12(C2×C12) = C3×C23.F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C101204(C2xC10).12(C2xC12)480,293
(C2×C10).13(C2×C12) = C6×D5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10240(C2xC10).13(C2xC12)480,1047
(C2×C10).14(C2×C12) = C6×C4.F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C10240(C2xC10).14(C2xC12)480,1048
(C2×C10).15(C2×C12) = C3×D5⋊M4(2)φ: C2×C12/C6 → C4 ⊆ Aut C2×C101204(C2xC10).15(C2xC12)480,1049
(C2×C10).16(C2×C12) = F5×C2×C12φ: C2×C12/C6 → C4 ⊆ Aut C2×C10120(C2xC10).16(C2xC12)480,1050
(C2×C10).17(C2×C12) = C6×C4⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C10120(C2xC10).17(C2xC12)480,1051
(C2×C10).18(C2×C12) = C3×D10.C23φ: C2×C12/C6 → C4 ⊆ Aut C2×C101204(C2xC10).18(C2xC12)480,1052
(C2×C10).19(C2×C12) = C2×C6×C5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C2×C10480(C2xC10).19(C2xC12)480,1057
(C2×C10).20(C2×C12) = C6×C22.F5φ: C2×C12/C6 → C4 ⊆ Aut C2×C10240(C2xC10).20(C2xC12)480,1058
(C2×C10).21(C2×C12) = C3×C23.1D10φ: C2×C12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).21(C2xC12)480,84
(C2×C10).22(C2×C12) = C3×C20.46D4φ: C2×C12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).22(C2xC12)480,101
(C2×C10).23(C2×C12) = C3×C4.12D20φ: C2×C12/C6 → C22 ⊆ Aut C2×C102404(C2xC10).23(C2xC12)480,102
(C2×C10).24(C2×C12) = C3×C23.11D10φ: C2×C12/C6 → C22 ⊆ Aut C2×C10240(C2xC10).24(C2xC12)480,670
(C2×C10).25(C2×C12) = C3×D5×M4(2)φ: C2×C12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).25(C2xC12)480,699
(C2×C10).26(C2×C12) = C3×D20.2C4φ: C2×C12/C6 → C22 ⊆ Aut C2×C102404(C2xC10).26(C2xC12)480,700
(C2×C10).27(C2×C12) = C3×D4.Dic5φ: C2×C12/C6 → C22 ⊆ Aut C2×C102404(C2xC10).27(C2xC12)480,741
(C2×C10).28(C2×C12) = C15×C8○D4φ: C2×C12/C12 → C2 ⊆ Aut C2×C102402(C2xC10).28(C2xC12)480,936
(C2×C10).29(C2×C12) = Dic5×C24φ: C2×C12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).29(C2xC12)480,91
(C2×C10).30(C2×C12) = C3×C20.8Q8φ: C2×C12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).30(C2xC12)480,92
(C2×C10).31(C2×C12) = C3×C40⋊8C4φ: C2×C12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).31(C2xC12)480,93
(C2×C10).32(C2×C12) = C3×D10⋊1C8φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).32(C2xC12)480,98
(C2×C10).33(C2×C12) = D5×C2×C24φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).33(C2xC12)480,692
(C2×C10).34(C2×C12) = C6×C8⋊D5φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).34(C2xC12)480,693
(C2×C10).35(C2×C12) = C3×D20.3C4φ: C2×C12/C12 → C2 ⊆ Aut C2×C102402(C2xC10).35(C2xC12)480,694
(C2×C10).36(C2×C12) = Dic5×C2×C12φ: C2×C12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).36(C2xC12)480,715
(C2×C10).37(C2×C12) = C6×C10.D4φ: C2×C12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).37(C2xC12)480,716
(C2×C10).38(C2×C12) = C6×D10⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).38(C2xC12)480,720
(C2×C10).39(C2×C12) = C15×C23⋊C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).39(C2xC12)480,202
(C2×C10).40(C2×C12) = C15×C4.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).40(C2xC12)480,203
(C2×C10).41(C2×C12) = C15×C4.10D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C102404(C2xC10).41(C2xC12)480,204
(C2×C10).42(C2×C12) = C15×C42⋊C2φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).42(C2xC12)480,922
(C2×C10).43(C2×C12) = M4(2)×C30φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).43(C2xC12)480,935
(C2×C10).44(C2×C12) = C12×C5⋊2C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).44(C2xC12)480,80
(C2×C10).45(C2×C12) = C3×C42.D5φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).45(C2xC12)480,81
(C2×C10).46(C2×C12) = C3×C20⋊3C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).46(C2xC12)480,82
(C2×C10).47(C2×C12) = C3×C20.55D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).47(C2xC12)480,108
(C2×C10).48(C2×C12) = C3×C10.10C42φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).48(C2xC12)480,109
(C2×C10).49(C2×C12) = C3×C20.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).49(C2xC12)480,111
(C2×C10).50(C2×C12) = C3×C23⋊Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).50(C2xC12)480,112
(C2×C10).51(C2×C12) = C3×C20.10D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C102404(C2xC10).51(C2xC12)480,114
(C2×C10).52(C2×C12) = C2×C6×C5⋊2C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).52(C2xC12)480,713
(C2×C10).53(C2×C12) = C6×C4.Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).53(C2xC12)480,714
(C2×C10).54(C2×C12) = C6×C4⋊Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).54(C2xC12)480,718
(C2×C10).55(C2×C12) = C3×C23.21D10φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).55(C2xC12)480,719
(C2×C10).56(C2×C12) = C15×C2.C42central extension (φ=1)480(C2xC10).56(C2xC12)480,198
(C2×C10).57(C2×C12) = C15×C8⋊C4central extension (φ=1)480(C2xC10).57(C2xC12)480,200
(C2×C10).58(C2×C12) = C15×C22⋊C8central extension (φ=1)240(C2xC10).58(C2xC12)480,201
(C2×C10).59(C2×C12) = C15×C4⋊C8central extension (φ=1)480(C2xC10).59(C2xC12)480,208
(C2×C10).60(C2×C12) = C4⋊C4×C30central extension (φ=1)480(C2xC10).60(C2xC12)480,921

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