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Extensions 1→N→G→Q→1 with N=C22×C10 and Q=C2×C6

Direct product G=N×Q with N=C22×C10 and Q=C2×C6
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C22×C10 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C22×C10)⋊(C2×C6) = C22×D5×A4φ: C2×C6/C2 → C6 ⊆ Aut C22×C1060(C2^2xC10):(C2xC6)480,1202
(C22×C10)⋊2(C2×C6) = C15×C22≀C2φ: C2×C6/C3 → C22 ⊆ Aut C22×C10120(C2^2xC10):2(C2xC6)480,925
(C22×C10)⋊3(C2×C6) = C15×2+ 1+4φ: C2×C6/C3 → C22 ⊆ Aut C22×C101204(C2^2xC10):3(C2xC6)480,1184
(C22×C10)⋊4(C2×C6) = C3×C23⋊D10φ: C2×C6/C3 → C22 ⊆ Aut C22×C10120(C2^2xC10):4(C2xC6)480,730
(C22×C10)⋊5(C2×C6) = C6×D4×D5φ: C2×C6/C3 → C22 ⊆ Aut C22×C10120(C2^2xC10):5(C2xC6)480,1139
(C22×C10)⋊6(C2×C6) = C3×D4⋊6D10φ: C2×C6/C3 → C22 ⊆ Aut C22×C101204(C2^2xC10):6(C2xC6)480,1141
(C22×C10)⋊7(C2×C6) = A4×C22×C10φ: C2×C6/C22 → C3 ⊆ Aut C22×C10120(C2^2xC10):7(C2xC6)480,1208
(C22×C10)⋊8(C2×C6) = D4×C2×C30φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10):8(C2xC6)480,1181
(C22×C10)⋊9(C2×C6) = C2×C6×C5⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10):9(C2xC6)480,1149
(C22×C10)⋊10(C2×C6) = D5×C23×C6φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10):10(C2xC6)480,1210

Non-split extensions G=N.Q with N=C22×C10 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C22×C10).1(C2×C6) = A4×Dic10φ: C2×C6/C2 → C6 ⊆ Aut C22×C101206-(C2^2xC10).1(C2xC6)480,1035
(C22×C10).2(C2×C6) = C4×D5×A4φ: C2×C6/C2 → C6 ⊆ Aut C22×C10606(C2^2xC10).2(C2xC6)480,1036
(C22×C10).3(C2×C6) = A4×D20φ: C2×C6/C2 → C6 ⊆ Aut C22×C10606+(C2^2xC10).3(C2xC6)480,1037
(C22×C10).4(C2×C6) = C2×A4×Dic5φ: C2×C6/C2 → C6 ⊆ Aut C22×C10120(C2^2xC10).4(C2xC6)480,1044
(C22×C10).5(C2×C6) = A4×C5⋊D4φ: C2×C6/C2 → C6 ⊆ Aut C22×C10606(C2^2xC10).5(C2xC6)480,1045
(C22×C10).6(C2×C6) = C15×C23⋊C4φ: C2×C6/C3 → C22 ⊆ Aut C22×C101204(C2^2xC10).6(C2xC6)480,202
(C22×C10).7(C2×C6) = C15×C4.4D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).7(C2xC6)480,929
(C22×C10).8(C2×C6) = C15×C42⋊2C2φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).8(C2xC6)480,931
(C22×C10).9(C2×C6) = C15×C4⋊1D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).9(C2xC6)480,932
(C22×C10).10(C2×C6) = C3×C23.1D10φ: C2×C6/C3 → C22 ⊆ Aut C22×C101204(C2^2xC10).10(C2xC6)480,84
(C22×C10).11(C2×C6) = C3×C23⋊Dic5φ: C2×C6/C3 → C22 ⊆ Aut C22×C101204(C2^2xC10).11(C2xC6)480,112
(C22×C10).12(C2×C6) = C3×C23.11D10φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).12(C2xC6)480,670
(C22×C10).13(C2×C6) = C3×Dic5.14D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).13(C2xC6)480,671
(C22×C10).14(C2×C6) = C3×C23.D10φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).14(C2xC6)480,672
(C22×C10).15(C2×C6) = C3×D5×C22⋊C4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10120(C2^2xC10).15(C2xC6)480,673
(C22×C10).16(C2×C6) = C3×Dic5⋊4D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).16(C2xC6)480,674
(C22×C10).17(C2×C6) = C3×C22⋊D20φ: C2×C6/C3 → C22 ⊆ Aut C22×C10120(C2^2xC10).17(C2xC6)480,675
(C22×C10).18(C2×C6) = C3×D10.12D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).18(C2xC6)480,676
(C22×C10).19(C2×C6) = C3×D10⋊D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).19(C2xC6)480,677
(C22×C10).20(C2×C6) = C3×Dic5.5D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).20(C2xC6)480,678
(C22×C10).21(C2×C6) = C3×C22.D20φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).21(C2xC6)480,679
(C22×C10).22(C2×C6) = C3×D4×Dic5φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).22(C2xC6)480,727
(C22×C10).23(C2×C6) = C3×C23.18D10φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).23(C2xC6)480,728
(C22×C10).24(C2×C6) = C3×C20.17D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).24(C2xC6)480,729
(C22×C10).25(C2×C6) = C3×C20⋊2D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).25(C2xC6)480,731
(C22×C10).26(C2×C6) = C3×Dic5⋊D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).26(C2xC6)480,732
(C22×C10).27(C2×C6) = C3×C20⋊D4φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).27(C2xC6)480,733
(C22×C10).28(C2×C6) = C6×D4⋊2D5φ: C2×C6/C3 → C22 ⊆ Aut C22×C10240(C2^2xC10).28(C2xC6)480,1140
(C22×C10).29(C2×C6) = A4×C2×C20φ: C2×C6/C22 → C3 ⊆ Aut C22×C10120(C2^2xC10).29(C2xC6)480,1126
(C22×C10).30(C2×C6) = C5×D4×A4φ: C2×C6/C22 → C3 ⊆ Aut C22×C10606(C2^2xC10).30(C2xC6)480,1127
(C22×C10).31(C2×C6) = C5×Q8×A4φ: C2×C6/C22 → C3 ⊆ Aut C22×C101206(C2^2xC10).31(C2xC6)480,1129
(C22×C10).32(C2×C6) = C22⋊C4×C30φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).32(C2xC6)480,920
(C22×C10).33(C2×C6) = C15×C42⋊C2φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).33(C2xC6)480,922
(C22×C10).34(C2×C6) = D4×C60φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).34(C2xC6)480,923
(C22×C10).35(C2×C6) = C15×C4⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).35(C2xC6)480,926
(C22×C10).36(C2×C6) = C15×C22⋊Q8φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).36(C2xC6)480,927
(C22×C10).37(C2×C6) = C15×C22.D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).37(C2xC6)480,928
(C22×C10).38(C2×C6) = C4○D4×C30φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).38(C2xC6)480,1183
(C22×C10).39(C2×C6) = C3×C10.10C42φ: C2×C6/C6 → C2 ⊆ Aut C22×C10480(C2^2xC10).39(C2xC6)480,109
(C22×C10).40(C2×C6) = Dic5×C2×C12φ: C2×C6/C6 → C2 ⊆ Aut C22×C10480(C2^2xC10).40(C2xC6)480,715
(C22×C10).41(C2×C6) = C6×C10.D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10480(C2^2xC10).41(C2xC6)480,716
(C22×C10).42(C2×C6) = C3×C20.48D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).42(C2xC6)480,717
(C22×C10).43(C2×C6) = C6×C4⋊Dic5φ: C2×C6/C6 → C2 ⊆ Aut C22×C10480(C2^2xC10).43(C2xC6)480,718
(C22×C10).44(C2×C6) = C3×C23.21D10φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).44(C2xC6)480,719
(C22×C10).45(C2×C6) = C6×D10⋊C4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).45(C2xC6)480,720
(C22×C10).46(C2×C6) = C12×C5⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).46(C2xC6)480,721
(C22×C10).47(C2×C6) = C3×C23.23D10φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).47(C2xC6)480,722
(C22×C10).48(C2×C6) = C3×C20⋊7D4φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).48(C2xC6)480,723
(C22×C10).49(C2×C6) = C6×C23.D5φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).49(C2xC6)480,745
(C22×C10).50(C2×C6) = C3×C24⋊2D5φ: C2×C6/C6 → C2 ⊆ Aut C22×C10120(C2^2xC10).50(C2xC6)480,746
(C22×C10).51(C2×C6) = C2×C6×Dic10φ: C2×C6/C6 → C2 ⊆ Aut C22×C10480(C2^2xC10).51(C2xC6)480,1135
(C22×C10).52(C2×C6) = D5×C22×C12φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).52(C2xC6)480,1136
(C22×C10).53(C2×C6) = C2×C6×D20φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).53(C2xC6)480,1137
(C22×C10).54(C2×C6) = C6×C4○D20φ: C2×C6/C6 → C2 ⊆ Aut C22×C10240(C2^2xC10).54(C2xC6)480,1138
(C22×C10).55(C2×C6) = Dic5×C22×C6φ: C2×C6/C6 → C2 ⊆ Aut C22×C10480(C2^2xC10).55(C2xC6)480,1148
(C22×C10).56(C2×C6) = C15×C2.C42central extension (φ=1)480(C2^2xC10).56(C2xC6)480,198
(C22×C10).57(C2×C6) = C4⋊C4×C30central extension (φ=1)480(C2^2xC10).57(C2xC6)480,921
(C22×C10).58(C2×C6) = Q8×C2×C30central extension (φ=1)480(C2^2xC10).58(C2xC6)480,1182

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