# Extensions 1→N→G→Q→1 with N=C22 and Q=D5×C2×C6

Direct product G=N×Q with N=C22 and Q=D5×C2×C6
dρLabelID
D5×C23×C6240D5xC2^3xC6480,1210

Semidirect products G=N:Q with N=C22 and Q=D5×C2×C6
extensionφ:Q→Aut NdρLabelID
C22⋊(D5×C2×C6) = C22×D5×A4φ: D5×C2×C6/C22×D5C3 ⊆ Aut C2260C2^2:(D5xC2xC6)480,1202
C222(D5×C2×C6) = C6×D4×D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C22120C2^2:2(D5xC2xC6)480,1139
C223(D5×C2×C6) = C2×C6×C5⋊D4φ: D5×C2×C6/C2×C30C2 ⊆ Aut C22240C2^2:3(D5xC2xC6)480,1149

Non-split extensions G=N.Q with N=C22 and Q=D5×C2×C6
extensionφ:Q→Aut NdρLabelID
C22.1(D5×C2×C6) = C6×D42D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C22240C2^2.1(D5xC2xC6)480,1140
C22.2(D5×C2×C6) = C3×D5×C4○D4φ: D5×C2×C6/C6×D5C2 ⊆ Aut C221204C2^2.2(D5xC2xC6)480,1145
C22.3(D5×C2×C6) = C3×D48D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C221204C2^2.3(D5xC2xC6)480,1146
C22.4(D5×C2×C6) = C3×D4.10D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C222404C2^2.4(D5xC2xC6)480,1147
C22.5(D5×C2×C6) = C6×C4○D20φ: D5×C2×C6/C2×C30C2 ⊆ Aut C22240C2^2.5(D5xC2xC6)480,1138
C22.6(D5×C2×C6) = C3×D46D10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C221204C2^2.6(D5xC2xC6)480,1141
C22.7(D5×C2×C6) = C3×Q8.10D10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C222404C2^2.7(D5xC2xC6)480,1144
C22.8(D5×C2×C6) = C12×Dic10central extension (φ=1)480C2^2.8(D5xC2xC6)480,661
C22.9(D5×C2×C6) = D5×C4×C12central extension (φ=1)240C2^2.9(D5xC2xC6)480,664
C22.10(D5×C2×C6) = C3×C42⋊D5central extension (φ=1)240C2^2.10(D5xC2xC6)480,665
C22.11(D5×C2×C6) = C12×D20central extension (φ=1)240C2^2.11(D5xC2xC6)480,666
C22.12(D5×C2×C6) = C3×C23.11D10central extension (φ=1)240C2^2.12(D5xC2xC6)480,670
C22.13(D5×C2×C6) = C3×D5×C22⋊C4central extension (φ=1)120C2^2.13(D5xC2xC6)480,673
C22.14(D5×C2×C6) = C3×Dic54D4central extension (φ=1)240C2^2.14(D5xC2xC6)480,674
C22.15(D5×C2×C6) = C3×Dic53Q8central extension (φ=1)480C2^2.15(D5xC2xC6)480,680
C22.16(D5×C2×C6) = C3×D5×C4⋊C4central extension (φ=1)240C2^2.16(D5xC2xC6)480,684
C22.17(D5×C2×C6) = C3×C4⋊C47D5central extension (φ=1)240C2^2.17(D5xC2xC6)480,685
C22.18(D5×C2×C6) = C3×D208C4central extension (φ=1)240C2^2.18(D5xC2xC6)480,686
C22.19(D5×C2×C6) = Dic5×C2×C12central extension (φ=1)480C2^2.19(D5xC2xC6)480,715
C22.20(D5×C2×C6) = C6×C10.D4central extension (φ=1)480C2^2.20(D5xC2xC6)480,716
C22.21(D5×C2×C6) = C6×C4⋊Dic5central extension (φ=1)480C2^2.21(D5xC2xC6)480,718
C22.22(D5×C2×C6) = C3×C23.21D10central extension (φ=1)240C2^2.22(D5xC2xC6)480,719
C22.23(D5×C2×C6) = C6×D10⋊C4central extension (φ=1)240C2^2.23(D5xC2xC6)480,720
C22.24(D5×C2×C6) = C12×C5⋊D4central extension (φ=1)240C2^2.24(D5xC2xC6)480,721
C22.25(D5×C2×C6) = C3×D4×Dic5central extension (φ=1)240C2^2.25(D5xC2xC6)480,727
C22.26(D5×C2×C6) = C3×Q8×Dic5central extension (φ=1)480C2^2.26(D5xC2xC6)480,738
C22.27(D5×C2×C6) = C6×C23.D5central extension (φ=1)240C2^2.27(D5xC2xC6)480,745
C22.28(D5×C2×C6) = C2×C6×Dic10central extension (φ=1)480C2^2.28(D5xC2xC6)480,1135
C22.29(D5×C2×C6) = D5×C22×C12central extension (φ=1)240C2^2.29(D5xC2xC6)480,1136
C22.30(D5×C2×C6) = C2×C6×D20central extension (φ=1)240C2^2.30(D5xC2xC6)480,1137
C22.31(D5×C2×C6) = C6×Q8×D5central extension (φ=1)240C2^2.31(D5xC2xC6)480,1142
C22.32(D5×C2×C6) = C6×Q82D5central extension (φ=1)240C2^2.32(D5xC2xC6)480,1143
C22.33(D5×C2×C6) = Dic5×C22×C6central extension (φ=1)480C2^2.33(D5xC2xC6)480,1148
C22.34(D5×C2×C6) = C3×C202Q8central stem extension (φ=1)480C2^2.34(D5xC2xC6)480,662
C22.35(D5×C2×C6) = C3×C20.6Q8central stem extension (φ=1)480C2^2.35(D5xC2xC6)480,663
C22.36(D5×C2×C6) = C3×C204D4central stem extension (φ=1)240C2^2.36(D5xC2xC6)480,667
C22.37(D5×C2×C6) = C3×C4.D20central stem extension (φ=1)240C2^2.37(D5xC2xC6)480,668
C22.38(D5×C2×C6) = C3×C422D5central stem extension (φ=1)240C2^2.38(D5xC2xC6)480,669
C22.39(D5×C2×C6) = C3×Dic5.14D4central stem extension (φ=1)240C2^2.39(D5xC2xC6)480,671
C22.40(D5×C2×C6) = C3×C23.D10central stem extension (φ=1)240C2^2.40(D5xC2xC6)480,672
C22.41(D5×C2×C6) = C3×C22⋊D20central stem extension (φ=1)120C2^2.41(D5xC2xC6)480,675
C22.42(D5×C2×C6) = C3×D10.12D4central stem extension (φ=1)240C2^2.42(D5xC2xC6)480,676
C22.43(D5×C2×C6) = C3×D10⋊D4central stem extension (φ=1)240C2^2.43(D5xC2xC6)480,677
C22.44(D5×C2×C6) = C3×Dic5.5D4central stem extension (φ=1)240C2^2.44(D5xC2xC6)480,678
C22.45(D5×C2×C6) = C3×C22.D20central stem extension (φ=1)240C2^2.45(D5xC2xC6)480,679
C22.46(D5×C2×C6) = C3×C20⋊Q8central stem extension (φ=1)480C2^2.46(D5xC2xC6)480,681
C22.47(D5×C2×C6) = C3×Dic5.Q8central stem extension (φ=1)480C2^2.47(D5xC2xC6)480,682
C22.48(D5×C2×C6) = C3×C4.Dic10central stem extension (φ=1)480C2^2.48(D5xC2xC6)480,683
C22.49(D5×C2×C6) = C3×D10.13D4central stem extension (φ=1)240C2^2.49(D5xC2xC6)480,687
C22.50(D5×C2×C6) = C3×C4⋊D20central stem extension (φ=1)240C2^2.50(D5xC2xC6)480,688
C22.51(D5×C2×C6) = C3×D10⋊Q8central stem extension (φ=1)240C2^2.51(D5xC2xC6)480,689
C22.52(D5×C2×C6) = C3×D102Q8central stem extension (φ=1)240C2^2.52(D5xC2xC6)480,690
C22.53(D5×C2×C6) = C3×C4⋊C4⋊D5central stem extension (φ=1)240C2^2.53(D5xC2xC6)480,691
C22.54(D5×C2×C6) = C3×C20.48D4central stem extension (φ=1)240C2^2.54(D5xC2xC6)480,717
C22.55(D5×C2×C6) = C3×C23.23D10central stem extension (φ=1)240C2^2.55(D5xC2xC6)480,722
C22.56(D5×C2×C6) = C3×C207D4central stem extension (φ=1)240C2^2.56(D5xC2xC6)480,723
C22.57(D5×C2×C6) = C3×C23.18D10central stem extension (φ=1)240C2^2.57(D5xC2xC6)480,728
C22.58(D5×C2×C6) = C3×C20.17D4central stem extension (φ=1)240C2^2.58(D5xC2xC6)480,729
C22.59(D5×C2×C6) = C3×C23⋊D10central stem extension (φ=1)120C2^2.59(D5xC2xC6)480,730
C22.60(D5×C2×C6) = C3×C202D4central stem extension (φ=1)240C2^2.60(D5xC2xC6)480,731
C22.61(D5×C2×C6) = C3×Dic5⋊D4central stem extension (φ=1)240C2^2.61(D5xC2xC6)480,732
C22.62(D5×C2×C6) = C3×C20⋊D4central stem extension (φ=1)240C2^2.62(D5xC2xC6)480,733
C22.63(D5×C2×C6) = C3×Dic5⋊Q8central stem extension (φ=1)480C2^2.63(D5xC2xC6)480,737
C22.64(D5×C2×C6) = C3×D103Q8central stem extension (φ=1)240C2^2.64(D5xC2xC6)480,739
C22.65(D5×C2×C6) = C3×C20.23D4central stem extension (φ=1)240C2^2.65(D5xC2xC6)480,740
C22.66(D5×C2×C6) = C3×C242D5central stem extension (φ=1)120C2^2.66(D5xC2xC6)480,746

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