# Extensions 1→N→G→Q→1 with N=C4 and Q=D5×C2×C6

Direct product G=N×Q with N=C4 and Q=D5×C2×C6
dρLabelID
D5×C22×C12240D5xC2^2xC12480,1136

Semidirect products G=N:Q with N=C4 and Q=D5×C2×C6
extensionφ:Q→Aut NdρLabelID
C41(D5×C2×C6) = C6×D4×D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4120C4:1(D5xC2xC6)480,1139
C42(D5×C2×C6) = C2×C6×D20φ: D5×C2×C6/C2×C30C2 ⊆ Aut C4240C4:2(D5xC2xC6)480,1137

Non-split extensions G=N.Q with N=C4 and Q=D5×C2×C6
extensionφ:Q→Aut NdρLabelID
C4.1(D5×C2×C6) = C3×D5×D8φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.1(D5xC2xC6)480,703
C4.2(D5×C2×C6) = C3×D8⋊D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.2(D5xC2xC6)480,704
C4.3(D5×C2×C6) = C3×D83D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.3(D5xC2xC6)480,705
C4.4(D5×C2×C6) = C3×D5×SD16φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.4(D5xC2xC6)480,706
C4.5(D5×C2×C6) = C3×D40⋊C2φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.5(D5xC2xC6)480,707
C4.6(D5×C2×C6) = C3×SD16⋊D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.6(D5xC2xC6)480,708
C4.7(D5×C2×C6) = C3×SD163D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.7(D5xC2xC6)480,709
C4.8(D5×C2×C6) = C3×D5×Q16φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.8(D5xC2xC6)480,710
C4.9(D5×C2×C6) = C3×Q16⋊D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.9(D5xC2xC6)480,711
C4.10(D5×C2×C6) = C3×Q8.D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.10(D5xC2xC6)480,712
C4.11(D5×C2×C6) = C6×D4⋊D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4240C4.11(D5xC2xC6)480,724
C4.12(D5×C2×C6) = C3×D4.D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.12(D5xC2xC6)480,725
C4.13(D5×C2×C6) = C6×D4.D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4240C4.13(D5xC2xC6)480,726
C4.14(D5×C2×C6) = C6×Q8⋊D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4240C4.14(D5xC2xC6)480,734
C4.15(D5×C2×C6) = C3×C20.C23φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.15(D5xC2xC6)480,735
C4.16(D5×C2×C6) = C6×C5⋊Q16φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4480C4.16(D5xC2xC6)480,736
C4.17(D5×C2×C6) = C3×D4⋊D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.17(D5xC2xC6)480,742
C4.18(D5×C2×C6) = C3×D4.8D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.18(D5xC2xC6)480,743
C4.19(D5×C2×C6) = C3×D4.9D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.19(D5xC2xC6)480,744
C4.20(D5×C2×C6) = C6×D42D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4240C4.20(D5xC2xC6)480,1140
C4.21(D5×C2×C6) = C3×D46D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.21(D5xC2xC6)480,1141
C4.22(D5×C2×C6) = C6×Q8×D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4240C4.22(D5xC2xC6)480,1142
C4.23(D5×C2×C6) = C6×Q82D5φ: D5×C2×C6/C6×D5C2 ⊆ Aut C4240C4.23(D5xC2xC6)480,1143
C4.24(D5×C2×C6) = C3×Q8.10D10φ: D5×C2×C6/C6×D5C2 ⊆ Aut C42404C4.24(D5xC2xC6)480,1144
C4.25(D5×C2×C6) = C3×D5×C4○D4φ: D5×C2×C6/C6×D5C2 ⊆ Aut C41204C4.25(D5xC2xC6)480,1145
C4.26(D5×C2×C6) = C6×C40⋊C2φ: D5×C2×C6/C2×C30C2 ⊆ Aut C4240C4.26(D5xC2xC6)480,695
C4.27(D5×C2×C6) = C6×D40φ: D5×C2×C6/C2×C30C2 ⊆ Aut C4240C4.27(D5xC2xC6)480,696
C4.28(D5×C2×C6) = C3×D407C2φ: D5×C2×C6/C2×C30C2 ⊆ Aut C42402C4.28(D5xC2xC6)480,697
C4.29(D5×C2×C6) = C6×Dic20φ: D5×C2×C6/C2×C30C2 ⊆ Aut C4480C4.29(D5xC2xC6)480,698
C4.30(D5×C2×C6) = C3×C8⋊D10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C41204C4.30(D5xC2xC6)480,701
C4.31(D5×C2×C6) = C3×C8.D10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C42404C4.31(D5xC2xC6)480,702
C4.32(D5×C2×C6) = C2×C6×Dic10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C4480C4.32(D5xC2xC6)480,1135
C4.33(D5×C2×C6) = C3×D48D10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C41204C4.33(D5xC2xC6)480,1146
C4.34(D5×C2×C6) = C3×D4.10D10φ: D5×C2×C6/C2×C30C2 ⊆ Aut C42404C4.34(D5xC2xC6)480,1147
C4.35(D5×C2×C6) = D5×C2×C24central extension (φ=1)240C4.35(D5xC2xC6)480,692
C4.36(D5×C2×C6) = C6×C8⋊D5central extension (φ=1)240C4.36(D5xC2xC6)480,693
C4.37(D5×C2×C6) = C3×D20.3C4central extension (φ=1)2402C4.37(D5xC2xC6)480,694
C4.38(D5×C2×C6) = C3×D5×M4(2)central extension (φ=1)1204C4.38(D5xC2xC6)480,699
C4.39(D5×C2×C6) = C3×D20.2C4central extension (φ=1)2404C4.39(D5xC2xC6)480,700
C4.40(D5×C2×C6) = C2×C6×C52C8central extension (φ=1)480C4.40(D5xC2xC6)480,713
C4.41(D5×C2×C6) = C6×C4.Dic5central extension (φ=1)240C4.41(D5xC2xC6)480,714
C4.42(D5×C2×C6) = C3×D4.Dic5central extension (φ=1)2404C4.42(D5xC2xC6)480,741
C4.43(D5×C2×C6) = C6×C4○D20central extension (φ=1)240C4.43(D5xC2xC6)480,1138

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