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Extensions 1→N→G→Q→1 with N=C10 and Q=C22×C12

Direct product G=N×Q with N=C10 and Q=C22×C12
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C10 and Q=C22×C12
extensionφ:Q→Aut NdρLabelID
C10⋊(C22×C12) = F5×C22×C6φ: C22×C12/C2×C6 → C4 ⊆ Aut C10120C10:(C2^2xC12)480,1205
C10⋊2(C22×C12) = D5×C22×C12φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10:2(C2^2xC12)480,1136
C10⋊3(C22×C12) = Dic5×C22×C6φ: C22×C12/C22×C6 → C2 ⊆ Aut C10480C10:3(C2^2xC12)480,1148

Non-split extensions G=N.Q with N=C10 and Q=C22×C12
extensionφ:Q→Aut NdρLabelID
C10.1(C22×C12) = C6×D5⋊C8φ: C22×C12/C2×C6 → C4 ⊆ Aut C10240C10.1(C2^2xC12)480,1047
C10.2(C22×C12) = C6×C4.F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C10240C10.2(C2^2xC12)480,1048
C10.3(C22×C12) = C3×D5⋊M4(2)φ: C22×C12/C2×C6 → C4 ⊆ Aut C101204C10.3(C2^2xC12)480,1049
C10.4(C22×C12) = F5×C2×C12φ: C22×C12/C2×C6 → C4 ⊆ Aut C10120C10.4(C2^2xC12)480,1050
C10.5(C22×C12) = C6×C4⋊F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C10120C10.5(C2^2xC12)480,1051
C10.6(C22×C12) = C3×D10.C23φ: C22×C12/C2×C6 → C4 ⊆ Aut C101204C10.6(C2^2xC12)480,1052
C10.7(C22×C12) = C3×D4.F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C102408C10.7(C2^2xC12)480,1053
C10.8(C22×C12) = C3×D4×F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C10608C10.8(C2^2xC12)480,1054
C10.9(C22×C12) = C3×Q8.F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C102408C10.9(C2^2xC12)480,1055
C10.10(C22×C12) = C3×Q8×F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C101208C10.10(C2^2xC12)480,1056
C10.11(C22×C12) = C2×C6×C5⋊C8φ: C22×C12/C2×C6 → C4 ⊆ Aut C10480C10.11(C2^2xC12)480,1057
C10.12(C22×C12) = C6×C22.F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C10240C10.12(C2^2xC12)480,1058
C10.13(C22×C12) = C6×C22⋊F5φ: C22×C12/C2×C6 → C4 ⊆ Aut C10120C10.13(C2^2xC12)480,1059
C10.14(C22×C12) = C12×Dic10φ: C22×C12/C2×C12 → C2 ⊆ Aut C10480C10.14(C2^2xC12)480,661
C10.15(C22×C12) = D5×C4×C12φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.15(C2^2xC12)480,664
C10.16(C22×C12) = C3×C42⋊D5φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.16(C2^2xC12)480,665
C10.17(C22×C12) = C12×D20φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.17(C2^2xC12)480,666
C10.18(C22×C12) = C3×C23.11D10φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.18(C2^2xC12)480,670
C10.19(C22×C12) = C3×D5×C22⋊C4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10120C10.19(C2^2xC12)480,673
C10.20(C22×C12) = C3×Dic5⋊4D4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.20(C2^2xC12)480,674
C10.21(C22×C12) = C3×Dic5⋊3Q8φ: C22×C12/C2×C12 → C2 ⊆ Aut C10480C10.21(C2^2xC12)480,680
C10.22(C22×C12) = C3×D5×C4⋊C4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.22(C2^2xC12)480,684
C10.23(C22×C12) = C3×C4⋊C4⋊7D5φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.23(C2^2xC12)480,685
C10.24(C22×C12) = C3×D20⋊8C4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.24(C2^2xC12)480,686
C10.25(C22×C12) = D5×C2×C24φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.25(C2^2xC12)480,692
C10.26(C22×C12) = C6×C8⋊D5φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.26(C2^2xC12)480,693
C10.27(C22×C12) = C3×D20.3C4φ: C22×C12/C2×C12 → C2 ⊆ Aut C102402C10.27(C2^2xC12)480,694
C10.28(C22×C12) = C3×D5×M4(2)φ: C22×C12/C2×C12 → C2 ⊆ Aut C101204C10.28(C2^2xC12)480,699
C10.29(C22×C12) = C3×D20.2C4φ: C22×C12/C2×C12 → C2 ⊆ Aut C102404C10.29(C2^2xC12)480,700
C10.30(C22×C12) = Dic5×C2×C12φ: C22×C12/C2×C12 → C2 ⊆ Aut C10480C10.30(C2^2xC12)480,715
C10.31(C22×C12) = C6×C10.D4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10480C10.31(C2^2xC12)480,716
C10.32(C22×C12) = C6×D10⋊C4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.32(C2^2xC12)480,720
C10.33(C22×C12) = C12×C5⋊D4φ: C22×C12/C2×C12 → C2 ⊆ Aut C10240C10.33(C2^2xC12)480,721
C10.34(C22×C12) = C2×C6×C5⋊2C8φ: C22×C12/C22×C6 → C2 ⊆ Aut C10480C10.34(C2^2xC12)480,713
C10.35(C22×C12) = C6×C4.Dic5φ: C22×C12/C22×C6 → C2 ⊆ Aut C10240C10.35(C2^2xC12)480,714
C10.36(C22×C12) = C6×C4⋊Dic5φ: C22×C12/C22×C6 → C2 ⊆ Aut C10480C10.36(C2^2xC12)480,718
C10.37(C22×C12) = C3×C23.21D10φ: C22×C12/C22×C6 → C2 ⊆ Aut C10240C10.37(C2^2xC12)480,719
C10.38(C22×C12) = C3×D4×Dic5φ: C22×C12/C22×C6 → C2 ⊆ Aut C10240C10.38(C2^2xC12)480,727
C10.39(C22×C12) = C3×Q8×Dic5φ: C22×C12/C22×C6 → C2 ⊆ Aut C10480C10.39(C2^2xC12)480,738
C10.40(C22×C12) = C3×D4.Dic5φ: C22×C12/C22×C6 → C2 ⊆ Aut C102404C10.40(C2^2xC12)480,741
C10.41(C22×C12) = C6×C23.D5φ: C22×C12/C22×C6 → C2 ⊆ Aut C10240C10.41(C2^2xC12)480,745
C10.42(C22×C12) = C22⋊C4×C30central extension (φ=1)240C10.42(C2^2xC12)480,920
C10.43(C22×C12) = C4⋊C4×C30central extension (φ=1)480C10.43(C2^2xC12)480,921
C10.44(C22×C12) = C15×C42⋊C2central extension (φ=1)240C10.44(C2^2xC12)480,922
C10.45(C22×C12) = D4×C60central extension (φ=1)240C10.45(C2^2xC12)480,923
C10.46(C22×C12) = Q8×C60central extension (φ=1)480C10.46(C2^2xC12)480,924
C10.47(C22×C12) = M4(2)×C30central extension (φ=1)240C10.47(C2^2xC12)480,935
C10.48(C22×C12) = C15×C8○D4central extension (φ=1)2402C10.48(C2^2xC12)480,936

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