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Extensions 1→N→G→Q→1 with N=C10 and Q=C2×Dic6

Direct product G=N×Q with N=C10 and Q=C2×Dic6
dρLabelID
C2×C10×Dic6480C2xC10xDic6480,1150

Semidirect products G=N:Q with N=C10 and Q=C2×Dic6
extensionφ:Q→Aut NdρLabelID
C10⋊1(C2×Dic6) = C2×D5×Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10:1(C2xDic6)480,1073
C10⋊2(C2×Dic6) = C22×C15⋊Q8φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10:2(C2xDic6)480,1121
C10⋊3(C2×Dic6) = C22×Dic30φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10:3(C2xDic6)480,1165

Non-split extensions G=N.Q with N=C10 and Q=C2×Dic6
extensionφ:Q→Aut NdρLabelID
C10.1(C2×Dic6) = Dic5⋊5Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.1(C2xDic6)480,399
C10.2(C2×Dic6) = Dic3⋊Dic10φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.2(C2xDic6)480,404
C10.3(C2×Dic6) = Dic15⋊Q8φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.3(C2xDic6)480,405
C10.4(C2×Dic6) = Dic5×Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.4(C2xDic6)480,408
C10.5(C2×Dic6) = Dic30⋊17C4φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.5(C2xDic6)480,409
C10.6(C2×Dic6) = Dic5.1Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.6(C2xDic6)480,410
C10.7(C2×Dic6) = Dic5.2Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.7(C2xDic6)480,411
C10.8(C2×Dic6) = D10⋊Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.8(C2xDic6)480,425
C10.9(C2×Dic6) = C60.67D4φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.9(C2xDic6)480,435
C10.10(C2×Dic6) = C60.68D4φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.10(C2xDic6)480,436
C10.11(C2×Dic6) = Dic5⋊Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.11(C2xDic6)480,452
C10.12(C2×Dic6) = Dic5.7Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.12(C2xDic6)480,454
C10.13(C2×Dic6) = D5×Dic3⋊C4φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.13(C2xDic6)480,468
C10.14(C2×Dic6) = D5×C4⋊Dic3φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.14(C2xDic6)480,488
C10.15(C2×Dic6) = D10⋊1Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.15(C2xDic6)480,497
C10.16(C2×Dic6) = D10⋊2Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.16(C2xDic6)480,498
C10.17(C2×Dic6) = Dic15.D4φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.17(C2xDic6)480,506
C10.18(C2×Dic6) = D10⋊4Dic6φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10240C10.18(C2xDic6)480,507
C10.19(C2×Dic6) = C60⋊Q8φ: C2×Dic6/Dic6 → C2 ⊆ Aut C10480C10.19(C2xDic6)480,544
C10.20(C2×Dic6) = C60.6Q8φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.20(C2xDic6)480,457
C10.21(C2×Dic6) = C12.Dic10φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.21(C2xDic6)480,460
C10.22(C2×Dic6) = C20.Dic6φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.22(C2xDic6)480,464
C10.23(C2×Dic6) = C4×C15⋊Q8φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.23(C2xDic6)480,543
C10.24(C2×Dic6) = C20⋊4Dic6φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.24(C2xDic6)480,545
C10.25(C2×Dic6) = C20⋊Dic6φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.25(C2xDic6)480,546
C10.26(C2×Dic6) = C2×C30.Q8φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.26(C2xDic6)480,617
C10.27(C2×Dic6) = C2×Dic15⋊5C4φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.27(C2xDic6)480,620
C10.28(C2×Dic6) = C2×C6.Dic10φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10480C10.28(C2xDic6)480,621
C10.29(C2×Dic6) = (C2×C30)⋊Q8φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10240C10.29(C2xDic6)480,650
C10.30(C2×Dic6) = (C2×C10)⋊8Dic6φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10240C10.30(C2xDic6)480,651
C10.31(C2×Dic6) = Dic15.48D4φ: C2×Dic6/C2×Dic3 → C2 ⊆ Aut C10240C10.31(C2xDic6)480,652
C10.32(C2×Dic6) = C4×Dic30φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.32(C2xDic6)480,833
C10.33(C2×Dic6) = C60⋊8Q8φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.33(C2xDic6)480,834
C10.34(C2×Dic6) = C60.24Q8φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.34(C2xDic6)480,835
C10.35(C2×Dic6) = C22⋊2Dic30φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10240C10.35(C2xDic6)480,843
C10.36(C2×Dic6) = C4⋊Dic30φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.36(C2xDic6)480,853
C10.37(C2×Dic6) = C4.Dic30φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.37(C2xDic6)480,855
C10.38(C2×Dic6) = C2×C30.4Q8φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.38(C2xDic6)480,888
C10.39(C2×Dic6) = C60.205D4φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10240C10.39(C2xDic6)480,889
C10.40(C2×Dic6) = C2×C60⋊5C4φ: C2×Dic6/C2×C12 → C2 ⊆ Aut C10480C10.40(C2xDic6)480,890
C10.41(C2×Dic6) = C20×Dic6central extension (φ=1)480C10.41(C2xDic6)480,747
C10.42(C2×Dic6) = C5×C12⋊2Q8central extension (φ=1)480C10.42(C2xDic6)480,748
C10.43(C2×Dic6) = C5×C12.6Q8central extension (φ=1)480C10.43(C2xDic6)480,749
C10.44(C2×Dic6) = C5×Dic3.D4central extension (φ=1)240C10.44(C2xDic6)480,757
C10.45(C2×Dic6) = C5×C12⋊Q8central extension (φ=1)480C10.45(C2xDic6)480,767
C10.46(C2×Dic6) = C5×C4.Dic6central extension (φ=1)480C10.46(C2xDic6)480,769
C10.47(C2×Dic6) = C10×Dic3⋊C4central extension (φ=1)480C10.47(C2xDic6)480,802
C10.48(C2×Dic6) = C5×C12.48D4central extension (φ=1)240C10.48(C2xDic6)480,803
C10.49(C2×Dic6) = C10×C4⋊Dic3central extension (φ=1)480C10.49(C2xDic6)480,804

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