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Extensions 1→N→G→Q→1 with N=C10 and Q=Dic3⋊C4

Direct product G=N×Q with N=C10 and Q=Dic3⋊C4
dρLabelID
C10×Dic3⋊C4480C10xDic3:C4480,802

Semidirect products G=N:Q with N=C10 and Q=Dic3⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊(Dic3⋊C4) = C2×Dic3⋊F5φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C10120C10:(Dic3:C4)480,1001
C10⋊2(Dic3⋊C4) = C2×Dic15⋊5C4φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10:2(Dic3:C4)480,620
C10⋊3(Dic3⋊C4) = C2×C6.Dic10φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10:3(Dic3:C4)480,621
C10⋊4(Dic3⋊C4) = C2×C30.4Q8φ: Dic3⋊C4/C2×C12 → C2 ⊆ Aut C10480C10:4(Dic3:C4)480,888

Non-split extensions G=N.Q with N=C10 and Q=Dic3⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(Dic3⋊C4) = Dic5.Dic6φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C101208C10.1(Dic3:C4)480,235
C10.2(Dic3⋊C4) = Dic5.4Dic6φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C101208C10.2(Dic3:C4)480,236
C10.3(Dic3⋊C4) = D10.Dic6φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C102408C10.3(Dic3:C4)480,237
C10.4(Dic3⋊C4) = D10.2Dic6φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C102408C10.4(Dic3:C4)480,238
C10.5(Dic3⋊C4) = D10.20D12φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C10120C10.5(Dic3:C4)480,243
C10.6(Dic3⋊C4) = C30.4M4(2)φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C10480C10.6(Dic3:C4)480,252
C10.7(Dic3⋊C4) = Dic15⋊C8φ: Dic3⋊C4/Dic3 → C4 ⊆ Aut C10480C10.7(Dic3:C4)480,253
C10.8(Dic3⋊C4) = C60.14Q8φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.8(Dic3:C4)480,59
C10.9(Dic3⋊C4) = C60.15Q8φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.9(Dic3:C4)480,60
C10.10(Dic3⋊C4) = C30.SD16φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.10(Dic3:C4)480,62
C10.11(Dic3⋊C4) = C60.Q8φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.11(Dic3:C4)480,63
C10.12(Dic3⋊C4) = C30.20D8φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.12(Dic3:C4)480,65
C10.13(Dic3⋊C4) = C60.5Q8φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.13(Dic3:C4)480,66
C10.14(Dic3⋊C4) = C60.D4φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C102404C10.14(Dic3:C4)480,68
C10.15(Dic3⋊C4) = C12.59D20φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C102404C10.15(Dic3:C4)480,69
C10.16(Dic3⋊C4) = C30.24C42φ: Dic3⋊C4/C2×Dic3 → C2 ⊆ Aut C10480C10.16(Dic3:C4)480,70
C10.17(Dic3⋊C4) = C60.1Q8φ: Dic3⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.17(Dic3:C4)480,167
C10.18(Dic3⋊C4) = C60.2Q8φ: Dic3⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.18(Dic3:C4)480,168
C10.19(Dic3⋊C4) = C60.26Q8φ: Dic3⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.19(Dic3:C4)480,174
C10.20(Dic3⋊C4) = C60.210D4φ: Dic3⋊C4/C2×C12 → C2 ⊆ Aut C102404C10.20(Dic3:C4)480,182
C10.21(Dic3⋊C4) = C30.29C42φ: Dic3⋊C4/C2×C12 → C2 ⊆ Aut C10480C10.21(Dic3:C4)480,191
C10.22(Dic3⋊C4) = C5×C6.Q16central extension (φ=1)480C10.22(Dic3:C4)480,126
C10.23(Dic3⋊C4) = C5×C12.Q8central extension (φ=1)480C10.23(Dic3:C4)480,127
C10.24(Dic3⋊C4) = C5×Dic3⋊C8central extension (φ=1)480C10.24(Dic3:C4)480,133
C10.25(Dic3⋊C4) = C5×C12.53D4central extension (φ=1)2404C10.25(Dic3:C4)480,141
C10.26(Dic3⋊C4) = C5×C6.C42central extension (φ=1)480C10.26(Dic3:C4)480,150

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