# Extensions 1→N→G→Q→1 with N=C12 and Q=C2×C10

Direct product G=N×Q with N=C12 and Q=C2×C10
dρLabelID
C22×C60240C2^2xC60240,185

Semidirect products G=N:Q with N=C12 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C12⋊(C2×C10) = C5×S3×D4φ: C2×C10/C5C22 ⊆ Aut C12604C12:(C2xC10)240,169
C122(C2×C10) = C10×D12φ: C2×C10/C10C2 ⊆ Aut C12120C12:2(C2xC10)240,167
C123(C2×C10) = S3×C2×C20φ: C2×C10/C10C2 ⊆ Aut C12120C12:3(C2xC10)240,166
C124(C2×C10) = D4×C30φ: C2×C10/C10C2 ⊆ Aut C12120C12:4(C2xC10)240,186

Non-split extensions G=N.Q with N=C12 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C10) = C5×D4⋊S3φ: C2×C10/C5C22 ⊆ Aut C121204C12.1(C2xC10)240,60
C12.2(C2×C10) = C5×D4.S3φ: C2×C10/C5C22 ⊆ Aut C121204C12.2(C2xC10)240,61
C12.3(C2×C10) = C5×Q82S3φ: C2×C10/C5C22 ⊆ Aut C121204C12.3(C2xC10)240,62
C12.4(C2×C10) = C5×C3⋊Q16φ: C2×C10/C5C22 ⊆ Aut C122404C12.4(C2xC10)240,63
C12.5(C2×C10) = C5×D42S3φ: C2×C10/C5C22 ⊆ Aut C121204C12.5(C2xC10)240,170
C12.6(C2×C10) = C5×S3×Q8φ: C2×C10/C5C22 ⊆ Aut C121204C12.6(C2xC10)240,171
C12.7(C2×C10) = C5×Q83S3φ: C2×C10/C5C22 ⊆ Aut C121204C12.7(C2xC10)240,172
C12.8(C2×C10) = C5×C24⋊C2φ: C2×C10/C10C2 ⊆ Aut C121202C12.8(C2xC10)240,51
C12.9(C2×C10) = C5×D24φ: C2×C10/C10C2 ⊆ Aut C121202C12.9(C2xC10)240,52
C12.10(C2×C10) = C5×Dic12φ: C2×C10/C10C2 ⊆ Aut C122402C12.10(C2xC10)240,53
C12.11(C2×C10) = C10×Dic6φ: C2×C10/C10C2 ⊆ Aut C12240C12.11(C2xC10)240,165
C12.12(C2×C10) = S3×C40φ: C2×C10/C10C2 ⊆ Aut C121202C12.12(C2xC10)240,49
C12.13(C2×C10) = C5×C8⋊S3φ: C2×C10/C10C2 ⊆ Aut C121202C12.13(C2xC10)240,50
C12.14(C2×C10) = C10×C3⋊C8φ: C2×C10/C10C2 ⊆ Aut C12240C12.14(C2xC10)240,54
C12.15(C2×C10) = C5×C4.Dic3φ: C2×C10/C10C2 ⊆ Aut C121202C12.15(C2xC10)240,55
C12.16(C2×C10) = C5×C4○D12φ: C2×C10/C10C2 ⊆ Aut C121202C12.16(C2xC10)240,168
C12.17(C2×C10) = C15×D8φ: C2×C10/C10C2 ⊆ Aut C121202C12.17(C2xC10)240,86
C12.18(C2×C10) = C15×SD16φ: C2×C10/C10C2 ⊆ Aut C121202C12.18(C2xC10)240,87
C12.19(C2×C10) = C15×Q16φ: C2×C10/C10C2 ⊆ Aut C122402C12.19(C2xC10)240,88
C12.20(C2×C10) = Q8×C30φ: C2×C10/C10C2 ⊆ Aut C12240C12.20(C2xC10)240,187
C12.21(C2×C10) = C15×C4○D4φ: C2×C10/C10C2 ⊆ Aut C121202C12.21(C2xC10)240,188
C12.22(C2×C10) = C15×M4(2)central extension (φ=1)1202C12.22(C2xC10)240,85

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