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

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

Semidirect products G=N:Q with N=C10 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
C10⋊(C2×C12) = C2×C6×F5φ: C2×C12/C6 → C4 ⊆ Aut C1060C10:(C2xC12)240,200
C10⋊2(C2×C12) = D5×C2×C12φ: C2×C12/C12 → C2 ⊆ Aut C10120C10:2(C2xC12)240,156
C10⋊3(C2×C12) = C2×C6×Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C10240C10:3(C2xC12)240,163

Non-split extensions G=N.Q with N=C10 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C12) = C3×D5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C101204C10.1(C2xC12)240,111
C10.2(C2×C12) = C3×C4.F5φ: C2×C12/C6 → C4 ⊆ Aut C101204C10.2(C2xC12)240,112
C10.3(C2×C12) = C12×F5φ: C2×C12/C6 → C4 ⊆ Aut C10604C10.3(C2xC12)240,113
C10.4(C2×C12) = C3×C4⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C10604C10.4(C2xC12)240,114
C10.5(C2×C12) = C6×C5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C10240C10.5(C2xC12)240,115
C10.6(C2×C12) = C3×C22.F5φ: C2×C12/C6 → C4 ⊆ Aut C101204C10.6(C2xC12)240,116
C10.7(C2×C12) = C3×C22⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C10604C10.7(C2xC12)240,117
C10.8(C2×C12) = D5×C24φ: C2×C12/C12 → C2 ⊆ Aut C101202C10.8(C2xC12)240,33
C10.9(C2×C12) = C3×C8⋊D5φ: C2×C12/C12 → C2 ⊆ Aut C101202C10.9(C2xC12)240,34
C10.10(C2×C12) = C3×C10.D4φ: C2×C12/C12 → C2 ⊆ Aut C10240C10.10(C2xC12)240,41
C10.11(C2×C12) = C3×D10⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C10120C10.11(C2xC12)240,43
C10.12(C2×C12) = C6×C5⋊2C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C10240C10.12(C2xC12)240,38
C10.13(C2×C12) = C3×C4.Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C101202C10.13(C2xC12)240,39
C10.14(C2×C12) = C12×Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C10240C10.14(C2xC12)240,40
C10.15(C2×C12) = C3×C4⋊Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C10240C10.15(C2xC12)240,42
C10.16(C2×C12) = C3×C23.D5φ: C2×C12/C2×C6 → C2 ⊆ Aut C10120C10.16(C2xC12)240,48
C10.17(C2×C12) = C15×C22⋊C4central extension (φ=1)120C10.17(C2xC12)240,82
C10.18(C2×C12) = C15×C4⋊C4central extension (φ=1)240C10.18(C2xC12)240,83
C10.19(C2×C12) = C15×M4(2)central extension (φ=1)1202C10.19(C2xC12)240,85

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