# Extensions 1→N→G→Q→1 with N=C23 and Q=C2×C30

Direct product G=N×Q with N=C23 and Q=C2×C30
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C23 and Q=C2×C30
extensionφ:Q→Aut NdρLabelID
C231(C2×C30) = C15×C22≀C2φ: C2×C30/C15C22 ⊆ Aut C23120C2^3:1(C2xC30)480,925
C232(C2×C30) = C15×2+ 1+4φ: C2×C30/C15C22 ⊆ Aut C231204C2^3:2(C2xC30)480,1184
C233(C2×C30) = A4×C22×C10φ: C2×C30/C2×C10C3 ⊆ Aut C23120C2^3:3(C2xC30)480,1208
C234(C2×C30) = D4×C2×C30φ: C2×C30/C30C2 ⊆ Aut C23240C2^3:4(C2xC30)480,1181

Non-split extensions G=N.Q with N=C23 and Q=C2×C30
extensionφ:Q→Aut NdρLabelID
C23.1(C2×C30) = C15×C23⋊C4φ: C2×C30/C15C22 ⊆ Aut C231204C2^3.1(C2xC30)480,202
C23.2(C2×C30) = C15×C4⋊D4φ: C2×C30/C15C22 ⊆ Aut C23240C2^3.2(C2xC30)480,926
C23.3(C2×C30) = C15×C4.4D4φ: C2×C30/C15C22 ⊆ Aut C23240C2^3.3(C2xC30)480,929
C23.4(C2×C30) = C15×C422C2φ: C2×C30/C15C22 ⊆ Aut C23240C2^3.4(C2xC30)480,931
C23.5(C2×C30) = C15×C41D4φ: C2×C30/C15C22 ⊆ Aut C23240C2^3.5(C2xC30)480,932
C23.6(C2×C30) = A4×C2×C20φ: C2×C30/C2×C10C3 ⊆ Aut C23120C2^3.6(C2xC30)480,1126
C23.7(C2×C30) = C5×D4×A4φ: C2×C30/C2×C10C3 ⊆ Aut C23606C2^3.7(C2xC30)480,1127
C23.8(C2×C30) = C5×Q8×A4φ: C2×C30/C2×C10C3 ⊆ Aut C231206C2^3.8(C2xC30)480,1129
C23.9(C2×C30) = C15×C42⋊C2φ: C2×C30/C30C2 ⊆ Aut C23240C2^3.9(C2xC30)480,922
C23.10(C2×C30) = D4×C60φ: C2×C30/C30C2 ⊆ Aut C23240C2^3.10(C2xC30)480,923
C23.11(C2×C30) = C15×C22⋊Q8φ: C2×C30/C30C2 ⊆ Aut C23240C2^3.11(C2xC30)480,927
C23.12(C2×C30) = C15×C22.D4φ: C2×C30/C30C2 ⊆ Aut C23240C2^3.12(C2xC30)480,928
C23.13(C2×C30) = C4○D4×C30φ: C2×C30/C30C2 ⊆ Aut C23240C2^3.13(C2xC30)480,1183
C23.14(C2×C30) = C15×C2.C42central extension (φ=1)480C2^3.14(C2xC30)480,198
C23.15(C2×C30) = C22⋊C4×C30central extension (φ=1)240C2^3.15(C2xC30)480,920
C23.16(C2×C30) = C4⋊C4×C30central extension (φ=1)480C2^3.16(C2xC30)480,921
C23.17(C2×C30) = Q8×C2×C30central extension (φ=1)480C2^3.17(C2xC30)480,1182

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