# Extensions 1→N→G→Q→1 with N=C30 and Q=C22

Direct product G=N×Q with N=C30 and Q=C22
dρLabelID
C22×C30120C2^2xC30120,47

Semidirect products G=N:Q with N=C30 and Q=C22
extensionφ:Q→Aut NdρLabelID
C30⋊C22 = C2×S3×D5φ: C22/C1C22 ⊆ Aut C30304+C30:C2^2120,42
C302C22 = C22×D15φ: C22/C2C2 ⊆ Aut C3060C30:2C2^2120,46
C303C22 = D5×C2×C6φ: C22/C2C2 ⊆ Aut C3060C30:3C2^2120,44
C304C22 = S3×C2×C10φ: C22/C2C2 ⊆ Aut C3060C30:4C2^2120,45

Non-split extensions G=N.Q with N=C30 and Q=C22
extensionφ:Q→Aut NdρLabelID
C30.1C22 = D5×Dic3φ: C22/C1C22 ⊆ Aut C30604-C30.1C2^2120,8
C30.2C22 = S3×Dic5φ: C22/C1C22 ⊆ Aut C30604-C30.2C2^2120,9
C30.3C22 = D30.C2φ: C22/C1C22 ⊆ Aut C30604+C30.3C2^2120,10
C30.4C22 = C15⋊D4φ: C22/C1C22 ⊆ Aut C30604-C30.4C2^2120,11
C30.5C22 = C3⋊D20φ: C22/C1C22 ⊆ Aut C30604+C30.5C2^2120,12
C30.6C22 = C5⋊D12φ: C22/C1C22 ⊆ Aut C30604+C30.6C2^2120,13
C30.7C22 = C15⋊Q8φ: C22/C1C22 ⊆ Aut C301204-C30.7C2^2120,14
C30.8C22 = Dic30φ: C22/C2C2 ⊆ Aut C301202-C30.8C2^2120,26
C30.9C22 = C4×D15φ: C22/C2C2 ⊆ Aut C30602C30.9C2^2120,27
C30.10C22 = D60φ: C22/C2C2 ⊆ Aut C30602+C30.10C2^2120,28
C30.11C22 = C2×Dic15φ: C22/C2C2 ⊆ Aut C30120C30.11C2^2120,29
C30.12C22 = C157D4φ: C22/C2C2 ⊆ Aut C30602C30.12C2^2120,30
C30.13C22 = C3×Dic10φ: C22/C2C2 ⊆ Aut C301202C30.13C2^2120,16
C30.14C22 = D5×C12φ: C22/C2C2 ⊆ Aut C30602C30.14C2^2120,17
C30.15C22 = C3×D20φ: C22/C2C2 ⊆ Aut C30602C30.15C2^2120,18
C30.16C22 = C6×Dic5φ: C22/C2C2 ⊆ Aut C30120C30.16C2^2120,19
C30.17C22 = C3×C5⋊D4φ: C22/C2C2 ⊆ Aut C30602C30.17C2^2120,20
C30.18C22 = C5×Dic6φ: C22/C2C2 ⊆ Aut C301202C30.18C2^2120,21
C30.19C22 = S3×C20φ: C22/C2C2 ⊆ Aut C30602C30.19C2^2120,22
C30.20C22 = C5×D12φ: C22/C2C2 ⊆ Aut C30602C30.20C2^2120,23
C30.21C22 = C10×Dic3φ: C22/C2C2 ⊆ Aut C30120C30.21C2^2120,24
C30.22C22 = C5×C3⋊D4φ: C22/C2C2 ⊆ Aut C30602C30.22C2^2120,25
C30.23C22 = D4×C15central extension (φ=1)602C30.23C2^2120,32
C30.24C22 = Q8×C15central extension (φ=1)1202C30.24C2^2120,33

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