# Extensions 1→N→G→Q→1 with N=C3×C30 and Q=C22

Direct product G=N×Q with N=C3×C30 and Q=C22
dρLabelID
C2×C6×C30360C2xC6xC30360,162

Semidirect products G=N:Q with N=C3×C30 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C3×C30)⋊1C22 = S3×C6×D5φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30):1C2^2360,151
(C3×C30)⋊2C22 = C2×D5×C3⋊S3φ: C22/C1C22 ⊆ Aut C3×C3090(C3xC30):2C2^2360,152
(C3×C30)⋊3C22 = C2×S3×D15φ: C22/C1C22 ⊆ Aut C3×C30604+(C3xC30):3C2^2360,154
(C3×C30)⋊4C22 = C2×D15⋊S3φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30):4C2^2360,155
(C3×C30)⋊5C22 = S32×C10φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30):5C2^2360,153
(C3×C30)⋊6C22 = C22×C3⋊D15φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30):6C2^2360,161
(C3×C30)⋊7C22 = C2×C6×D15φ: C22/C2C2 ⊆ Aut C3×C30120(C3xC30):7C2^2360,159
(C3×C30)⋊8C22 = D5×C62φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30):8C2^2360,157
(C3×C30)⋊9C22 = S3×C2×C30φ: C22/C2C2 ⊆ Aut C3×C30120(C3xC30):9C2^2360,158
(C3×C30)⋊10C22 = C3⋊S3×C2×C10φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30):10C2^2360,160

Non-split extensions G=N.Q with N=C3×C30 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C3×C30).1C22 = C3×D5×Dic3φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).1C2^2360,58
(C3×C30).2C22 = C3×S3×Dic5φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).2C2^2360,59
(C3×C30).3C22 = C3×D30.C2φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).3C2^2360,60
(C3×C30).4C22 = C3×C15⋊D4φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).4C2^2360,61
(C3×C30).5C22 = C3×C3⋊D20φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).5C2^2360,62
(C3×C30).6C22 = C3×C5⋊D12φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).6C2^2360,63
(C3×C30).7C22 = C3×C15⋊Q8φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).7C2^2360,64
(C3×C30).8C22 = D5×C3⋊Dic3φ: C22/C1C22 ⊆ Aut C3×C30180(C3xC30).8C2^2360,65
(C3×C30).9C22 = C3⋊S3×Dic5φ: C22/C1C22 ⊆ Aut C3×C30180(C3xC30).9C2^2360,66
(C3×C30).10C22 = C30.D6φ: C22/C1C22 ⊆ Aut C3×C30180(C3xC30).10C2^2360,67
(C3×C30).11C22 = C30.12D6φ: C22/C1C22 ⊆ Aut C3×C30180(C3xC30).11C2^2360,68
(C3×C30).12C22 = C327D20φ: C22/C1C22 ⊆ Aut C3×C30180(C3xC30).12C2^2360,69
(C3×C30).13C22 = C15⋊D12φ: C22/C1C22 ⊆ Aut C3×C30180(C3xC30).13C2^2360,70
(C3×C30).14C22 = C15⋊Dic6φ: C22/C1C22 ⊆ Aut C3×C30360(C3xC30).14C2^2360,71
(C3×C30).15C22 = Dic3×D15φ: C22/C1C22 ⊆ Aut C3×C301204-(C3xC30).15C2^2360,77
(C3×C30).16C22 = S3×Dic15φ: C22/C1C22 ⊆ Aut C3×C301204-(C3xC30).16C2^2360,78
(C3×C30).17C22 = C6.D30φ: C22/C1C22 ⊆ Aut C3×C30604+(C3xC30).17C2^2360,79
(C3×C30).18C22 = D6⋊D15φ: C22/C1C22 ⊆ Aut C3×C301204-(C3xC30).18C2^2360,80
(C3×C30).19C22 = C3⋊D60φ: C22/C1C22 ⊆ Aut C3×C30604+(C3xC30).19C2^2360,81
(C3×C30).20C22 = D62D15φ: C22/C1C22 ⊆ Aut C3×C30604+(C3xC30).20C2^2360,82
(C3×C30).21C22 = C3⋊Dic30φ: C22/C1C22 ⊆ Aut C3×C301204-(C3xC30).21C2^2360,83
(C3×C30).22C22 = D30.S3φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).22C2^2360,84
(C3×C30).23C22 = Dic15⋊S3φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).23C2^2360,85
(C3×C30).24C22 = D30⋊S3φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).24C2^2360,86
(C3×C30).25C22 = C323D20φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).25C2^2360,87
(C3×C30).26C22 = C323Dic10φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).26C2^2360,88
(C3×C30).27C22 = C5×S3×Dic3φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).27C2^2360,72
(C3×C30).28C22 = C5×C6.D6φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).28C2^2360,73
(C3×C30).29C22 = C5×D6⋊S3φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).29C2^2360,74
(C3×C30).30C22 = C5×C3⋊D12φ: C22/C1C22 ⊆ Aut C3×C30604(C3xC30).30C2^2360,75
(C3×C30).31C22 = C5×C322Q8φ: C22/C1C22 ⊆ Aut C3×C301204(C3xC30).31C2^2360,76
(C3×C30).32C22 = C12.D15φ: C22/C2C2 ⊆ Aut C3×C30360(C3xC30).32C2^2360,110
(C3×C30).33C22 = C4×C3⋊D15φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).33C2^2360,111
(C3×C30).34C22 = C60⋊S3φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).34C2^2360,112
(C3×C30).35C22 = C2×C3⋊Dic15φ: C22/C2C2 ⊆ Aut C3×C30360(C3xC30).35C2^2360,113
(C3×C30).36C22 = C62⋊D5φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).36C2^2360,114
(C3×C30).37C22 = C3×Dic30φ: C22/C2C2 ⊆ Aut C3×C301202(C3xC30).37C2^2360,100
(C3×C30).38C22 = C12×D15φ: C22/C2C2 ⊆ Aut C3×C301202(C3xC30).38C2^2360,101
(C3×C30).39C22 = C3×D60φ: C22/C2C2 ⊆ Aut C3×C301202(C3xC30).39C2^2360,102
(C3×C30).40C22 = C6×Dic15φ: C22/C2C2 ⊆ Aut C3×C30120(C3xC30).40C2^2360,103
(C3×C30).41C22 = C3×C157D4φ: C22/C2C2 ⊆ Aut C3×C30602(C3xC30).41C2^2360,104
(C3×C30).42C22 = C32×Dic10φ: C22/C2C2 ⊆ Aut C3×C30360(C3xC30).42C2^2360,90
(C3×C30).43C22 = D5×C3×C12φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).43C2^2360,91
(C3×C30).44C22 = C32×D20φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).44C2^2360,92
(C3×C30).45C22 = C3×C6×Dic5φ: C22/C2C2 ⊆ Aut C3×C30360(C3xC30).45C2^2360,93
(C3×C30).46C22 = C32×C5⋊D4φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).46C2^2360,94
(C3×C30).47C22 = C15×Dic6φ: C22/C2C2 ⊆ Aut C3×C301202(C3xC30).47C2^2360,95
(C3×C30).48C22 = S3×C60φ: C22/C2C2 ⊆ Aut C3×C301202(C3xC30).48C2^2360,96
(C3×C30).49C22 = C15×D12φ: C22/C2C2 ⊆ Aut C3×C301202(C3xC30).49C2^2360,97
(C3×C30).50C22 = Dic3×C30φ: C22/C2C2 ⊆ Aut C3×C30120(C3xC30).50C2^2360,98
(C3×C30).51C22 = C15×C3⋊D4φ: C22/C2C2 ⊆ Aut C3×C30602(C3xC30).51C2^2360,99
(C3×C30).52C22 = C5×C324Q8φ: C22/C2C2 ⊆ Aut C3×C30360(C3xC30).52C2^2360,105
(C3×C30).53C22 = C3⋊S3×C20φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).53C2^2360,106
(C3×C30).54C22 = C5×C12⋊S3φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).54C2^2360,107
(C3×C30).55C22 = C10×C3⋊Dic3φ: C22/C2C2 ⊆ Aut C3×C30360(C3xC30).55C2^2360,108
(C3×C30).56C22 = C5×C327D4φ: C22/C2C2 ⊆ Aut C3×C30180(C3xC30).56C2^2360,109
(C3×C30).57C22 = D4×C3×C15central extension (φ=1)180(C3xC30).57C2^2360,116
(C3×C30).58C22 = Q8×C3×C15central extension (φ=1)360(C3xC30).58C2^2360,117

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