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Extensions 1→N→G→Q→1 with N=C2×C120 and Q=C2

Direct product G=N×Q with N=C2×C120 and Q=C2
dρLabelID
C22×C120480C2^2xC120480,934

Semidirect products G=N:Q with N=C2×C120 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C120)⋊1C2 = C3×D10⋊1C8φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):1C2480,98
(C2×C120)⋊2C2 = C3×D20⋊5C4φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):2C2480,99
(C2×C120)⋊3C2 = C5×D6⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):3C2480,139
(C2×C120)⋊4C2 = C5×C2.D24φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):4C2480,140
(C2×C120)⋊5C2 = D30⋊3C8φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):5C2480,180
(C2×C120)⋊6C2 = D60⋊8C4φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):6C2480,181
(C2×C120)⋊7C2 = C15×C22⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):7C2480,201
(C2×C120)⋊8C2 = C15×D4⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):8C2480,205
(C2×C120)⋊9C2 = C2×D120φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):9C2480,868
(C2×C120)⋊10C2 = C40.69D6φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):10C2480,869
(C2×C120)⋊11C2 = C2×C24⋊D5φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):11C2480,867
(C2×C120)⋊12C2 = C6×D40φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):12C2480,696
(C2×C120)⋊13C2 = C3×D40⋊7C2φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):13C2480,697
(C2×C120)⋊14C2 = C2×C8×D15φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):14C2480,864
(C2×C120)⋊15C2 = C2×C40⋊S3φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):15C2480,865
(C2×C120)⋊16C2 = D60.6C4φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):16C2480,866
(C2×C120)⋊17C2 = C10×D24φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):17C2480,782
(C2×C120)⋊18C2 = C5×C4○D24φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):18C2480,783
(C2×C120)⋊19C2 = C6×C40⋊C2φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):19C2480,695
(C2×C120)⋊20C2 = C10×C24⋊C2φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):20C2480,781
(C2×C120)⋊21C2 = D5×C2×C24φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):21C2480,692
(C2×C120)⋊22C2 = C6×C8⋊D5φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):22C2480,693
(C2×C120)⋊23C2 = C3×D20.3C4φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):23C2480,694
(C2×C120)⋊24C2 = D8×C30φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):24C2480,937
(C2×C120)⋊25C2 = C15×C4○D8φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):25C2480,940
(C2×C120)⋊26C2 = S3×C2×C40φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):26C2480,778
(C2×C120)⋊27C2 = C10×C8⋊S3φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):27C2480,779
(C2×C120)⋊28C2 = C5×C8○D12φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):28C2480,780
(C2×C120)⋊29C2 = SD16×C30φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):29C2480,938
(C2×C120)⋊30C2 = M4(2)×C30φ: C2/C1 → C2 ⊆ Aut C2×C120240(C2xC120):30C2480,935
(C2×C120)⋊31C2 = C15×C8○D4φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120):31C2480,936

Non-split extensions G=N.Q with N=C2×C120 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C120).1C2 = C3×C20.8Q8φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).1C2480,92
(C2×C120).2C2 = C3×C20.44D4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).2C2480,94
(C2×C120).3C2 = C5×Dic3⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).3C2480,133
(C2×C120).4C2 = C5×C2.Dic12φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).4C2480,135
(C2×C120).5C2 = C60.26Q8φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).5C2480,174
(C2×C120).6C2 = Dic30⋊8C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).6C2480,176
(C2×C120).7C2 = C15×Q8⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).7C2480,206
(C2×C120).8C2 = C15×C4⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).8C2480,208
(C2×C120).9C2 = C120⋊9C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).9C2480,178
(C2×C120).10C2 = C2×Dic60φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).10C2480,870
(C2×C120).11C2 = C4.18D60φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).11C2480,179
(C2×C120).12C2 = C120⋊10C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).12C2480,177
(C2×C120).13C2 = C3×C40⋊5C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).13C2480,96
(C2×C120).14C2 = C6×Dic20φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).14C2480,698
(C2×C120).15C2 = C3×C40.6C4φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).15C2480,97
(C2×C120).16C2 = C2×C15⋊3C16φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).16C2480,171
(C2×C120).17C2 = C60.7C8φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).17C2480,172
(C2×C120).18C2 = C8×Dic15φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).18C2480,173
(C2×C120).19C2 = C120⋊13C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).19C2480,175
(C2×C120).20C2 = C5×C24⋊1C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).20C2480,137
(C2×C120).21C2 = C10×Dic12φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).21C2480,784
(C2×C120).22C2 = C5×C24.C4φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).22C2480,138
(C2×C120).23C2 = C3×C40⋊6C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).23C2480,95
(C2×C120).24C2 = C5×C8⋊Dic3φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).24C2480,136
(C2×C120).25C2 = C6×C5⋊2C16φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).25C2480,89
(C2×C120).26C2 = C3×C20.4C8φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).26C2480,90
(C2×C120).27C2 = Dic5×C24φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).27C2480,91
(C2×C120).28C2 = C3×C40⋊8C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).28C2480,93
(C2×C120).29C2 = C15×C2.D8φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).29C2480,210
(C2×C120).30C2 = Q16×C30φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).30C2480,939
(C2×C120).31C2 = C15×C8.C4φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).31C2480,211
(C2×C120).32C2 = C10×C3⋊C16φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).32C2480,130
(C2×C120).33C2 = C5×C12.C8φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).33C2480,131
(C2×C120).34C2 = Dic3×C40φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).34C2480,132
(C2×C120).35C2 = C5×C24⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).35C2480,134
(C2×C120).36C2 = C15×C4.Q8φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).36C2480,209
(C2×C120).37C2 = C15×C8⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C120480(C2xC120).37C2480,200
(C2×C120).38C2 = C15×M5(2)φ: C2/C1 → C2 ⊆ Aut C2×C1202402(C2xC120).38C2480,213

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