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Extensions 1→N→G→Q→1 with N=C120 and Q=C4

Direct product G=N×Q with N=C120 and Q=C4
dρLabelID
C4×C120480C4xC120480,199

Semidirect products G=N:Q with N=C120 and Q=C4
extensionφ:Q→Aut NdρLabelID
C120⋊1C4 = D5.D24φ: C4/C1 → C4 ⊆ Aut C1201204C120:1C4480,299
C120⋊2C4 = C120⋊C4φ: C4/C1 → C4 ⊆ Aut C1201204C120:2C4480,298
C120⋊3C4 = C3×D5.D8φ: C4/C1 → C4 ⊆ Aut C1201204C120:3C4480,274
C120⋊4C4 = C8×C3⋊F5φ: C4/C1 → C4 ⊆ Aut C1201204C120:4C4480,296
C120⋊5C4 = C24⋊F5φ: C4/C1 → C4 ⊆ Aut C1201204C120:5C4480,297
C120⋊6C4 = C3×C40⋊C4φ: C4/C1 → C4 ⊆ Aut C1201204C120:6C4480,273
C120⋊7C4 = F5×C24φ: C4/C1 → C4 ⊆ Aut C1201204C120:7C4480,271
C120⋊8C4 = C3×C8⋊F5φ: C4/C1 → C4 ⊆ Aut C1201204C120:8C4480,272
C120⋊9C4 = C120⋊9C4φ: C4/C2 → C2 ⊆ Aut C120480C120:9C4480,178
C120⋊10C4 = C120⋊10C4φ: C4/C2 → C2 ⊆ Aut C120480C120:10C4480,177
C120⋊11C4 = C3×C40⋊5C4φ: C4/C2 → C2 ⊆ Aut C120480C120:11C4480,96
C120⋊12C4 = C8×Dic15φ: C4/C2 → C2 ⊆ Aut C120480C120:12C4480,173
C120⋊13C4 = C120⋊13C4φ: C4/C2 → C2 ⊆ Aut C120480C120:13C4480,175
C120⋊14C4 = C5×C24⋊1C4φ: C4/C2 → C2 ⊆ Aut C120480C120:14C4480,137
C120⋊15C4 = C3×C40⋊6C4φ: C4/C2 → C2 ⊆ Aut C120480C120:15C4480,95
C120⋊16C4 = C5×C8⋊Dic3φ: C4/C2 → C2 ⊆ Aut C120480C120:16C4480,136
C120⋊17C4 = Dic5×C24φ: C4/C2 → C2 ⊆ Aut C120480C120:17C4480,91
C120⋊18C4 = C3×C40⋊8C4φ: C4/C2 → C2 ⊆ Aut C120480C120:18C4480,93
C120⋊19C4 = C15×C2.D8φ: C4/C2 → C2 ⊆ Aut C120480C120:19C4480,210
C120⋊20C4 = Dic3×C40φ: C4/C2 → C2 ⊆ Aut C120480C120:20C4480,132
C120⋊21C4 = C5×C24⋊C4φ: C4/C2 → C2 ⊆ Aut C120480C120:21C4480,134
C120⋊22C4 = C15×C4.Q8φ: C4/C2 → C2 ⊆ Aut C120480C120:22C4480,209
C120⋊23C4 = C15×C8⋊C4φ: C4/C2 → C2 ⊆ Aut C120480C120:23C4480,200

Non-split extensions G=N.Q with N=C120 and Q=C4
extensionφ:Q→Aut NdρLabelID
C120.1C4 = C24.1F5φ: C4/C1 → C4 ⊆ Aut C1202404C120.1C4480,301
C120.2C4 = C40.Dic3φ: C4/C1 → C4 ⊆ Aut C1202404C120.2C4480,300
C120.3C4 = C3×D10.Q8φ: C4/C1 → C4 ⊆ Aut C1202404C120.3C4480,276
C120.4C4 = C15⋊C32φ: C4/C1 → C4 ⊆ Aut C1204804C120.4C4480,6
C120.5C4 = C24.F5φ: C4/C1 → C4 ⊆ Aut C1202404C120.5C4480,294
C120.6C4 = C120.C4φ: C4/C1 → C4 ⊆ Aut C1202404C120.6C4480,295
C120.7C4 = C3×C40.C4φ: C4/C1 → C4 ⊆ Aut C1202404C120.7C4480,275
C120.8C4 = C3×C5⋊C32φ: C4/C1 → C4 ⊆ Aut C1204804C120.8C4480,5
C120.9C4 = C3×D5⋊C16φ: C4/C1 → C4 ⊆ Aut C1202404C120.9C4480,269
C120.10C4 = C3×C8.F5φ: C4/C1 → C4 ⊆ Aut C1202404C120.10C4480,270
C120.11C4 = C4.18D60φ: C4/C2 → C2 ⊆ Aut C1202402C120.11C4480,179
C120.12C4 = C15⋊3C32φ: C4/C2 → C2 ⊆ Aut C1204802C120.12C4480,3
C120.13C4 = C2×C15⋊3C16φ: C4/C2 → C2 ⊆ Aut C120480C120.13C4480,171
C120.14C4 = C60.7C8φ: C4/C2 → C2 ⊆ Aut C1202402C120.14C4480,172
C120.15C4 = C5×C24.C4φ: C4/C2 → C2 ⊆ Aut C1202402C120.15C4480,138
C120.16C4 = C3×C40.6C4φ: C4/C2 → C2 ⊆ Aut C1202402C120.16C4480,97
C120.17C4 = C3×C5⋊2C32φ: C4/C2 → C2 ⊆ Aut C1204802C120.17C4480,2
C120.18C4 = C6×C5⋊2C16φ: C4/C2 → C2 ⊆ Aut C120480C120.18C4480,89
C120.19C4 = C3×C20.4C8φ: C4/C2 → C2 ⊆ Aut C1202402C120.19C4480,90
C120.20C4 = C5×C3⋊C32φ: C4/C2 → C2 ⊆ Aut C1204802C120.20C4480,1
C120.21C4 = C10×C3⋊C16φ: C4/C2 → C2 ⊆ Aut C120480C120.21C4480,130
C120.22C4 = C5×C12.C8φ: C4/C2 → C2 ⊆ Aut C1202402C120.22C4480,131
C120.23C4 = C15×C8.C4φ: C4/C2 → C2 ⊆ Aut C1202402C120.23C4480,211
C120.24C4 = C15×M5(2)φ: C4/C2 → C2 ⊆ Aut C1202402C120.24C4480,213

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