# Extensions 1→N→G→Q→1 with N=C240 and Q=C2

Direct product G=N×Q with N=C240 and Q=C2
dρLabelID
C2×C240480C2xC240480,212

Semidirect products G=N:Q with N=C240 and Q=C2
extensionφ:Q→Aut NdρLabelID
C2401C2 = D240φ: C2/C1C2 ⊆ Aut C2402402+C240:1C2480,159
C2402C2 = C48⋊D5φ: C2/C1C2 ⊆ Aut C2402402C240:2C2480,160
C2403C2 = C3×D80φ: C2/C1C2 ⊆ Aut C2402402C240:3C2480,77
C2404C2 = C5×D48φ: C2/C1C2 ⊆ Aut C2402402C240:4C2480,118
C2405C2 = C3×C16⋊D5φ: C2/C1C2 ⊆ Aut C2402402C240:5C2480,78
C2406C2 = C16×D15φ: C2/C1C2 ⊆ Aut C2402402C240:6C2480,157
C2407C2 = C80⋊S3φ: C2/C1C2 ⊆ Aut C2402402C240:7C2480,158
C2408C2 = C5×C48⋊C2φ: C2/C1C2 ⊆ Aut C2402402C240:8C2480,119
C2409C2 = C15×D16φ: C2/C1C2 ⊆ Aut C2402402C240:9C2480,214
C24010C2 = D5×C48φ: C2/C1C2 ⊆ Aut C2402402C240:10C2480,75
C24011C2 = C3×C80⋊C2φ: C2/C1C2 ⊆ Aut C2402402C240:11C2480,76
C24012C2 = C15×SD32φ: C2/C1C2 ⊆ Aut C2402402C240:12C2480,215
C24013C2 = S3×C80φ: C2/C1C2 ⊆ Aut C2402402C240:13C2480,116
C24014C2 = C5×D6.C8φ: C2/C1C2 ⊆ Aut C2402402C240:14C2480,117
C24015C2 = C15×M5(2)φ: C2/C1C2 ⊆ Aut C2402402C240:15C2480,213

Non-split extensions G=N.Q with N=C240 and Q=C2
extensionφ:Q→Aut NdρLabelID
C240.1C2 = Dic120φ: C2/C1C2 ⊆ Aut C2404802-C240.1C2480,161
C240.2C2 = C3×Dic40φ: C2/C1C2 ⊆ Aut C2404802C240.2C2480,79
C240.3C2 = C5×Dic24φ: C2/C1C2 ⊆ Aut C2404802C240.3C2480,120
C240.4C2 = C153C32φ: C2/C1C2 ⊆ Aut C2404802C240.4C2480,3
C240.5C2 = C15×Q32φ: C2/C1C2 ⊆ Aut C2404802C240.5C2480,216
C240.6C2 = C3×C52C32φ: C2/C1C2 ⊆ Aut C2404802C240.6C2480,2
C240.7C2 = C5×C3⋊C32φ: C2/C1C2 ⊆ Aut C2404802C240.7C2480,1

׿
×
𝔽