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Extensions 1→N→G→Q→1 with N=C2×C12 and Q=F5

Direct product G=N×Q with N=C2×C12 and Q=F5
dρLabelID
F5×C2×C12120F5xC2xC12480,1050

Semidirect products G=N:Q with N=C2×C12 and Q=F5
extensionφ:Q→Aut NdρLabelID
(C2×C12)⋊1F5 = C3×D10.D4φ: F5/C5 → C4 ⊆ Aut C2×C121204(C2xC12):1F5480,279
(C2×C12)⋊2F5 = (C2×C60)⋊C4φ: F5/C5 → C4 ⊆ Aut C2×C121204(C2xC12):2F5480,304
(C2×C12)⋊3F5 = C3×D10.3Q8φ: F5/D5 → C2 ⊆ Aut C2×C12120(C2xC12):3F5480,286
(C2×C12)⋊4F5 = D10.10D12φ: F5/D5 → C2 ⊆ Aut C2×C12120(C2xC12):4F5480,311
(C2×C12)⋊5F5 = C2×C60⋊C4φ: F5/D5 → C2 ⊆ Aut C2×C12120(C2xC12):5F5480,1064
(C2×C12)⋊6F5 = (C2×C12)⋊6F5φ: F5/D5 → C2 ⊆ Aut C2×C121204(C2xC12):6F5480,1065
(C2×C12)⋊7F5 = C2×C4×C3⋊F5φ: F5/D5 → C2 ⊆ Aut C2×C12120(C2xC12):7F5480,1063
(C2×C12)⋊8F5 = C6×C4⋊F5φ: F5/D5 → C2 ⊆ Aut C2×C12120(C2xC12):8F5480,1051
(C2×C12)⋊9F5 = C3×D10.C23φ: F5/D5 → C2 ⊆ Aut C2×C121204(C2xC12):9F5480,1052

Non-split extensions G=N.Q with N=C2×C12 and Q=F5
extensionφ:Q→Aut NdρLabelID
(C2×C12).1F5 = C3×Dic5.D4φ: F5/C5 → C4 ⊆ Aut C2×C122404(C2xC12).1F5480,285
(C2×C12).2F5 = (C2×C60).C4φ: F5/C5 → C4 ⊆ Aut C2×C122404(C2xC12).2F5480,310
(C2×C12).3F5 = C3×C10.C42φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).3F5480,282
(C2×C12).4F5 = C3×D10⋊C8φ: F5/D5 → C2 ⊆ Aut C2×C12240(C2xC12).4F5480,283
(C2×C12).5F5 = C3×Dic5⋊C8φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).5F5480,284
(C2×C12).6F5 = C30.11C42φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).6F5480,307
(C2×C12).7F5 = C30.7M4(2)φ: F5/D5 → C2 ⊆ Aut C2×C12240(C2xC12).7F5480,308
(C2×C12).8F5 = Dic5.13D12φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).8F5480,309
(C2×C12).9F5 = C60⋊C8φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).9F5480,306
(C2×C12).10F5 = C2×C12.F5φ: F5/D5 → C2 ⊆ Aut C2×C12240(C2xC12).10F5480,1061
(C2×C12).11F5 = C60.C8φ: F5/D5 → C2 ⊆ Aut C2×C122404(C2xC12).11F5480,303
(C2×C12).12F5 = C60.59(C2×C4)φ: F5/D5 → C2 ⊆ Aut C2×C121204(C2xC12).12F5480,1062
(C2×C12).13F5 = C2×C15⋊C16φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).13F5480,302
(C2×C12).14F5 = C4×C15⋊C8φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).14F5480,305
(C2×C12).15F5 = C2×C60.C4φ: F5/D5 → C2 ⊆ Aut C2×C12240(C2xC12).15F5480,1060
(C2×C12).16F5 = C3×C20.C8φ: F5/D5 → C2 ⊆ Aut C2×C122404(C2xC12).16F5480,278
(C2×C12).17F5 = C3×C20⋊C8φ: F5/D5 → C2 ⊆ Aut C2×C12480(C2xC12).17F5480,281
(C2×C12).18F5 = C6×C4.F5φ: F5/D5 → C2 ⊆ Aut C2×C12240(C2xC12).18F5480,1048
(C2×C12).19F5 = C3×D5⋊M4(2)φ: F5/D5 → C2 ⊆ Aut C2×C121204(C2xC12).19F5480,1049
(C2×C12).20F5 = C6×C5⋊C16central extension (φ=1)480(C2xC12).20F5480,277
(C2×C12).21F5 = C12×C5⋊C8central extension (φ=1)480(C2xC12).21F5480,280
(C2×C12).22F5 = C6×D5⋊C8central extension (φ=1)240(C2xC12).22F5480,1047

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