# Extensions 1→N→G→Q→1 with N=C2×D4 and Q=C10

Direct product G=N×Q with N=C2×D4 and Q=C10
dρLabelID
D4×C2×C1080D4xC2xC10160,229

Semidirect products G=N:Q with N=C2×D4 and Q=C10
extensionφ:Q→Out NdρLabelID
(C2×D4)⋊1C10 = C5×C22≀C2φ: C10/C5C2 ⊆ Out C2×D440(C2xD4):1C10160,181
(C2×D4)⋊2C10 = C5×C4⋊D4φ: C10/C5C2 ⊆ Out C2×D480(C2xD4):2C10160,182
(C2×D4)⋊3C10 = C5×C41D4φ: C10/C5C2 ⊆ Out C2×D480(C2xD4):3C10160,188
(C2×D4)⋊4C10 = C10×D8φ: C10/C5C2 ⊆ Out C2×D480(C2xD4):4C10160,193
(C2×D4)⋊5C10 = C5×C8⋊C22φ: C10/C5C2 ⊆ Out C2×D4404(C2xD4):5C10160,197
(C2×D4)⋊6C10 = C5×2+ 1+4φ: C10/C5C2 ⊆ Out C2×D4404(C2xD4):6C10160,232
(C2×D4)⋊7C10 = C10×C4○D4φ: trivial image80(C2xD4):7C10160,231

Non-split extensions G=N.Q with N=C2×D4 and Q=C10
extensionφ:Q→Out NdρLabelID
(C2×D4).1C10 = C5×C23⋊C4φ: C10/C5C2 ⊆ Out C2×D4404(C2xD4).1C10160,49
(C2×D4).2C10 = C5×C4.D4φ: C10/C5C2 ⊆ Out C2×D4404(C2xD4).2C10160,50
(C2×D4).3C10 = C5×D4⋊C4φ: C10/C5C2 ⊆ Out C2×D480(C2xD4).3C10160,52
(C2×D4).4C10 = C5×C22.D4φ: C10/C5C2 ⊆ Out C2×D480(C2xD4).4C10160,184
(C2×D4).5C10 = C5×C4.4D4φ: C10/C5C2 ⊆ Out C2×D480(C2xD4).5C10160,185
(C2×D4).6C10 = C10×SD16φ: C10/C5C2 ⊆ Out C2×D480(C2xD4).6C10160,194
(C2×D4).7C10 = D4×C20φ: trivial image80(C2xD4).7C10160,179

׿
×
𝔽