# Extensions 1→N→G→Q→1 with N=C5×M4(2) and Q=C6

Direct product G=N×Q with N=C5×M4(2) and Q=C6
dρLabelID
M4(2)×C30240M4(2)xC30480,935

Semidirect products G=N:Q with N=C5×M4(2) and Q=C6
extensionφ:Q→Out NdρLabelID
(C5×M4(2))⋊1C6 = C3×C8⋊D10φ: C6/C3C2 ⊆ Out C5×M4(2)1204(C5xM4(2)):1C6480,701
(C5×M4(2))⋊2C6 = C3×C8.D10φ: C6/C3C2 ⊆ Out C5×M4(2)2404(C5xM4(2)):2C6480,702
(C5×M4(2))⋊3C6 = C3×D5×M4(2)φ: C6/C3C2 ⊆ Out C5×M4(2)1204(C5xM4(2)):3C6480,699
(C5×M4(2))⋊4C6 = C3×D20.2C4φ: C6/C3C2 ⊆ Out C5×M4(2)2404(C5xM4(2)):4C6480,700
(C5×M4(2))⋊5C6 = C15×C8⋊C22φ: C6/C3C2 ⊆ Out C5×M4(2)1204(C5xM4(2)):5C6480,941
(C5×M4(2))⋊6C6 = C15×C8.C22φ: C6/C3C2 ⊆ Out C5×M4(2)2404(C5xM4(2)):6C6480,942
(C5×M4(2))⋊7C6 = C3×C20.46D4φ: C6/C3C2 ⊆ Out C5×M4(2)1204(C5xM4(2)):7C6480,101
(C5×M4(2))⋊8C6 = C3×D207C4φ: C6/C3C2 ⊆ Out C5×M4(2)1204(C5xM4(2)):8C6480,103
(C5×M4(2))⋊9C6 = C15×C4.D4φ: C6/C3C2 ⊆ Out C5×M4(2)1204(C5xM4(2)):9C6480,203
(C5×M4(2))⋊10C6 = C15×C4≀C2φ: C6/C3C2 ⊆ Out C5×M4(2)1202(C5xM4(2)):10C6480,207
(C5×M4(2))⋊11C6 = C15×C8○D4φ: trivial image2402(C5xM4(2)):11C6480,936

Non-split extensions G=N.Q with N=C5×M4(2) and Q=C6
extensionφ:Q→Out NdρLabelID
(C5×M4(2)).1C6 = C3×C20.53D4φ: C6/C3C2 ⊆ Out C5×M4(2)2404(C5xM4(2)).1C6480,100
(C5×M4(2)).2C6 = C3×C4.12D20φ: C6/C3C2 ⊆ Out C5×M4(2)2404(C5xM4(2)).2C6480,102
(C5×M4(2)).3C6 = C15×C4.10D4φ: C6/C3C2 ⊆ Out C5×M4(2)2404(C5xM4(2)).3C6480,204
(C5×M4(2)).4C6 = C15×C8.C4φ: C6/C3C2 ⊆ Out C5×M4(2)2402(C5xM4(2)).4C6480,211

׿
×
𝔽