Extensions 1→N→G→Q→1 with N=C5×M4(2) and Q=C4

Direct product G=N×Q with N=C5×M4(2) and Q=C4
dρLabelID
M4(2)×C20160M4(2)xC20320,905

Semidirect products G=N:Q with N=C5×M4(2) and Q=C4
extensionφ:Q→Out NdρLabelID
(C5×M4(2))⋊1C4 = M4(2)⋊1F5φ: C4/C1C4 ⊆ Out C5×M4(2)408(C5xM4(2)):1C4320,1065
(C5×M4(2))⋊2C4 = M4(2)⋊F5φ: C4/C1C4 ⊆ Out C5×M4(2)408(C5xM4(2)):2C4320,237
(C5×M4(2))⋊3C4 = M4(2)⋊3F5φ: C4/C1C4 ⊆ Out C5×M4(2)408(C5xM4(2)):3C4320,238
(C5×M4(2))⋊4C4 = M4(2)⋊4F5φ: C4/C1C4 ⊆ Out C5×M4(2)808(C5xM4(2)):4C4320,240
(C5×M4(2))⋊5C4 = M4(2)×F5φ: C4/C1C4 ⊆ Out C5×M4(2)408(C5xM4(2)):5C4320,1064
(C5×M4(2))⋊6C4 = M4(2)⋊5F5φ: C4/C1C4 ⊆ Out C5×M4(2)808(C5xM4(2)):6C4320,1066
(C5×M4(2))⋊7C4 = C23.47D20φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)):7C4320,748
(C5×M4(2))⋊8C4 = M4(2)×Dic5φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)):8C4320,744
(C5×M4(2))⋊9C4 = C20.37C42φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)):9C4320,749
(C5×M4(2))⋊10C4 = C5×M4(2)⋊C4φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)):10C4320,929
(C5×M4(2))⋊11C4 = M4(2)⋊Dic5φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)):11C4320,112
(C5×M4(2))⋊12C4 = C20.33C42φ: C4/C2C2 ⊆ Out C5×M4(2)80(C5xM4(2)):12C4320,113
(C5×M4(2))⋊13C4 = M4(2)⋊4Dic5φ: C4/C2C2 ⊆ Out C5×M4(2)804(C5xM4(2)):13C4320,117
(C5×M4(2))⋊14C4 = C5×C426C4φ: C4/C2C2 ⊆ Out C5×M4(2)80(C5xM4(2)):14C4320,144
(C5×M4(2))⋊15C4 = C5×C22.C42φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)):15C4320,148
(C5×M4(2))⋊16C4 = C5×M4(2)⋊4C4φ: C4/C2C2 ⊆ Out C5×M4(2)804(C5xM4(2)):16C4320,149
(C5×M4(2))⋊17C4 = C5×C82M4(2)φ: trivial image160(C5xM4(2)):17C4320,906

Non-split extensions G=N.Q with N=C5×M4(2) and Q=C4
extensionφ:Q→Out NdρLabelID
(C5×M4(2)).1C4 = M4(2).1F5φ: C4/C1C4 ⊆ Out C5×M4(2)808(C5xM4(2)).1C4320,1067
(C5×M4(2)).2C4 = D20.C8φ: C4/C1C4 ⊆ Out C5×M4(2)1608(C5xM4(2)).2C4320,236
(C5×M4(2)).3C4 = M4(2).F5φ: C4/C1C4 ⊆ Out C5×M4(2)808(C5xM4(2)).3C4320,239
(C5×M4(2)).4C4 = Dic10.C8φ: C4/C1C4 ⊆ Out C5×M4(2)1608(C5xM4(2)).4C4320,1063
(C5×M4(2)).5C4 = M4(2).Dic5φ: C4/C2C2 ⊆ Out C5×M4(2)804(C5xM4(2)).5C4320,752
(C5×M4(2)).6C4 = C40.70C23φ: C4/C2C2 ⊆ Out C5×M4(2)1604(C5xM4(2)).6C4320,767
(C5×M4(2)).7C4 = C5×M4(2).C4φ: C4/C2C2 ⊆ Out C5×M4(2)804(C5xM4(2)).7C4320,931
(C5×M4(2)).8C4 = C20.34C42φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)).8C4320,116
(C5×M4(2)).9C4 = C40.92D4φ: C4/C2C2 ⊆ Out C5×M4(2)1604(C5xM4(2)).9C4320,119
(C5×M4(2)).10C4 = C5×C4.C42φ: C4/C2C2 ⊆ Out C5×M4(2)160(C5xM4(2)).10C4320,146
(C5×M4(2)).11C4 = C5×D4.C8φ: C4/C2C2 ⊆ Out C5×M4(2)1602(C5xM4(2)).11C4320,155
(C5×M4(2)).12C4 = C5×D4○C16φ: trivial image1602(C5xM4(2)).12C4320,1005

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