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Extensions 1→N→G→Q→1 with N=M5(2) and Q=C22

Direct product G=N×Q with N=M5(2) and Q=C22
dρLabelID
C22×M5(2)64C2^2xM5(2)128,2137

Semidirect products G=N:Q with N=M5(2) and Q=C22
extensionφ:Q→Out NdρLabelID
M5(2)⋊1C22 = D8⋊D4φ: C22/C1 → C22 ⊆ Out M5(2)168+M5(2):1C2^2128,922
M5(2)⋊2C22 = D8.D4φ: C22/C1 → C22 ⊆ Out M5(2)328-M5(2):2C2^2128,923
M5(2)⋊3C22 = Q16.10D4φ: C22/C1 → C22 ⊆ Out M5(2)324+M5(2):3C2^2128,924
M5(2)⋊4C22 = D8.3D4φ: C22/C1 → C22 ⊆ Out M5(2)324M5(2):4C2^2128,926
M5(2)⋊5C22 = C2×C16⋊C22φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2):5C2^2128,2144
M5(2)⋊6C22 = C2×Q32⋊C2φ: C22/C2 → C2 ⊆ Out M5(2)64M5(2):6C2^2128,2145
M5(2)⋊7C22 = D16⋊C22φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2):7C2^2128,2146
M5(2)⋊8C22 = D4○D16φ: C22/C2 → C2 ⊆ Out M5(2)324+M5(2):8C2^2128,2147
M5(2)⋊9C22 = D4○SD32φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2):9C2^2128,2148
M5(2)⋊10C22 = C2×C23.C8φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2):10C2^2128,846
M5(2)⋊11C22 = C2×D4.C8φ: C22/C2 → C2 ⊆ Out M5(2)64M5(2):11C2^2128,848
M5(2)⋊12C22 = M5(2)⋊12C22φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2):12C2^2128,849
M5(2)⋊13C22 = C2×D8⋊2C4φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2):13C2^2128,876
M5(2)⋊14C22 = C23.13D8φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2):14C2^2128,877
M5(2)⋊15C22 = C2×M5(2)⋊C2φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2):15C2^2128,878
M5(2)⋊16C22 = C2×D4○C16φ: trivial image64M5(2):16C2^2128,2138
M5(2)⋊17C22 = Q8○M5(2)φ: trivial image324M5(2):17C2^2128,2139

Non-split extensions G=N.Q with N=M5(2) and Q=C22
extensionφ:Q→Out NdρLabelID
M5(2).1C22 = Q16.D4φ: C22/C1 → C22 ⊆ Out M5(2)324M5(2).1C2^2128,925
M5(2).2C22 = D8.12D4φ: C22/C1 → C22 ⊆ Out M5(2)644-M5(2).2C2^2128,927
M5(2).3C22 = C8.3D8φ: C22/C1 → C22 ⊆ Out M5(2)324M5(2).3C2^2128,944
M5(2).4C22 = D8⋊3D4φ: C22/C1 → C22 ⊆ Out M5(2)164+M5(2).4C2^2128,945
M5(2).5C22 = C8.5D8φ: C22/C1 → C22 ⊆ Out M5(2)324-M5(2).5C2^2128,946
M5(2).6C22 = D8⋊3Q8φ: C22/C1 → C22 ⊆ Out M5(2)164M5(2).6C2^2128,962
M5(2).7C22 = D8.2Q8φ: C22/C1 → C22 ⊆ Out M5(2)324M5(2).7C2^2128,963
M5(2).8C22 = M5(2).C22φ: C22/C1 → C22 ⊆ Out M5(2)168+M5(2).8C2^2128,970
M5(2).9C22 = C23.10SD16φ: C22/C1 → C22 ⊆ Out M5(2)328-M5(2).9C2^2128,971
M5(2).10C22 = C8.5M4(2)φ: C22/C1 → C22 ⊆ Out M5(2)164M5(2).10C2^2128,897
M5(2).11C22 = C8.19M4(2)φ: C22/C1 → C22 ⊆ Out M5(2)324M5(2).11C2^2128,898
M5(2).12C22 = Q32⋊C4φ: C22/C1 → C22 ⊆ Out M5(2)328-M5(2).12C2^2128,912
M5(2).13C22 = D16⋊C4φ: C22/C1 → C22 ⊆ Out M5(2)168+M5(2).13C2^2128,913
M5(2).14C22 = Q8○D16φ: C22/C2 → C2 ⊆ Out M5(2)644-M5(2).14C2^2128,2149
M5(2).15C22 = C2×C8.Q8φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2).15C2^2128,886
M5(2).16C22 = M5(2)⋊3C4φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).16C2^2128,887
M5(2).17C22 = C2×C16⋊C4φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2).17C2^2128,841
M5(2).18C22 = C8.23C42φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).18C2^2128,842
M5(2).19C22 = M5(2).19C22φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).19C2^2128,847
M5(2).20C22 = C2×C8.17D4φ: C22/C2 → C2 ⊆ Out M5(2)64M5(2).20C2^2128,879
M5(2).21C22 = C23.21SD16φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).21C2^2128,880
M5(2).22C22 = C2×C8.C8φ: C22/C2 → C2 ⊆ Out M5(2)32M5(2).22C2^2128,884
M5(2).23C22 = M4(2).1C8φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).23C2^2128,885
M5(2).24C22 = C16○D8φ: C22/C2 → C2 ⊆ Out M5(2)322M5(2).24C2^2128,902
M5(2).25C22 = D8.C8φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).25C2^2128,903
M5(2).26C22 = D4.3D8φ: C22/C2 → C2 ⊆ Out M5(2)324+M5(2).26C2^2128,953
M5(2).27C22 = D4.4D8φ: C22/C2 → C2 ⊆ Out M5(2)644-M5(2).27C2^2128,954
M5(2).28C22 = D4.5D8φ: C22/C2 → C2 ⊆ Out M5(2)324M5(2).28C2^2128,955

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