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Extensions 1→N→G→Q→1 with N=C22 and Q=C4⋊F5

Direct product G=N×Q with N=C22 and Q=C4⋊F5
dρLabelID
C22×C4⋊F580C2^2xC4:F5320,1591

Semidirect products G=N:Q with N=C22 and Q=C4⋊F5
extensionφ:Q→Aut NdρLabelID
C22⋊1(C4⋊F5) = D10⋊6(C4⋊C4)φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C2280C2^2:1(C4:F5)320,1103
C22⋊2(C4⋊F5) = D10⋊(C4⋊C4)φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C2240C2^2:2(C4:F5)320,1037

Non-split extensions G=N.Q with N=C22 and Q=C4⋊F5
extensionφ:Q→Aut NdρLabelID
C22.1(C4⋊F5) = C20.24C42φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C22804C2^2.1(C4:F5)320,233
C22.2(C4⋊F5) = C20.25C42φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C22804C2^2.2(C4:F5)320,235
C22.3(C4⋊F5) = C22⋊F5⋊C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C2280C2^2.3(C4:F5)320,255
C22.4(C4⋊F5) = C22.F5⋊C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C22160C2^2.4(C4:F5)320,257
C22.5(C4⋊F5) = (C2×C8)⋊6F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C22804C2^2.5(C4:F5)320,1059
C22.6(C4⋊F5) = (C8×D5).C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C22804C2^2.6(C4:F5)320,1062
C22.7(C4⋊F5) = C20⋊8M4(2)φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C22160C2^2.7(C4:F5)320,1096
C22.8(C4⋊F5) = (C22×F5)⋊C4φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22408+C2^2.8(C4:F5)320,204
C22.9(C4⋊F5) = C22⋊C4.F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22808-C2^2.9(C4:F5)320,205
C22.10(C4⋊F5) = M4(2)⋊3F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22408C2^2.10(C4:F5)320,238
C22.11(C4⋊F5) = M4(2).F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22808C2^2.11(C4:F5)320,239
C22.12(C4⋊F5) = C20⋊C8⋊C2φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22160C2^2.12(C4:F5)320,1034
C22.13(C4⋊F5) = M4(2)⋊1F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22408C2^2.13(C4:F5)320,1065
C22.14(C4⋊F5) = M4(2).1F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C22808C2^2.14(C4:F5)320,1067
C22.15(C4⋊F5) = C40⋊2C8central extension (φ=1)320C2^2.15(C4:F5)320,219
C22.16(C4⋊F5) = C40⋊1C8central extension (φ=1)320C2^2.16(C4:F5)320,220
C22.17(C4⋊F5) = C20.26M4(2)central extension (φ=1)320C2^2.17(C4:F5)320,221
C22.18(C4⋊F5) = Dic5.13D8central extension (φ=1)320C2^2.18(C4:F5)320,222
C22.19(C4⋊F5) = D10.10D8central extension (φ=1)80C2^2.19(C4:F5)320,231
C22.20(C4⋊F5) = C20.10C42central extension (φ=1)160C2^2.20(C4:F5)320,234
C22.21(C4⋊F5) = C10.(C4⋊C8)central extension (φ=1)320C2^2.21(C4:F5)320,256
C22.22(C4⋊F5) = C2×C40⋊C4central extension (φ=1)80C2^2.22(C4:F5)320,1057
C22.23(C4⋊F5) = C2×D5.D8central extension (φ=1)80C2^2.23(C4:F5)320,1058
C22.24(C4⋊F5) = C2×C40.C4central extension (φ=1)160C2^2.24(C4:F5)320,1060
C22.25(C4⋊F5) = C2×D10.Q8central extension (φ=1)160C2^2.25(C4:F5)320,1061
C22.26(C4⋊F5) = C2×C20⋊C8central extension (φ=1)320C2^2.26(C4:F5)320,1085
C22.27(C4⋊F5) = C2×Dic5⋊C8central extension (φ=1)320C2^2.27(C4:F5)320,1090
C22.28(C4⋊F5) = C2×D10.3Q8central extension (φ=1)80C2^2.28(C4:F5)320,1100

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