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

Direct product G=N×Q with N=C4 and Q=C4⋊F5
dρLabelID
C4×C4⋊F580C4xC4:F5320,1025

Semidirect products G=N:Q with N=C4 and Q=C4⋊F5
extensionφ:Q→Aut NdρLabelID
C4⋊1(C4⋊F5) = C42⋊8F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C480C4:1(C4:F5)320,1026
C4⋊2(C4⋊F5) = C20⋊(C4⋊C4)φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C480C4:2(C4:F5)320,1050

Non-split extensions G=N.Q with N=C4 and Q=C4⋊F5
extensionφ:Q→Aut NdρLabelID
C4.1(C4⋊F5) = C80⋊4C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4804C4.1(C4:F5)320,185
C4.2(C4⋊F5) = C80⋊5C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4804C4.2(C4:F5)320,186
C4.3(C4⋊F5) = C80⋊2C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4804C4.3(C4:F5)320,187
C4.4(C4⋊F5) = C80⋊3C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4804C4.4(C4:F5)320,188
C4.5(C4⋊F5) = C16.F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C41604C4.5(C4:F5)320,189
C4.6(C4⋊F5) = C80.2C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C41604C4.6(C4:F5)320,190
C4.7(C4⋊F5) = C42⋊3F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4804C4.7(C4:F5)320,201
C4.8(C4⋊F5) = (C2×C8)⋊F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4804C4.8(C4:F5)320,232
C4.9(C4⋊F5) = C20⋊3M4(2)φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4160C4.9(C4:F5)320,1019
C4.10(C4⋊F5) = C42.14F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4160C4.10(C4:F5)320,1020
C4.11(C4⋊F5) = C42⋊9F5φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C480C4.11(C4:F5)320,1027
C4.12(C4⋊F5) = C2×C40⋊C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C480C4.12(C4:F5)320,1057
C4.13(C4⋊F5) = C2×D5.D8φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C480C4.13(C4:F5)320,1058
C4.14(C4⋊F5) = C2×C40.C4φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4160C4.14(C4:F5)320,1060
C4.15(C4⋊F5) = C2×D10.Q8φ: C4⋊F5/C4×D5 → C2 ⊆ Aut C4160C4.15(C4:F5)320,1061
C4.16(C4⋊F5) = D10.18D8φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C480C4.16(C4:F5)320,212
C4.17(C4⋊F5) = C20.C42φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C480C4.17(C4:F5)320,213
C4.18(C4⋊F5) = M4(2)⋊F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C4408C4.18(C4:F5)320,237
C4.19(C4⋊F5) = M4(2)⋊4F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C4808C4.19(C4:F5)320,240
C4.20(C4⋊F5) = C4⋊C4.9F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C4160C4.20(C4:F5)320,1046
C4.21(C4⋊F5) = M4(2)⋊1F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C4408C4.21(C4:F5)320,1065
C4.22(C4⋊F5) = M4(2).1F5φ: C4⋊F5/C2×F5 → C2 ⊆ Aut C4808C4.22(C4:F5)320,1067
C4.23(C4⋊F5) = C20⋊C16central extension (φ=1)320C4.23(C4:F5)320,196
C4.24(C4⋊F5) = C42.9F5central extension (φ=1)804C4.24(C4:F5)320,199
C4.25(C4⋊F5) = C42⋊6F5central extension (φ=1)404C4.25(C4:F5)320,200
C4.26(C4⋊F5) = C10.M5(2)central extension (φ=1)320C4.26(C4:F5)320,226
C4.27(C4⋊F5) = C40.1C8central extension (φ=1)804C4.27(C4:F5)320,227
C4.28(C4⋊F5) = D10.3M4(2)central extension (φ=1)80C4.28(C4:F5)320,230
C4.29(C4⋊F5) = C42.11F5central extension (φ=1)160C4.29(C4:F5)320,1017
C4.30(C4⋊F5) = (C2×C8)⋊6F5central extension (φ=1)804C4.30(C4:F5)320,1059
C4.31(C4⋊F5) = (C8×D5).C4central extension (φ=1)804C4.31(C4:F5)320,1062

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