# Extensions 1→N→G→Q→1 with N=C10 and Q=C2×S4

Direct product G=N×Q with N=C10 and Q=C2×S4
dρLabelID
C2×C10×S460C2xC10xS4480,1198

Semidirect products G=N:Q with N=C10 and Q=C2×S4
extensionφ:Q→Aut NdρLabelID
C101(C2×S4) = C2×D5×S4φ: C2×S4/S4C2 ⊆ Aut C10306+C10:1(C2xS4)480,1193
C102(C2×S4) = C22×C5⋊S4φ: C2×S4/C2×A4C2 ⊆ Aut C1060C10:2(C2xS4)480,1199

Non-split extensions G=N.Q with N=C10 and Q=C2×S4
extensionφ:Q→Aut NdρLabelID
C10.1(C2×S4) = CSU2(𝔽3)⋊D5φ: C2×S4/S4C2 ⊆ Aut C101604C10.1(C2xS4)480,967
C10.2(C2×S4) = Dic5.6S4φ: C2×S4/S4C2 ⊆ Aut C10804C10.2(C2xS4)480,968
C10.3(C2×S4) = Dic5.7S4φ: C2×S4/S4C2 ⊆ Aut C10804+C10.3(C2xS4)480,969
C10.4(C2×S4) = GL2(𝔽3)⋊D5φ: C2×S4/S4C2 ⊆ Aut C10804+C10.4(C2xS4)480,970
C10.5(C2×S4) = D5×CSU2(𝔽3)φ: C2×S4/S4C2 ⊆ Aut C10804-C10.5(C2xS4)480,971
C10.6(C2×S4) = D10.1S4φ: C2×S4/S4C2 ⊆ Aut C10804-C10.6(C2xS4)480,972
C10.7(C2×S4) = D10.2S4φ: C2×S4/S4C2 ⊆ Aut C10804C10.7(C2xS4)480,973
C10.8(C2×S4) = D5×GL2(𝔽3)φ: C2×S4/S4C2 ⊆ Aut C10404C10.8(C2xS4)480,974
C10.9(C2×S4) = A4⋊Dic10φ: C2×S4/S4C2 ⊆ Aut C101206-C10.9(C2xS4)480,975
C10.10(C2×S4) = Dic5×S4φ: C2×S4/S4C2 ⊆ Aut C10606-C10.10(C2xS4)480,976
C10.11(C2×S4) = Dic52S4φ: C2×S4/S4C2 ⊆ Aut C10606C10.11(C2xS4)480,977
C10.12(C2×S4) = Dic5⋊S4φ: C2×S4/S4C2 ⊆ Aut C10606C10.12(C2xS4)480,978
C10.13(C2×S4) = D5×A4⋊C4φ: C2×S4/S4C2 ⊆ Aut C10606C10.13(C2xS4)480,979
C10.14(C2×S4) = D10⋊S4φ: C2×S4/S4C2 ⊆ Aut C10606C10.14(C2xS4)480,980
C10.15(C2×S4) = A4⋊D20φ: C2×S4/S4C2 ⊆ Aut C10606+C10.15(C2xS4)480,981
C10.16(C2×S4) = C20.1S4φ: C2×S4/C2×A4C2 ⊆ Aut C101206-C10.16(C2xS4)480,1024
C10.17(C2×S4) = C4×C5⋊S4φ: C2×S4/C2×A4C2 ⊆ Aut C10606C10.17(C2xS4)480,1025
C10.18(C2×S4) = C20⋊S4φ: C2×S4/C2×A4C2 ⊆ Aut C10606+C10.18(C2xS4)480,1026
C10.19(C2×S4) = C2×Q8.D15φ: C2×S4/C2×A4C2 ⊆ Aut C10160C10.19(C2xS4)480,1027
C10.20(C2×S4) = C2×Q8⋊D15φ: C2×S4/C2×A4C2 ⊆ Aut C1080C10.20(C2xS4)480,1028
C10.21(C2×S4) = Q8.D30φ: C2×S4/C2×A4C2 ⊆ Aut C10804C10.21(C2xS4)480,1029
C10.22(C2×S4) = C20.2S4φ: C2×S4/C2×A4C2 ⊆ Aut C101604-C10.22(C2xS4)480,1030
C10.23(C2×S4) = C20.6S4φ: C2×S4/C2×A4C2 ⊆ Aut C10804C10.23(C2xS4)480,1031
C10.24(C2×S4) = C20.3S4φ: C2×S4/C2×A4C2 ⊆ Aut C10804+C10.24(C2xS4)480,1032
C10.25(C2×S4) = C2×A4⋊Dic5φ: C2×S4/C2×A4C2 ⊆ Aut C10120C10.25(C2xS4)480,1033
C10.26(C2×S4) = C242D15φ: C2×S4/C2×A4C2 ⊆ Aut C10606C10.26(C2xS4)480,1034
C10.27(C2×S4) = C5×A4⋊Q8central extension (φ=1)1206C10.27(C2xS4)480,1013
C10.28(C2×S4) = C20×S4central extension (φ=1)603C10.28(C2xS4)480,1014
C10.29(C2×S4) = C5×C4⋊S4central extension (φ=1)606C10.29(C2xS4)480,1015
C10.30(C2×S4) = C10×CSU2(𝔽3)central extension (φ=1)160C10.30(C2xS4)480,1016
C10.31(C2×S4) = C10×GL2(𝔽3)central extension (φ=1)80C10.31(C2xS4)480,1017
C10.32(C2×S4) = C5×Q8.D6central extension (φ=1)804C10.32(C2xS4)480,1018
C10.33(C2×S4) = C5×C4.S4central extension (φ=1)1604C10.33(C2xS4)480,1019
C10.34(C2×S4) = C5×C4.6S4central extension (φ=1)802C10.34(C2xS4)480,1020
C10.35(C2×S4) = C5×C4.3S4central extension (φ=1)804C10.35(C2xS4)480,1021
C10.36(C2×S4) = C10×A4⋊C4central extension (φ=1)120C10.36(C2xS4)480,1022
C10.37(C2×S4) = C5×A4⋊D4central extension (φ=1)606C10.37(C2xS4)480,1023

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