# Extensions 1→N→G→Q→1 with N=C10 and Q=C2×Q8

Direct product G=N×Q with N=C10 and Q=C2×Q8
dρLabelID
Q8×C2×C10160Q8xC2xC10160,230

Semidirect products G=N:Q with N=C10 and Q=C2×Q8
extensionφ:Q→Aut NdρLabelID
C101(C2×Q8) = C22×Dic10φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10:1(C2xQ8)160,213
C102(C2×Q8) = C2×Q8×D5φ: C2×Q8/Q8C2 ⊆ Aut C1080C10:2(C2xQ8)160,220

Non-split extensions G=N.Q with N=C10 and Q=C2×Q8
extensionφ:Q→Aut NdρLabelID
C10.1(C2×Q8) = C4×Dic10φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.1(C2xQ8)160,89
C10.2(C2×Q8) = C202Q8φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.2(C2xQ8)160,90
C10.3(C2×Q8) = C20.6Q8φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.3(C2xQ8)160,91
C10.4(C2×Q8) = Dic5.14D4φ: C2×Q8/C2×C4C2 ⊆ Aut C1080C10.4(C2xQ8)160,99
C10.5(C2×Q8) = C20⋊Q8φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.5(C2xQ8)160,109
C10.6(C2×Q8) = C4.Dic10φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.6(C2xQ8)160,111
C10.7(C2×Q8) = C2×C10.D4φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.7(C2xQ8)160,144
C10.8(C2×Q8) = C20.48D4φ: C2×Q8/C2×C4C2 ⊆ Aut C1080C10.8(C2xQ8)160,145
C10.9(C2×Q8) = C2×C4⋊Dic5φ: C2×Q8/C2×C4C2 ⊆ Aut C10160C10.9(C2xQ8)160,146
C10.10(C2×Q8) = Dic53Q8φ: C2×Q8/Q8C2 ⊆ Aut C10160C10.10(C2xQ8)160,108
C10.11(C2×Q8) = Dic5.Q8φ: C2×Q8/Q8C2 ⊆ Aut C10160C10.11(C2xQ8)160,110
C10.12(C2×Q8) = D5×C4⋊C4φ: C2×Q8/Q8C2 ⊆ Aut C1080C10.12(C2xQ8)160,112
C10.13(C2×Q8) = D10⋊Q8φ: C2×Q8/Q8C2 ⊆ Aut C1080C10.13(C2xQ8)160,117
C10.14(C2×Q8) = D102Q8φ: C2×Q8/Q8C2 ⊆ Aut C1080C10.14(C2xQ8)160,118
C10.15(C2×Q8) = Dic5⋊Q8φ: C2×Q8/Q8C2 ⊆ Aut C10160C10.15(C2xQ8)160,165
C10.16(C2×Q8) = Q8×Dic5φ: C2×Q8/Q8C2 ⊆ Aut C10160C10.16(C2xQ8)160,166
C10.17(C2×Q8) = D103Q8φ: C2×Q8/Q8C2 ⊆ Aut C1080C10.17(C2xQ8)160,167
C10.18(C2×Q8) = C10×C4⋊C4central extension (φ=1)160C10.18(C2xQ8)160,177
C10.19(C2×Q8) = Q8×C20central extension (φ=1)160C10.19(C2xQ8)160,180
C10.20(C2×Q8) = C5×C22⋊Q8central extension (φ=1)80C10.20(C2xQ8)160,183
C10.21(C2×Q8) = C5×C42.C2central extension (φ=1)160C10.21(C2xQ8)160,186
C10.22(C2×Q8) = C5×C4⋊Q8central extension (φ=1)160C10.22(C2xQ8)160,189

׿
×
𝔽