Extensions 1→N→G→Q→1 with N=C10 and Q=C8⋊C4

Direct product G=N×Q with N=C10 and Q=C8⋊C4
dρLabelID
C10×C8⋊C4320C10xC8:C4320,904

Semidirect products G=N:Q with N=C10 and Q=C8⋊C4
extensionφ:Q→Aut NdρLabelID
C101(C8⋊C4) = C2×C8⋊F5φ: C8⋊C4/C8C4 ⊆ Aut C1080C10:1(C8:C4)320,1055
C102(C8⋊C4) = C2×C10.C42φ: C8⋊C4/C2×C4C4 ⊆ Aut C10320C10:2(C8:C4)320,1087
C103(C8⋊C4) = C2×C42.D5φ: C8⋊C4/C42C2 ⊆ Aut C10320C10:3(C8:C4)320,548
C104(C8⋊C4) = C2×C408C4φ: C8⋊C4/C2×C8C2 ⊆ Aut C10320C10:4(C8:C4)320,727

Non-split extensions G=N.Q with N=C10 and Q=C8⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(C8⋊C4) = C16⋊F5φ: C8⋊C4/C8C4 ⊆ Aut C10804C10.1(C8:C4)320,183
C10.2(C8⋊C4) = C164F5φ: C8⋊C4/C8C4 ⊆ Aut C10804C10.2(C8:C4)320,184
C10.3(C8⋊C4) = C40⋊C8φ: C8⋊C4/C8C4 ⊆ Aut C10320C10.3(C8:C4)320,217
C10.4(C8⋊C4) = D10.3M4(2)φ: C8⋊C4/C8C4 ⊆ Aut C1080C10.4(C8:C4)320,230
C10.5(C8⋊C4) = C42.3F5φ: C8⋊C4/C2×C4C4 ⊆ Aut C10804C10.5(C8:C4)320,198
C10.6(C8⋊C4) = C20.31M4(2)φ: C8⋊C4/C2×C4C4 ⊆ Aut C10320C10.6(C8:C4)320,218
C10.7(C8⋊C4) = C20.23C42φ: C8⋊C4/C2×C4C4 ⊆ Aut C10804C10.7(C8:C4)320,228
C10.8(C8⋊C4) = C10.(C4⋊C8)φ: C8⋊C4/C2×C4C4 ⊆ Aut C10320C10.8(C8:C4)320,256
C10.9(C8⋊C4) = C42.279D10φ: C8⋊C4/C42C2 ⊆ Aut C10320C10.9(C8:C4)320,12
C10.10(C8⋊C4) = C20.45C42φ: C8⋊C4/C42C2 ⊆ Aut C10804C10.10(C8:C4)320,24
C10.11(C8⋊C4) = (C2×C20)⋊8C8φ: C8⋊C4/C42C2 ⊆ Aut C10320C10.11(C8:C4)320,82
C10.12(C8⋊C4) = C408C8φ: C8⋊C4/C2×C8C2 ⊆ Aut C10320C10.12(C8:C4)320,13
C10.13(C8⋊C4) = C80⋊C4φ: C8⋊C4/C2×C8C2 ⊆ Aut C10804C10.13(C8:C4)320,70
C10.14(C8⋊C4) = (C2×C40)⋊15C4φ: C8⋊C4/C2×C8C2 ⊆ Aut C10320C10.14(C8:C4)320,108
C10.15(C8⋊C4) = C5×C8⋊C8central extension (φ=1)320C10.15(C8:C4)320,127
C10.16(C8⋊C4) = C5×C22.7C42central extension (φ=1)320C10.16(C8:C4)320,141
C10.17(C8⋊C4) = C5×C16⋊C4central extension (φ=1)804C10.17(C8:C4)320,152

׿
×
𝔽