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

Direct product G=N×Q with N=C10 and Q=C4⋊C8
dρLabelID
C10×C4⋊C8320C10xC4:C8320,923

Semidirect products G=N:Q with N=C10 and Q=C4⋊C8
extensionφ:Q→Aut NdρLabelID
C10⋊1(C4⋊C8) = C2×C20⋊C8φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10:1(C4:C8)320,1085
C10⋊2(C4⋊C8) = C2×Dic5⋊C8φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10:2(C4:C8)320,1090
C10⋊3(C4⋊C8) = C2×C20⋊3C8φ: C4⋊C8/C42 → C2 ⊆ Aut C10320C10:3(C4:C8)320,550
C10⋊4(C4⋊C8) = C2×C20.8Q8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C10320C10:4(C4:C8)320,726

Non-split extensions G=N.Q with N=C10 and Q=C4⋊C8
extensionφ:Q→Aut NdρLabelID
C10.1(C4⋊C8) = C20⋊C16φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.1(C4:C8)320,196
C10.2(C4⋊C8) = C42.9F5φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10804C10.2(C4:C8)320,199
C10.3(C4⋊C8) = C40⋊2C8φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.3(C4:C8)320,219
C10.4(C4⋊C8) = C40⋊1C8φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.4(C4:C8)320,220
C10.5(C4⋊C8) = C20.26M4(2)φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.5(C4:C8)320,221
C10.6(C4⋊C8) = Dic5.13D8φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.6(C4:C8)320,222
C10.7(C4⋊C8) = C10.M5(2)φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.7(C4:C8)320,226
C10.8(C4⋊C8) = C40.1C8φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10804C10.8(C4:C8)320,227
C10.9(C4⋊C8) = C10.(C4⋊C8)φ: C4⋊C8/C2×C4 → C4 ⊆ Aut C10320C10.9(C4:C8)320,256
C10.10(C4⋊C8) = C40⋊6C8φ: C4⋊C8/C42 → C2 ⊆ Aut C10320C10.10(C4:C8)320,15
C10.11(C4⋊C8) = C40⋊5C8φ: C4⋊C8/C42 → C2 ⊆ Aut C10320C10.11(C4:C8)320,16
C10.12(C4⋊C8) = C20⋊3C16φ: C4⋊C8/C42 → C2 ⊆ Aut C10320C10.12(C4:C8)320,20
C10.13(C4⋊C8) = C40.7C8φ: C4⋊C8/C42 → C2 ⊆ Aut C10802C10.13(C4:C8)320,21
C10.14(C4⋊C8) = (C2×C20)⋊8C8φ: C4⋊C8/C42 → C2 ⊆ Aut C10320C10.14(C4:C8)320,82
C10.15(C4⋊C8) = C20.53D8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C10320C10.15(C4:C8)320,37
C10.16(C4⋊C8) = C20.39SD16φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C10320C10.16(C4:C8)320,38
C10.17(C4⋊C8) = C40.88D4φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C10320C10.17(C4:C8)320,59
C10.18(C4⋊C8) = C40.9Q8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C10804C10.18(C4:C8)320,69
C10.19(C4⋊C8) = (C2×C40)⋊15C4φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C10320C10.19(C4:C8)320,108
C10.20(C4⋊C8) = C5×C8⋊2C8central extension (φ=1)320C10.20(C4:C8)320,139
C10.21(C4⋊C8) = C5×C8⋊1C8central extension (φ=1)320C10.21(C4:C8)320,140
C10.22(C4⋊C8) = C5×C22.7C42central extension (φ=1)320C10.22(C4:C8)320,141
C10.23(C4⋊C8) = C5×C4⋊C16central extension (φ=1)320C10.23(C4:C8)320,168
C10.24(C4⋊C8) = C5×C8.C8central extension (φ=1)802C10.24(C4:C8)320,169

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