# Extensions 1→N→G→Q→1 with N=C10 and Q=C2×C3⋊C8

Direct product G=N×Q with N=C10 and Q=C2×C3⋊C8
dρLabelID
C2×C10×C3⋊C8480C2xC10xC3:C8480,799

Semidirect products G=N:Q with N=C10 and Q=C2×C3⋊C8
extensionφ:Q→Aut NdρLabelID
C101(C2×C3⋊C8) = C2×C60.C4φ: C2×C3⋊C8/C12C4 ⊆ Aut C10240C10:1(C2xC3:C8)480,1060
C102(C2×C3⋊C8) = C22×C15⋊C8φ: C2×C3⋊C8/C2×C6C4 ⊆ Aut C10480C10:2(C2xC3:C8)480,1070
C103(C2×C3⋊C8) = C2×D5×C3⋊C8φ: C2×C3⋊C8/C3⋊C8C2 ⊆ Aut C10240C10:3(C2xC3:C8)480,357
C104(C2×C3⋊C8) = C22×C153C8φ: C2×C3⋊C8/C2×C12C2 ⊆ Aut C10480C10:4(C2xC3:C8)480,885

Non-split extensions G=N.Q with N=C10 and Q=C2×C3⋊C8
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C3⋊C8) = C24.F5φ: C2×C3⋊C8/C12C4 ⊆ Aut C102404C10.1(C2xC3:C8)480,294
C10.2(C2×C3⋊C8) = C120.C4φ: C2×C3⋊C8/C12C4 ⊆ Aut C102404C10.2(C2xC3:C8)480,295
C10.3(C2×C3⋊C8) = C4×C15⋊C8φ: C2×C3⋊C8/C12C4 ⊆ Aut C10480C10.3(C2xC3:C8)480,305
C10.4(C2×C3⋊C8) = C30.7M4(2)φ: C2×C3⋊C8/C12C4 ⊆ Aut C10240C10.4(C2xC3:C8)480,308
C10.5(C2×C3⋊C8) = Dic5.13D12φ: C2×C3⋊C8/C12C4 ⊆ Aut C10480C10.5(C2xC3:C8)480,309
C10.6(C2×C3⋊C8) = C2×C15⋊C16φ: C2×C3⋊C8/C2×C6C4 ⊆ Aut C10480C10.6(C2xC3:C8)480,302
C10.7(C2×C3⋊C8) = C60.C8φ: C2×C3⋊C8/C2×C6C4 ⊆ Aut C102404C10.7(C2xC3:C8)480,303
C10.8(C2×C3⋊C8) = C60⋊C8φ: C2×C3⋊C8/C2×C6C4 ⊆ Aut C10480C10.8(C2xC3:C8)480,306
C10.9(C2×C3⋊C8) = C30.22M4(2)φ: C2×C3⋊C8/C2×C6C4 ⊆ Aut C10240C10.9(C2xC3:C8)480,317
C10.10(C2×C3⋊C8) = D5×C3⋊C16φ: C2×C3⋊C8/C3⋊C8C2 ⊆ Aut C102404C10.10(C2xC3:C8)480,7
C10.11(C2×C3⋊C8) = C40.51D6φ: C2×C3⋊C8/C3⋊C8C2 ⊆ Aut C102404C10.11(C2xC3:C8)480,10
C10.12(C2×C3⋊C8) = Dic5×C3⋊C8φ: C2×C3⋊C8/C3⋊C8C2 ⊆ Aut C10480C10.12(C2xC3:C8)480,25
C10.13(C2×C3⋊C8) = C60.93D4φ: C2×C3⋊C8/C3⋊C8C2 ⊆ Aut C10240C10.13(C2xC3:C8)480,31
C10.14(C2×C3⋊C8) = C60.13Q8φ: C2×C3⋊C8/C3⋊C8C2 ⊆ Aut C10480C10.14(C2xC3:C8)480,58
C10.15(C2×C3⋊C8) = C4×C153C8φ: C2×C3⋊C8/C2×C12C2 ⊆ Aut C10480C10.15(C2xC3:C8)480,162
C10.16(C2×C3⋊C8) = C605C8φ: C2×C3⋊C8/C2×C12C2 ⊆ Aut C10480C10.16(C2xC3:C8)480,164
C10.17(C2×C3⋊C8) = C2×C153C16φ: C2×C3⋊C8/C2×C12C2 ⊆ Aut C10480C10.17(C2xC3:C8)480,171
C10.18(C2×C3⋊C8) = C60.7C8φ: C2×C3⋊C8/C2×C12C2 ⊆ Aut C102402C10.18(C2xC3:C8)480,172
C10.19(C2×C3⋊C8) = C60.212D4φ: C2×C3⋊C8/C2×C12C2 ⊆ Aut C10240C10.19(C2xC3:C8)480,190
C10.20(C2×C3⋊C8) = C20×C3⋊C8central extension (φ=1)480C10.20(C2xC3:C8)480,121
C10.21(C2×C3⋊C8) = C5×C12⋊C8central extension (φ=1)480C10.21(C2xC3:C8)480,123
C10.22(C2×C3⋊C8) = C10×C3⋊C16central extension (φ=1)480C10.22(C2xC3:C8)480,130
C10.23(C2×C3⋊C8) = C5×C12.C8central extension (φ=1)2402C10.23(C2xC3:C8)480,131
C10.24(C2×C3⋊C8) = C5×C12.55D4central extension (φ=1)240C10.24(C2xC3:C8)480,149

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