# Extensions 1→N→G→Q→1 with N=C10 and Q=C6.D4

Direct product G=N×Q with N=C10 and Q=C6.D4
dρLabelID
C10×C6.D4240C10xC6.D4480,831

Semidirect products G=N:Q with N=C10 and Q=C6.D4
extensionφ:Q→Aut NdρLabelID
C10⋊(C6.D4) = C2×D10.D6φ: C6.D4/C2×C6C4 ⊆ Aut C10120C10:(C6.D4)480,1072
C102(C6.D4) = C2×D10⋊Dic3φ: C6.D4/C2×Dic3C2 ⊆ Aut C10240C10:2(C6.D4)480,611
C103(C6.D4) = C2×C30.38D4φ: C6.D4/C22×C6C2 ⊆ Aut C10240C10:3(C6.D4)480,917

Non-split extensions G=N.Q with N=C10 and Q=C6.D4
extensionφ:Q→Aut NdρLabelID
C10.1(C6.D4) = (C2×C60)⋊C4φ: C6.D4/C2×C6C4 ⊆ Aut C101204C10.1(C6.D4)480,304
C10.2(C6.D4) = C30.7M4(2)φ: C6.D4/C2×C6C4 ⊆ Aut C10240C10.2(C6.D4)480,308
C10.3(C6.D4) = (C2×C60).C4φ: C6.D4/C2×C6C4 ⊆ Aut C102404C10.3(C6.D4)480,310
C10.4(C6.D4) = D10.10D12φ: C6.D4/C2×C6C4 ⊆ Aut C10120C10.4(C6.D4)480,311
C10.5(C6.D4) = D20⋊Dic3φ: C6.D4/C2×C6C4 ⊆ Aut C101208C10.5(C6.D4)480,312
C10.6(C6.D4) = Dic10⋊Dic3φ: C6.D4/C2×C6C4 ⊆ Aut C101208C10.6(C6.D4)480,313
C10.7(C6.D4) = Dic102Dic3φ: C6.D4/C2×C6C4 ⊆ Aut C101208C10.7(C6.D4)480,314
C10.8(C6.D4) = D202Dic3φ: C6.D4/C2×C6C4 ⊆ Aut C101208C10.8(C6.D4)480,315
C10.9(C6.D4) = C3⋊(C23⋊F5)φ: C6.D4/C2×C6C4 ⊆ Aut C101204C10.9(C6.D4)480,316
C10.10(C6.D4) = C30.22M4(2)φ: C6.D4/C2×C6C4 ⊆ Aut C10240C10.10(C6.D4)480,317
C10.11(C6.D4) = C5⋊(C12.D4)φ: C6.D4/C2×C6C4 ⊆ Aut C101204C10.11(C6.D4)480,318
C10.12(C6.D4) = C60.93D4φ: C6.D4/C2×Dic3C2 ⊆ Aut C10240C10.12(C6.D4)480,31
C10.13(C6.D4) = C60.28D4φ: C6.D4/C2×Dic3C2 ⊆ Aut C101204C10.13(C6.D4)480,34
C10.14(C6.D4) = C12.6D20φ: C6.D4/C2×Dic3C2 ⊆ Aut C102404C10.14(C6.D4)480,37
C10.15(C6.D4) = C30.D8φ: C6.D4/C2×Dic3C2 ⊆ Aut C10240C10.15(C6.D4)480,40
C10.16(C6.D4) = C6.D40φ: C6.D4/C2×Dic3C2 ⊆ Aut C10240C10.16(C6.D4)480,41
C10.17(C6.D4) = C30.Q16φ: C6.D4/C2×Dic3C2 ⊆ Aut C10480C10.17(C6.D4)480,46
C10.18(C6.D4) = C6.Dic20φ: C6.D4/C2×Dic3C2 ⊆ Aut C10480C10.18(C6.D4)480,47
C10.19(C6.D4) = C60.96D4φ: C6.D4/C2×Dic3C2 ⊆ Aut C101204C10.19(C6.D4)480,52
C10.20(C6.D4) = C60.97D4φ: C6.D4/C2×Dic3C2 ⊆ Aut C101204C10.20(C6.D4)480,53
C10.21(C6.D4) = C30.24C42φ: C6.D4/C2×Dic3C2 ⊆ Aut C10480C10.21(C6.D4)480,70
C10.22(C6.D4) = (C2×C6).D20φ: C6.D4/C2×Dic3C2 ⊆ Aut C101204C10.22(C6.D4)480,71
C10.23(C6.D4) = C60.212D4φ: C6.D4/C22×C6C2 ⊆ Aut C10240C10.23(C6.D4)480,190
C10.24(C6.D4) = C30.29C42φ: C6.D4/C22×C6C2 ⊆ Aut C10480C10.24(C6.D4)480,191
C10.25(C6.D4) = D4⋊Dic15φ: C6.D4/C22×C6C2 ⊆ Aut C10240C10.25(C6.D4)480,192
C10.26(C6.D4) = C60.8D4φ: C6.D4/C22×C6C2 ⊆ Aut C101204C10.26(C6.D4)480,193
C10.27(C6.D4) = C23.7D30φ: C6.D4/C22×C6C2 ⊆ Aut C101204C10.27(C6.D4)480,194
C10.28(C6.D4) = Q82Dic15φ: C6.D4/C22×C6C2 ⊆ Aut C10480C10.28(C6.D4)480,195
C10.29(C6.D4) = C60.10D4φ: C6.D4/C22×C6C2 ⊆ Aut C102404C10.29(C6.D4)480,196
C10.30(C6.D4) = Q83Dic15φ: C6.D4/C22×C6C2 ⊆ Aut C101204C10.30(C6.D4)480,197
C10.31(C6.D4) = C5×C12.55D4central extension (φ=1)240C10.31(C6.D4)480,149
C10.32(C6.D4) = C5×C6.C42central extension (φ=1)480C10.32(C6.D4)480,150
C10.33(C6.D4) = C5×D4⋊Dic3central extension (φ=1)240C10.33(C6.D4)480,151
C10.34(C6.D4) = C5×C12.D4central extension (φ=1)1204C10.34(C6.D4)480,152
C10.35(C6.D4) = C5×C23.7D6central extension (φ=1)1204C10.35(C6.D4)480,153
C10.36(C6.D4) = C5×Q82Dic3central extension (φ=1)480C10.36(C6.D4)480,154
C10.37(C6.D4) = C5×C12.10D4central extension (φ=1)2404C10.37(C6.D4)480,155
C10.38(C6.D4) = C5×Q83Dic3central extension (φ=1)1204C10.38(C6.D4)480,156

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