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Extensions 1→N→G→Q→1 with N=C10 and Q=Q8⋊3S3

Direct product G=N×Q with N=C10 and Q=Q8⋊3S3
dρLabelID
C10×Q8⋊3S3240C10xQ8:3S3480,1158

Semidirect products G=N:Q with N=C10 and Q=Q8⋊3S3
extensionφ:Q→Aut NdρLabelID
C10⋊1(Q8⋊3S3) = C2×D60⋊C2φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10:1(Q8:3S3)480,1081
C10⋊2(Q8⋊3S3) = C2×D12⋊D5φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10:2(Q8:3S3)480,1079
C10⋊3(Q8⋊3S3) = C2×Q8⋊3D15φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10:3(Q8:3S3)480,1173

Non-split extensions G=N.Q with N=C10 and Q=Q8⋊3S3
extensionφ:Q→Aut NdρLabelID
C10.1(Q8⋊3S3) = (C2×C20).D6φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.1(Q8:3S3)480,402
C10.2(Q8⋊3S3) = Dic3×Dic10φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10480C10.2(Q8:3S3)480,406
C10.3(Q8⋊3S3) = Dic5.1Dic6φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10480C10.3(Q8:3S3)480,410
C10.4(Q8⋊3S3) = (S3×C20)⋊5C4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.4(Q8:3S3)480,414
C10.5(Q8⋊3S3) = C60⋊5C4⋊C2φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.5(Q8:3S3)480,418
C10.6(Q8⋊3S3) = C4⋊Dic5⋊S3φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.6(Q8:3S3)480,421
C10.7(Q8⋊3S3) = D6⋊Dic5⋊C2φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.7(Q8:3S3)480,427
C10.8(Q8⋊3S3) = C60.46D4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.8(Q8:3S3)480,445
C10.9(Q8⋊3S3) = C60.47D4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.9(Q8:3S3)480,450
C10.10(Q8⋊3S3) = C10.D4⋊S3φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.10(Q8:3S3)480,456
C10.11(Q8⋊3S3) = C60.6Q8φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10480C10.11(Q8:3S3)480,457
C10.12(Q8⋊3S3) = D30.23(C2×C4)φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.12(Q8:3S3)480,479
C10.13(Q8⋊3S3) = D30⋊Q8φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.13(Q8:3S3)480,487
C10.14(Q8⋊3S3) = D30⋊D4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.14(Q8:3S3)480,496
C10.15(Q8⋊3S3) = D60⋊14C4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.15(Q8:3S3)480,504
C10.16(Q8⋊3S3) = D30.6D4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.16(Q8:3S3)480,509
C10.17(Q8⋊3S3) = D30.7D4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.17(Q8:3S3)480,514
C10.18(Q8⋊3S3) = C15⋊22(C4×D4)φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.18(Q8:3S3)480,522
C10.19(Q8⋊3S3) = C60⋊6D4φ: Q8⋊3S3/C4×S3 → C2 ⊆ Aut C10240C10.19(Q8:3S3)480,536
C10.20(Q8⋊3S3) = Dic15⋊6Q8φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10480C10.20(Q8:3S3)480,407
C10.21(Q8⋊3S3) = Dic5.2Dic6φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10480C10.21(Q8:3S3)480,411
C10.22(Q8⋊3S3) = C4⋊Dic3⋊D5φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.22(Q8:3S3)480,413
C10.23(Q8⋊3S3) = D6⋊C4.D5φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.23(Q8:3S3)480,417
C10.24(Q8⋊3S3) = (C4×D15)⋊8C4φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.24(Q8:3S3)480,423
C10.25(Q8⋊3S3) = D30.35D4φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.25(Q8:3S3)480,431
C10.26(Q8⋊3S3) = D6⋊Dic5.C2φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.26(Q8:3S3)480,443
C10.27(Q8⋊3S3) = C60.89D4φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.27(Q8:3S3)480,446
C10.28(Q8⋊3S3) = C12.Dic10φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10480C10.28(Q8:3S3)480,460
C10.29(Q8⋊3S3) = D30⋊10Q8φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.29(Q8:3S3)480,466
C10.30(Q8⋊3S3) = (S3×Dic5)⋊C4φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.30(Q8:3S3)480,476
C10.31(Q8⋊3S3) = Dic15⋊14D4φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.31(Q8:3S3)480,482
C10.32(Q8⋊3S3) = D6⋊1Dic10φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.32(Q8:3S3)480,486
C10.33(Q8⋊3S3) = Dic5⋊D12φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.33(Q8:3S3)480,492
C10.34(Q8⋊3S3) = (C2×D12).D5φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.34(Q8:3S3)480,499
C10.35(Q8⋊3S3) = D6.D20φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.35(Q8:3S3)480,503
C10.36(Q8⋊3S3) = Dic15⋊8D4φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.36(Q8:3S3)480,511
C10.37(Q8⋊3S3) = C20⋊2D12φ: Q8⋊3S3/D12 → C2 ⊆ Aut C10240C10.37(Q8:3S3)480,542
C10.38(Q8⋊3S3) = C4.Dic30φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10480C10.38(Q8:3S3)480,855
C10.39(Q8⋊3S3) = C4⋊C4⋊7D15φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.39(Q8:3S3)480,857
C10.40(Q8⋊3S3) = D60⋊11C4φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.40(Q8:3S3)480,858
C10.41(Q8⋊3S3) = D30.29D4φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.41(Q8:3S3)480,859
C10.42(Q8⋊3S3) = C4⋊D60φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.42(Q8:3S3)480,860
C10.43(Q8⋊3S3) = C4⋊C4⋊D15φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.43(Q8:3S3)480,863
C10.44(Q8⋊3S3) = Q8×Dic15φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10480C10.44(Q8:3S3)480,910
C10.45(Q8⋊3S3) = D30⋊7Q8φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.45(Q8:3S3)480,911
C10.46(Q8⋊3S3) = C60.23D4φ: Q8⋊3S3/C3×Q8 → C2 ⊆ Aut C10240C10.46(Q8:3S3)480,912
C10.47(Q8⋊3S3) = C5×C4.Dic6central extension (φ=1)480C10.47(Q8:3S3)480,769
C10.48(Q8⋊3S3) = C5×C4⋊C4⋊7S3central extension (φ=1)240C10.48(Q8:3S3)480,771
C10.49(Q8⋊3S3) = C5×Dic3⋊5D4central extension (φ=1)240C10.49(Q8:3S3)480,772
C10.50(Q8⋊3S3) = C5×D6.D4central extension (φ=1)240C10.50(Q8:3S3)480,773
C10.51(Q8⋊3S3) = C5×C12⋊D4central extension (φ=1)240C10.51(Q8:3S3)480,774
C10.52(Q8⋊3S3) = C5×C4⋊C4⋊S3central extension (φ=1)240C10.52(Q8:3S3)480,777
C10.53(Q8⋊3S3) = C5×Q8×Dic3central extension (φ=1)480C10.53(Q8:3S3)480,824
C10.54(Q8⋊3S3) = C5×D6⋊3Q8central extension (φ=1)240C10.54(Q8:3S3)480,825
C10.55(Q8⋊3S3) = C5×C12.23D4central extension (φ=1)240C10.55(Q8:3S3)480,826

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