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

Direct product G=N×Q with N=Q8 and Q=S3×C10
dρLabelID
S3×Q8×C10240S3xQ8xC10480,1157

Semidirect products G=N:Q with N=Q8 and Q=S3×C10
extensionφ:Q→Out NdρLabelID
Q8⋊(S3×C10) = C10×GL2(𝔽3)φ: S3×C10/C10 → S3 ⊆ Out Q880Q8:(S3xC10)480,1017
Q8⋊2(S3×C10) = C5×S3×SD16φ: S3×C10/C5×S3 → C2 ⊆ Out Q81204Q8:2(S3xC10)480,792
Q8⋊3(S3×C10) = C5×Q8⋊3D6φ: S3×C10/C5×S3 → C2 ⊆ Out Q81204Q8:3(S3xC10)480,793
Q8⋊4(S3×C10) = C10×Q8⋊2S3φ: S3×C10/C30 → C2 ⊆ Out Q8240Q8:4(S3xC10)480,820
Q8⋊5(S3×C10) = C5×D4⋊D6φ: S3×C10/C30 → C2 ⊆ Out Q81204Q8:5(S3xC10)480,828
Q8⋊6(S3×C10) = C10×Q8⋊3S3φ: trivial image240Q8:6(S3xC10)480,1158
Q8⋊7(S3×C10) = C5×S3×C4○D4φ: trivial image1204Q8:7(S3xC10)480,1160
Q8⋊8(S3×C10) = C5×D4○D12φ: trivial image1204Q8:8(S3xC10)480,1161

Non-split extensions G=N.Q with N=Q8 and Q=S3×C10
extensionφ:Q→Out NdρLabelID
Q8.1(S3×C10) = C10×CSU2(𝔽3)φ: S3×C10/C10 → S3 ⊆ Out Q8160Q8.1(S3xC10)480,1016
Q8.2(S3×C10) = C5×Q8.D6φ: S3×C10/C10 → S3 ⊆ Out Q8804Q8.2(S3xC10)480,1018
Q8.3(S3×C10) = C5×C4.S4φ: S3×C10/C10 → S3 ⊆ Out Q81604Q8.3(S3xC10)480,1019
Q8.4(S3×C10) = C5×C4.6S4φ: S3×C10/C10 → S3 ⊆ Out Q8802Q8.4(S3xC10)480,1020
Q8.5(S3×C10) = C5×C4.3S4φ: S3×C10/C10 → S3 ⊆ Out Q8804Q8.5(S3xC10)480,1021
Q8.6(S3×C10) = C5×D4.D6φ: S3×C10/C5×S3 → C2 ⊆ Out Q82404Q8.6(S3xC10)480,794
Q8.7(S3×C10) = C5×Q8.7D6φ: S3×C10/C5×S3 → C2 ⊆ Out Q82404Q8.7(S3xC10)480,795
Q8.8(S3×C10) = C5×S3×Q16φ: S3×C10/C5×S3 → C2 ⊆ Out Q82404Q8.8(S3xC10)480,796
Q8.9(S3×C10) = C5×Q16⋊S3φ: S3×C10/C5×S3 → C2 ⊆ Out Q82404Q8.9(S3xC10)480,797
Q8.10(S3×C10) = C5×D24⋊C2φ: S3×C10/C5×S3 → C2 ⊆ Out Q82404Q8.10(S3xC10)480,798
Q8.11(S3×C10) = C5×Q8.11D6φ: S3×C10/C30 → C2 ⊆ Out Q82404Q8.11(S3xC10)480,821
Q8.12(S3×C10) = C10×C3⋊Q16φ: S3×C10/C30 → C2 ⊆ Out Q8480Q8.12(S3xC10)480,822
Q8.13(S3×C10) = C5×Q8.13D6φ: S3×C10/C30 → C2 ⊆ Out Q82404Q8.13(S3xC10)480,829
Q8.14(S3×C10) = C5×Q8.14D6φ: S3×C10/C30 → C2 ⊆ Out Q82404Q8.14(S3xC10)480,830
Q8.15(S3×C10) = C5×Q8.15D6φ: trivial image2404Q8.15(S3xC10)480,1159
Q8.16(S3×C10) = C5×Q8○D12φ: trivial image2404Q8.16(S3xC10)480,1162

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