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Extensions 1→N→G→Q→1 with N=C10 and Q=Q8⋊C4

Direct product G=N×Q with N=C10 and Q=Q8⋊C4
dρLabelID
C10×Q8⋊C4320C10xQ8:C4320,916

Semidirect products G=N:Q with N=C10 and Q=Q8⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊(Q8⋊C4) = C2×Q8⋊F5φ: Q8⋊C4/Q8 → C4 ⊆ Aut C1080C10:(Q8:C4)320,1119
C10⋊2(Q8⋊C4) = C2×C10.Q16φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C10320C10:2(Q8:C4)320,596
C10⋊3(Q8⋊C4) = C2×C20.44D4φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C10320C10:3(Q8:C4)320,730
C10⋊4(Q8⋊C4) = C2×Q8⋊Dic5φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C10320C10:4(Q8:C4)320,851

Non-split extensions G=N.Q with N=C10 and Q=Q8⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(Q8⋊C4) = D10.1Q16φ: Q8⋊C4/Q8 → C4 ⊆ Aut C1080C10.1(Q8:C4)320,207
C10.2(Q8⋊C4) = Dic10⋊1C8φ: Q8⋊C4/Q8 → C4 ⊆ Aut C10320C10.2(Q8:C4)320,210
C10.3(Q8⋊C4) = Dic5.D8φ: Q8⋊C4/Q8 → C4 ⊆ Aut C10320C10.3(Q8:C4)320,211
C10.4(Q8⋊C4) = D10.18D8φ: Q8⋊C4/Q8 → C4 ⊆ Aut C1080C10.4(Q8:C4)320,212
C10.5(Q8⋊C4) = D10.Q16φ: Q8⋊C4/Q8 → C4 ⊆ Aut C1080C10.5(Q8:C4)320,264
C10.6(Q8⋊C4) = Dic5.12Q16φ: Q8⋊C4/Q8 → C4 ⊆ Aut C10320C10.6(Q8:C4)320,268
C10.7(Q8⋊C4) = Dic5.Q16φ: Q8⋊C4/Q8 → C4 ⊆ Aut C10320C10.7(Q8:C4)320,269
C10.8(Q8⋊C4) = C4⋊Dic5⋊C4φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C1080C10.8(Q8:C4)320,10
C10.9(Q8⋊C4) = Dic10⋊4C8φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C10320C10.9(Q8:C4)320,42
C10.10(Q8⋊C4) = C20.2D8φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C10320C10.10(Q8:C4)320,44
C10.11(Q8⋊C4) = C20.31C42φ: Q8⋊C4/C4⋊C4 → C2 ⊆ Aut C10320C10.11(Q8:C4)320,87
C10.12(Q8⋊C4) = Dic10⋊3C8φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.12(Q8:C4)320,14
C10.13(Q8⋊C4) = C23.30D20φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C1080C10.13(Q8:C4)320,25
C10.14(Q8⋊C4) = C4.Dic20φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.14(Q8:C4)320,39
C10.15(Q8⋊C4) = C20.47D8φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.15(Q8:C4)320,40
C10.16(Q8⋊C4) = C20.39C42φ: Q8⋊C4/C2×C8 → C2 ⊆ Aut C10320C10.16(Q8:C4)320,109
C10.17(Q8⋊C4) = C20.26Q16φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C10320C10.17(Q8:C4)320,93
C10.18(Q8⋊C4) = C10.29C4≀C2φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C1080C10.18(Q8:C4)320,96
C10.19(Q8⋊C4) = C20.5Q16φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C10320C10.19(Q8:C4)320,104
C10.20(Q8⋊C4) = C20.10D8φ: Q8⋊C4/C2×Q8 → C2 ⊆ Aut C10320C10.20(Q8:C4)320,105
C10.21(Q8⋊C4) = C5×Q8⋊C8central extension (φ=1)320C10.21(Q8:C4)320,131
C10.22(Q8⋊C4) = C5×C23.31D4central extension (φ=1)80C10.22(Q8:C4)320,133
C10.23(Q8⋊C4) = C5×C4.10D8central extension (φ=1)320C10.23(Q8:C4)320,137
C10.24(Q8⋊C4) = C5×C4.6Q16central extension (φ=1)320C10.24(Q8:C4)320,138
C10.25(Q8⋊C4) = C5×C22.4Q16central extension (φ=1)320C10.25(Q8:C4)320,145

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