Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₄×C₈

Direct product G=N×Q with N=C₁₀ and Q=C₄×C₈

		d	ρ	Label	ID
C₂×C₄×C₄₀		320		C2xC4xC40	320,903

Semidirect products G=N:Q with N=C₁₀ and Q=C₄×C₈

extension	φ:Q→Aut N	d	Label	ID
C₁₀⋊₁(C₄×C₈) = C₂×C₈×F₅	φ: C₄×C₈/C₈ → C₄ ⊆ Aut C₁₀	80	C10:1(C4xC8)	320,1054
C₁₀⋊₂(C₄×C₈) = C₂×C₄×C₅⋊C₈	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320	C10:2(C4xC8)	320,1084
C₁₀⋊₃(C₄×C₈) = C₂×C₄×C₅⋊₂C₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₁₀	320	C10:3(C4xC8)	320,547
C₁₀⋊₄(C₄×C₈) = C₂×C₈×Dic₅	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₁₀	320	C10:4(C4xC8)	320,725

Non-split extensions G=N.Q with N=C₁₀ and Q=C₄×C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₄×C₈) = C₁₆×F₅	φ: C₄×C₈/C₈ → C₄ ⊆ Aut C₁₀	80	4	C10.1(C4xC8)	320,181
C₁₀.₂(C₄×C₈) = C₁₆⋊₇F₅	φ: C₄×C₈/C₈ → C₄ ⊆ Aut C₁₀	80	4	C10.2(C4xC8)	320,182
C₁₀.₃(C₄×C₈) = C₂₀.₃₁M₄(2)	φ: C₄×C₈/C₈ → C₄ ⊆ Aut C₁₀	320		C10.3(C4xC8)	320,218
C₁₀.₄(C₄×C₈) = D₁₀.₃M₄(2)	φ: C₄×C₈/C₈ → C₄ ⊆ Aut C₁₀	80		C10.4(C4xC8)	320,230
C₁₀.₅(C₄×C₈) = C₄×C₅⋊C₁₆	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.5(C4xC8)	320,195
C₁₀.₆(C₄×C₈) = C₄².₄F₅	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.6(C4xC8)	320,197
C₁₀.₇(C₄×C₈) = C₈×C₅⋊C₈	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.7(C4xC8)	320,216
C₁₀.₈(C₄×C₈) = C₄₀⋊C₈	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.8(C4xC8)	320,217
C₁₀.₉(C₄×C₈) = Dic₅⋊C₁₆	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.9(C4xC8)	320,223
C₁₀.₁₀(C₄×C₈) = C₄₀.C₈	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.10(C4xC8)	320,224
C₁₀.₁₁(C₄×C₈) = C₁₀.(C₄⋊C₈)	φ: C₄×C₈/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.11(C4xC8)	320,256
C₁₀.₁₂(C₄×C₈) = C₈×C₅⋊₂C₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₁₀	320		C10.12(C4xC8)	320,11
C₁₀.₁₃(C₄×C₈) = C₄₀⋊₈C₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₁₀	320		C10.13(C4xC8)	320,13
C₁₀.₁₄(C₄×C₈) = C₄×C₅⋊₂C₁₆	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₁₀	320		C10.14(C4xC8)	320,18
C₁₀.₁₅(C₄×C₈) = C₄₀.₁₀C₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₁₀	320		C10.15(C4xC8)	320,19
C₁₀.₁₆(C₄×C₈) = (C₂×C₂₀)⋊₈C₈	φ: C₄×C₈/C₄² → C₂ ⊆ Aut C₁₀	320		C10.16(C4xC8)	320,82
C₁₀.₁₇(C₄×C₈) = C₄².₂₇₉D₁₀	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10.17(C4xC8)	320,12
C₁₀.₁₈(C₄×C₈) = C₁₆×Dic₅	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10.18(C4xC8)	320,58
C₁₀.₁₉(C₄×C₈) = C₈₀⋊₁₇C₄	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10.19(C4xC8)	320,60
C₁₀.₂₀(C₄×C₈) = (C₂×C₄₀)⋊₁₅C₄	φ: C₄×C₈/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10.20(C4xC8)	320,108
C₁₀.₂₁(C₄×C₈) = C₅×C₈⋊C₈	central extension (φ=1)	320		C10.21(C4xC8)	320,127
C₁₀.₂₂(C₄×C₈) = C₅×C₂².₇C₄²	central extension (φ=1)	320		C10.22(C4xC8)	320,141
C₁₀.₂₃(C₄×C₈) = C₅×C₁₆⋊₅C₄	central extension (φ=1)	320		C10.23(C4xC8)	320,151

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Extensions 1→N→G→Q→1 with N=C10 and Q=C4×C8

Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₄×C₈