Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₄≀C₂

Direct product G=N×Q with N=C₁₀ and Q=C₄≀C₂

		d	ρ	Label	ID
C₁₀×C₄≀C₂		80		C10xC4wrC2	320,921

Semidirect products G=N:Q with N=C₁₀ and Q=C₄≀C₂

extension	φ:Q→Aut N	d	Label	ID
C₁₀⋊₁C₄≀C₂ = C₂×D₄⋊F₅	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	80	C10:1C4wrC2	320,1106
C₁₀⋊₂C₄≀C₂ = C₂×Q₈⋊₂F₅	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	80	C10:2C4wrC2	320,1121
C₁₀⋊₃C₄≀C₂ = C₂×D₂₀⋊₄C₄	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	80	C10:3C4wrC2	320,554
C₁₀⋊₄C₄≀C₂ = C₂×D₂₀⋊₇C₄	φ: C₄≀C₂/M₄(2) → C₂ ⊆ Aut C₁₀	80	C10:4C4wrC2	320,765
C₁₀⋊₅C₄≀C₂ = C₂×D₄⋊₂Dic₅	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	80	C10:5C4wrC2	320,862

Non-split extensions G=N.Q with N=C₁₀ and Q=C₄≀C₂

extension	φ:Q→Aut N	d	Label	ID
C₁₀.₁C₄≀C₂ = D₁₀.₁Q₁₆	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	80	C10.1C4wrC2	320,207
C₁₀.₂C₄≀C₂ = C₁₀.C₄≀C₂	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	320	C10.2C4wrC2	320,208
C₁₀.₃C₄≀C₂ = Dic₁₀⋊₁C₈	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	320	C10.3C4wrC2	320,210
C₁₀.₄C₄≀C₂ = D₁₀.SD₁₆	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	80	C10.4C4wrC2	320,258
C₁₀.₅C₄≀C₂ = (C₂×D₄).F₅	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	160	C10.5C4wrC2	320,259
C₁₀.₆C₄≀C₂ = Dic₅.₂₃D₈	φ: C₄≀C₂/D₄ → C₄ ⊆ Aut C₁₀	160	C10.6C4wrC2	320,262
C₁₀.₇C₄≀C₂ = D₁₀.₁D₈	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	80	C10.7C4wrC2	320,206
C₁₀.₈C₄≀C₂ = D₂₀⋊C₈	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	160	C10.8C4wrC2	320,209
C₁₀.₉C₄≀C₂ = C₂₀.C₄²	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	80	C10.9C4wrC2	320,213
C₁₀.₁₀C₄≀C₂ = D₁₀.Q₁₆	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	80	C10.10C4wrC2	320,264
C₁₀.₁₁C₄≀C₂ = (C₂×Q₈).F₅	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	160	C10.11C4wrC2	320,265
C₁₀.₁₂C₄≀C₂ = Dic₅.₁₂Q₁₆	φ: C₄≀C₂/Q₈ → C₄ ⊆ Aut C₁₀	320	C10.12C4wrC2	320,268
C₁₀.₁₃C₄≀C₂ = (C₂×D₂₀)⋊C₄	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	80	C10.13C4wrC2	320,9
C₁₀.₁₄C₄≀C₂ = C₄⋊Dic₅⋊C₄	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	80	C10.14C4wrC2	320,10
C₁₀.₁₅C₄≀C₂ = Dic₁₀⋊₃C₈	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	320	C10.15C4wrC2	320,14
C₁₀.₁₆C₄≀C₂ = D₂₀⋊₃C₈	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	160	C10.16C4wrC2	320,17
C₁₀.₁₇C₄≀C₂ = C₄².D₁₀	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	160	C10.17C4wrC2	320,22
C₁₀.₁₈C₄≀C₂ = C₄².₂D₁₀	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	320	C10.18C4wrC2	320,23
C₁₀.₁₉C₄≀C₂ = C₄²⋊₆Dic₅	φ: C₄≀C₂/C₄² → C₂ ⊆ Aut C₁₀	80	C10.19C4wrC2	320,81
C₁₀.₂₀C₄≀C₂ = C₂³.₃₀D₂₀	φ: C₄≀C₂/M₄(2) → C₂ ⊆ Aut C₁₀	80	C10.20C4wrC2	320,25
C₁₀.₂₁C₄≀C₂ = C₂².₂D₄₀	φ: C₄≀C₂/M₄(2) → C₂ ⊆ Aut C₁₀	80	C10.21C4wrC2	320,28
C₁₀.₂₂C₄≀C₂ = D₂₀⋊₄C₈	φ: C₄≀C₂/M₄(2) → C₂ ⊆ Aut C₁₀	160	C10.22C4wrC2	320,41
C₁₀.₂₃C₄≀C₂ = Dic₁₀⋊₄C₈	φ: C₄≀C₂/M₄(2) → C₂ ⊆ Aut C₁₀	320	C10.23C4wrC2	320,42
C₁₀.₂₄C₄≀C₂ = C₂₀.₃₃C₄²	φ: C₄≀C₂/M₄(2) → C₂ ⊆ Aut C₁₀	80	C10.24C4wrC2	320,113
C₁₀.₂₅C₄≀C₂ = C₂₀.₃₂C₄²	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	80	C10.25C4wrC2	320,90
C₁₀.₂₆C₄≀C₂ = C₂₀.₅₇D₈	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	160	C10.26C4wrC2	320,92
C₁₀.₂₇C₄≀C₂ = C₂₀.₂₆Q₁₆	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	320	C10.27C4wrC2	320,93
C₁₀.₂₈C₄≀C₂ = C₄⋊C₄⋊Dic₅	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	80	C10.28C4wrC2	320,95
C₁₀.₂₉C₄≀C₂ = C₁₀.₂₉C₄≀C₂	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	80	C10.29C4wrC2	320,96
C₁₀.₃₀C₄≀C₂ = C₄².₇D₁₀	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	160	C10.30C4wrC2	320,98
C₁₀.₃₁C₄≀C₂ = C₄².₈D₁₀	φ: C₄≀C₂/C₄○D₄ → C₂ ⊆ Aut C₁₀	320	C10.31C4wrC2	320,101
C₁₀.₃₂C₄≀C₂ = C₅×D₄⋊C₈	central extension (φ=1)	160	C10.32C4wrC2	320,130
C₁₀.₃₃C₄≀C₂ = C₅×Q₈⋊C₈	central extension (φ=1)	320	C10.33C4wrC2	320,131
C₁₀.₃₄C₄≀C₂ = C₅×C₂².SD₁₆	central extension (φ=1)	80	C10.34C4wrC2	320,132
C₁₀.₃₅C₄≀C₂ = C₅×C₂³.₃₁D₄	central extension (φ=1)	80	C10.35C4wrC2	320,133
C₁₀.₃₆C₄≀C₂ = C₅×C₄².C₂²	central extension (φ=1)	160	C10.36C4wrC2	320,134
C₁₀.₃₇C₄≀C₂ = C₅×C₄².₂C₂²	central extension (φ=1)	320	C10.37C4wrC2	320,135
C₁₀.₃₈C₄≀C₂ = C₅×C₄²⋊₆C₄	central extension (φ=1)	80	C10.38C4wrC2	320,144

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Extensions 1→N→G→Q→1 with N=C10 and Q=C4≀C2

Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₄≀C₂