Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂×C₅₀

Direct product G=N×Q with N=C₄ and Q=C₂×C₅₀

		d	ρ	Label	ID
C₂²×C₁₀₀		400		C2^2xC100	400,45

Semidirect products G=N:Q with N=C₄ and Q=C₂×C₅₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂×C₅₀) = D₄×C₅₀	φ: C₂×C₅₀/C₅₀ → C₂ ⊆ Aut C₄	200		C4:(C2xC50)	400,46

Non-split extensions G=N.Q with N=C₄ and Q=C₂×C₅₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×C₅₀) = D₈×C₂₅	φ: C₂×C₅₀/C₅₀ → C₂ ⊆ Aut C₄	200	2	C4.1(C2xC50)	400,25
C₄.₂(C₂×C₅₀) = SD₁₆×C₂₅	φ: C₂×C₅₀/C₅₀ → C₂ ⊆ Aut C₄	200	2	C4.2(C2xC50)	400,26
C₄.₃(C₂×C₅₀) = Q₁₆×C₂₅	φ: C₂×C₅₀/C₅₀ → C₂ ⊆ Aut C₄	400	2	C4.3(C2xC50)	400,27
C₄.₄(C₂×C₅₀) = Q₈×C₅₀	φ: C₂×C₅₀/C₅₀ → C₂ ⊆ Aut C₄	400		C4.4(C2xC50)	400,47
C₄.₅(C₂×C₅₀) = M₄(2)×C₂₅	central extension (φ=1)	200	2	C4.5(C2xC50)	400,24
C₄.₆(C₂×C₅₀) = C₄○D₄×C₂₅	central extension (φ=1)	200	2	C4.6(C2xC50)	400,48

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