Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂×C₁₀

Direct product G=N×Q with N=C₂₀ and Q=C₂×C₁₀

		d	ρ	Label	ID
C₂×C₁₀×C₂₀		400		C2xC10xC20	400,201

Semidirect products G=N:Q with N=C₂₀ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊(C₂×C₁₀) = C₅×D₄×D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	40	4	C20:(C2xC10)	400,185
C₂₀⋊₂(C₂×C₁₀) = C₁₀×D₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80		C20:2(C2xC10)	400,183
C₂₀⋊₃(C₂×C₁₀) = D₅×C₂×C₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80		C20:3(C2xC10)	400,182
C₂₀⋊₄(C₂×C₁₀) = D₄×C₅×C₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200		C20:4(C2xC10)	400,202

Non-split extensions G=N.Q with N=C₂₀ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁(C₂×C₁₀) = C₅×D₄⋊D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	40	4	C20.1(C2xC10)	400,87
C₂₀.₂(C₂×C₁₀) = C₅×D₄.D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	40	4	C20.2(C2xC10)	400,88
C₂₀.₃(C₂×C₁₀) = C₅×Q₈⋊D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	80	4	C20.3(C2xC10)	400,89
C₂₀.₄(C₂×C₁₀) = C₅×C₅⋊Q₁₆	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	80	4	C20.4(C2xC10)	400,90
C₂₀.₅(C₂×C₁₀) = C₅×D₄⋊₂D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	40	4	C20.5(C2xC10)	400,186
C₂₀.₆(C₂×C₁₀) = C₅×Q₈×D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	80	4	C20.6(C2xC10)	400,187
C₂₀.₇(C₂×C₁₀) = C₅×Q₈⋊₂D₅	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂₀	80	4	C20.7(C2xC10)	400,188
C₂₀.₈(C₂×C₁₀) = C₅×C₄₀⋊C₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80	2	C20.8(C2xC10)	400,78
C₂₀.₉(C₂×C₁₀) = C₅×D₄₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80	2	C20.9(C2xC10)	400,79
C₂₀.₁₀(C₂×C₁₀) = C₅×Dic₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80	2	C20.10(C2xC10)	400,80
C₂₀.₁₁(C₂×C₁₀) = C₁₀×Dic₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80		C20.11(C2xC10)	400,181
C₂₀.₁₂(C₂×C₁₀) = C₅×C₄○D₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	40	2	C20.12(C2xC10)	400,184
C₂₀.₁₃(C₂×C₁₀) = D₅×C₄₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80	2	C20.13(C2xC10)	400,76
C₂₀.₁₄(C₂×C₁₀) = C₅×C₈⋊D₅	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80	2	C20.14(C2xC10)	400,77
C₂₀.₁₅(C₂×C₁₀) = C₁₀×C₅⋊₂C₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	80		C20.15(C2xC10)	400,81
C₂₀.₁₆(C₂×C₁₀) = C₅×C₄.Dic₅	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	40	2	C20.16(C2xC10)	400,82
C₂₀.₁₇(C₂×C₁₀) = D₈×C₂₅	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200	2	C20.17(C2xC10)	400,25
C₂₀.₁₈(C₂×C₁₀) = SD₁₆×C₂₅	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200	2	C20.18(C2xC10)	400,26
C₂₀.₁₉(C₂×C₁₀) = Q₁₆×C₂₅	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	400	2	C20.19(C2xC10)	400,27
C₂₀.₂₀(C₂×C₁₀) = D₄×C₅₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200		C20.20(C2xC10)	400,46
C₂₀.₂₁(C₂×C₁₀) = Q₈×C₅₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	400		C20.21(C2xC10)	400,47
C₂₀.₂₂(C₂×C₁₀) = C₄○D₄×C₂₅	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200	2	C20.22(C2xC10)	400,48
C₂₀.₂₃(C₂×C₁₀) = D₈×C₅²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200		C20.23(C2xC10)	400,113
C₂₀.₂₄(C₂×C₁₀) = SD₁₆×C₅²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200		C20.24(C2xC10)	400,114
C₂₀.₂₅(C₂×C₁₀) = Q₁₆×C₅²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	400		C20.25(C2xC10)	400,115
C₂₀.₂₆(C₂×C₁₀) = Q₈×C₅×C₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	400		C20.26(C2xC10)	400,203
C₂₀.₂₇(C₂×C₁₀) = C₄○D₄×C₅²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂₀	200		C20.27(C2xC10)	400,204
C₂₀.₂₈(C₂×C₁₀) = M₄(2)×C₂₅	central extension (φ=1)	200	2	C20.28(C2xC10)	400,24
C₂₀.₂₉(C₂×C₁₀) = M₄(2)×C₅²	central extension (φ=1)	200		C20.29(C2xC10)	400,112

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Extensions 1→N→G→Q→1 with N=C20 and Q=C2×C10

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂×C₁₀