Extensions 1→N→G→Q→1 with N=C₅×C₂₀ and Q=C₂²

Direct product G=N×Q with N=C₅×C₂₀ and Q=C₂²

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

Semidirect products G=N:Q with N=C₅×C₂₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₂₀)⋊₁C₂² = D₅×D₂₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4+	(C5xC20):1C2^2	400,170
(C₅×C₂₀)⋊₂C₂² = C₂₀⋊D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20):2C2^2	400,171
(C₅×C₂₀)⋊₃C₂² = C₅×D₄×D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20):3C2^2	400,185
(C₅×C₂₀)⋊₄C₂² = D₄×C₅⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	100		(C5xC20):4C2^2	400,195
(C₅×C₂₀)⋊₅C₂² = C₄×D₅²	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20):5C2^2	400,169
(C₅×C₂₀)⋊₆C₂² = C₂×C₂₀⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20):6C2^2	400,193
(C₅×C₂₀)⋊₇C₂² = C₁₀×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20):7C2^2	400,183
(C₅×C₂₀)⋊₈C₂² = D₅×C₂×C₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20):8C2^2	400,182
(C₅×C₂₀)⋊₉C₂² = C₂×C₄×C₅⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20):9C2^2	400,192
(C₅×C₂₀)⋊₁₀C₂² = D₄×C₅×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20):10C2^2	400,202

Non-split extensions G=N.Q with N=C₅×C₂₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₂₀).₁C₂² = C₅²⋊₂D₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).1C2^2	400,64
(C₅×C₂₀).₂C₂² = C₅⋊D₄₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4+	(C5xC20).2C2^2	400,65
(C₅×C₂₀).₃C₂² = D₂₀.D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).3C2^2	400,66
(C₅×C₂₀).₄C₂² = C₅²⋊₃SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4-	(C5xC20).4C2^2	400,67
(C₅×C₂₀).₅C₂² = C₅²⋊₄SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4+	(C5xC20).5C2^2	400,68
(C₅×C₂₀).₆C₂² = C₅²⋊₂Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).6C2^2	400,69
(C₅×C₂₀).₇C₂² = C₅²⋊₃Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4-	(C5xC20).7C2^2	400,70
(C₅×C₂₀).₈C₂² = C₅×D₄⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).8C2^2	400,87
(C₅×C₂₀).₉C₂² = C₅×D₄.D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).9C2^2	400,88
(C₅×C₂₀).₁₀C₂² = C₅×Q₈⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).10C2^2	400,89
(C₅×C₂₀).₁₁C₂² = C₅×C₅⋊Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).11C2^2	400,90
(C₅×C₂₀).₁₂C₂² = C₅²⋊₇D₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	200		(C5xC20).12C2^2	400,103
(C₅×C₂₀).₁₃C₂² = C₅²⋊₈SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	200		(C5xC20).13C2^2	400,104
(C₅×C₂₀).₁₄C₂² = C₅²⋊₁₀SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	200		(C5xC20).14C2^2	400,105
(C₅×C₂₀).₁₅C₂² = C₅²⋊₇Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	400		(C5xC20).15C2^2	400,106
(C₅×C₂₀).₁₆C₂² = D₅×Dic₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4-	(C5xC20).16C2^2	400,163
(C₅×C₂₀).₁₇C₂² = D₂₀⋊₅D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4-	(C5xC20).17C2^2	400,164
(C₅×C₂₀).₁₈C₂² = D₂₀⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).18C2^2	400,165
(C₅×C₂₀).₁₉C₂² = Dic₁₀⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).19C2^2	400,166
(C₅×C₂₀).₂₀C₂² = Dic₁₀⋊₅D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4+	(C5xC20).20C2^2	400,168
(C₅×C₂₀).₂₁C₂² = C₅×D₄⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).21C2^2	400,186
(C₅×C₂₀).₂₂C₂² = C₅×Q₈×D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).22C2^2	400,187
(C₅×C₂₀).₂₃C₂² = C₅×Q₈⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).23C2^2	400,188
(C₅×C₂₀).₂₄C₂² = C₂₀.D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	200		(C5xC20).24C2^2	400,196
(C₅×C₂₀).₂₅C₂² = Q₈×C₅⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	200		(C5xC20).25C2^2	400,197
(C₅×C₂₀).₂₆C₂² = C₂₀.₂₆D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	200		(C5xC20).26C2^2	400,198
(C₅×C₂₀).₂₇C₂² = D₅×C₅⋊₂C₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).27C2^2	400,60
(C₅×C₂₀).₂₈C₂² = C₂₀.₂₉D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).28C2^2	400,61
(C₅×C₂₀).₂₉C₂² = C₂₀.₃₀D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	80	4	(C5xC20).29C2^2	400,62
(C₅×C₂₀).₃₀C₂² = C₂₀.₃₁D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).30C2^2	400,63
(C₅×C₂₀).₃₁C₂² = D₁₀.₉D₁₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₂₀	40	4	(C5xC20).31C2^2	400,167
(C₅×C₂₀).₃₂C₂² = C₄₀⋊₂D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).32C2^2	400,94
(C₅×C₂₀).₃₃C₂² = C₅²⋊₅D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).33C2^2	400,95
(C₅×C₂₀).₃₄C₂² = C₄₀.D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).34C2^2	400,96
(C₅×C₂₀).₃₅C₂² = C₂×C₅²⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).35C2^2	400,191
(C₅×C₂₀).₃₆C₂² = C₂₀.₅₀D₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).36C2^2	400,194
(C₅×C₂₀).₃₇C₂² = C₅×C₄₀⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80	2	(C5xC20).37C2^2	400,78
(C₅×C₂₀).₃₈C₂² = C₅×D₄₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80	2	(C5xC20).38C2^2	400,79
(C₅×C₂₀).₃₉C₂² = C₅×Dic₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80	2	(C5xC20).39C2^2	400,80
(C₅×C₂₀).₄₀C₂² = C₁₀×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20).40C2^2	400,181
(C₅×C₂₀).₄₁C₂² = C₅×C₄○D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	40	2	(C5xC20).41C2^2	400,184
(C₅×C₂₀).₄₂C₂² = D₅×C₄₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80	2	(C5xC20).42C2^2	400,76
(C₅×C₂₀).₄₃C₂² = C₅×C₈⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80	2	(C5xC20).43C2^2	400,77
(C₅×C₂₀).₄₄C₂² = C₁₀×C₅⋊₂C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20).44C2^2	400,81
(C₅×C₂₀).₄₅C₂² = C₅×C₄.Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	40	2	(C5xC20).45C2^2	400,82
(C₅×C₂₀).₄₆C₂² = C₈×C₅⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).46C2^2	400,92
(C₅×C₂₀).₄₇C₂² = C₄₀⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).47C2^2	400,93
(C₅×C₂₀).₄₈C₂² = C₂×C₅²⋊₇C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).48C2^2	400,97
(C₅×C₂₀).₄₉C₂² = C₂₀.₅₉D₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).49C2^2	400,98
(C₅×C₂₀).₅₀C₂² = D₈×C₅²	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).50C2^2	400,113
(C₅×C₂₀).₅₁C₂² = SD₁₆×C₅²	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).51C2^2	400,114
(C₅×C₂₀).₅₂C₂² = Q₁₆×C₅²	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).52C2^2	400,115
(C₅×C₂₀).₅₃C₂² = Q₈×C₅×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).53C2^2	400,203
(C₅×C₂₀).₅₄C₂² = M₄(2)×C₅²	central extension (φ=1)	200		(C5xC20).54C2^2	400,112
(C₅×C₂₀).₅₅C₂² = C₄○D₄×C₅²	central extension (φ=1)	200		(C5xC20).55C2^2	400,204

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Extensions 1→N→G→Q→1 with N=C5×C20 and Q=C22

Extensions 1→N→G→Q→1 with N=C₅×C₂₀ and Q=C₂²