Extensions 1→N→G→Q→1 with N=C₅×C₁₀ and Q=C₂³

Direct product G=N×Q with N=C₅×C₁₀ and Q=C₂³

		d	ρ	Label	ID
C₂²×C₁₀²		400		C2^2xC10^2	400,221

Semidirect products G=N:Q with N=C₅×C₁₀ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
(C₅×C₁₀)⋊C₂³ = C₂²×D₅²	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	(C5xC10):C2^3	400,218
(C₅×C₁₀)⋊₂C₂³ = D₅×C₂²×C₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80	(C5xC10):2C2^3	400,219
(C₅×C₁₀)⋊₃C₂³ = C₂³×C₅⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200	(C5xC10):3C2^3	400,220

Non-split extensions G=N.Q with N=C₅×C₁₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀).₁C₂³ = D₅×Dic₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	80	4-	(C5xC10).1C2^3	400,163
(C₅×C₁₀).₂C₂³ = D₂₀⋊₅D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	80	4-	(C5xC10).2C2^3	400,164
(C₅×C₁₀).₃C₂³ = D₂₀⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).3C2^3	400,165
(C₅×C₁₀).₄C₂³ = Dic₁₀⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).4C2^3	400,166
(C₅×C₁₀).₅C₂³ = D₁₀.₉D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).5C2^3	400,167
(C₅×C₁₀).₆C₂³ = Dic₁₀⋊₅D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4+	(C5xC10).6C2^3	400,168
(C₅×C₁₀).₇C₂³ = C₄×D₅²	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).7C2^3	400,169
(C₅×C₁₀).₈C₂³ = D₅×D₂₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4+	(C5xC10).8C2^3	400,170
(C₅×C₁₀).₉C₂³ = C₂₀⋊D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).9C2^3	400,171
(C₅×C₁₀).₁₀C₂³ = C₂×D₅×Dic₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	80		(C5xC10).10C2^3	400,172
(C₅×C₁₀).₁₁C₂³ = Dic₅.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).11C2^3	400,173
(C₅×C₁₀).₁₂C₂³ = D₁₀.₄D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4-	(C5xC10).12C2^3	400,174
(C₅×C₁₀).₁₃C₂³ = C₂×Dic₅⋊₂D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40		(C5xC10).13C2^3	400,175
(C₅×C₁₀).₁₄C₂³ = C₂×C₅²⋊₂D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	80		(C5xC10).14C2^3	400,176
(C₅×C₁₀).₁₅C₂³ = C₂×C₅⋊D₂₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40		(C5xC10).15C2^3	400,177
(C₅×C₁₀).₁₆C₂³ = C₂×C₅²⋊₂Q₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	80		(C5xC10).16C2^3	400,178
(C₅×C₁₀).₁₇C₂³ = D₅×C₅⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	40	4	(C5xC10).17C2^3	400,179
(C₅×C₁₀).₁₈C₂³ = D₁₀⋊D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₅×C₁₀	20	4+	(C5xC10).18C2^3	400,180
(C₅×C₁₀).₁₉C₂³ = C₁₀×Dic₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80		(C5xC10).19C2^3	400,181
(C₅×C₁₀).₂₀C₂³ = D₅×C₂×C₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80		(C5xC10).20C2^3	400,182
(C₅×C₁₀).₂₁C₂³ = C₁₀×D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80		(C5xC10).21C2^3	400,183
(C₅×C₁₀).₂₂C₂³ = C₅×C₄○D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	40	2	(C5xC10).22C2^3	400,184
(C₅×C₁₀).₂₃C₂³ = C₅×D₄×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	40	4	(C5xC10).23C2^3	400,185
(C₅×C₁₀).₂₄C₂³ = C₅×D₄⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	40	4	(C5xC10).24C2^3	400,186
(C₅×C₁₀).₂₅C₂³ = C₅×Q₈×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80	4	(C5xC10).25C2^3	400,187
(C₅×C₁₀).₂₆C₂³ = C₅×Q₈⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80	4	(C5xC10).26C2^3	400,188
(C₅×C₁₀).₂₇C₂³ = Dic₅×C₂×C₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	80		(C5xC10).27C2^3	400,189
(C₅×C₁₀).₂₈C₂³ = C₁₀×C₅⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	40		(C5xC10).28C2^3	400,190
(C₅×C₁₀).₂₉C₂³ = C₂×C₅²⋊₄Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	400		(C5xC10).29C2^3	400,191
(C₅×C₁₀).₃₀C₂³ = C₂×C₄×C₅⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).30C2^3	400,192
(C₅×C₁₀).₃₁C₂³ = C₂×C₂₀⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).31C2^3	400,193
(C₅×C₁₀).₃₂C₂³ = C₂₀.₅₀D₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).32C2^3	400,194
(C₅×C₁₀).₃₃C₂³ = D₄×C₅⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10).33C2^3	400,195
(C₅×C₁₀).₃₄C₂³ = C₂₀.D₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).34C2^3	400,196
(C₅×C₁₀).₃₅C₂³ = Q₈×C₅⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).35C2^3	400,197
(C₅×C₁₀).₃₆C₂³ = C₂₀.₂₆D₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).36C2^3	400,198
(C₅×C₁₀).₃₇C₂³ = C₂²×C₅²⋊₆C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	400		(C5xC10).37C2^3	400,199
(C₅×C₁₀).₃₈C₂³ = C₂×C₅²⋊₇D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).38C2^3	400,200
(C₅×C₁₀).₃₉C₂³ = D₄×C₅×C₁₀	central extension (φ=1)	200		(C5xC10).39C2^3	400,202
(C₅×C₁₀).₄₀C₂³ = Q₈×C₅×C₁₀	central extension (φ=1)	400		(C5xC10).40C2^3	400,203
(C₅×C₁₀).₄₁C₂³ = C₄○D₄×C₅²	central extension (φ=1)	200		(C5xC10).41C2^3	400,204

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Extensions 1→N→G→Q→1 with N=C5×C10 and Q=C23

Extensions 1→N→G→Q→1 with N=C₅×C₁₀ and Q=C₂³