Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂³

Direct product G=N×Q with N=C₂₀ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₂₀		160		C2^3xC20	160,228

Semidirect products G=N:Q with N=C₂₀ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
C₂₀⋊C₂³ = C₂×D₄×D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	C20:C2^3	160,217
C₂₀⋊₂C₂³ = C₂²×D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	C20:2C2^3	160,215
C₂₀⋊₃C₂³ = D₅×C₂²×C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	C20:3C2^3	160,214
C₂₀⋊₄C₂³ = D₄×C₂×C₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	C20:4C2^3	160,229

Non-split extensions G=N.Q with N=C₂₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁C₂³ = D₅×D₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4+	C20.1C2^3	160,131
C₂₀.₂C₂³ = D₈⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.2C2^3	160,132
C₂₀.₃C₂³ = D₈⋊₃D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.3C2^3	160,133
C₂₀.₄C₂³ = D₅×SD₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.4C2^3	160,134
C₂₀.₅C₂³ = D₄₀⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4+	C20.5C2^3	160,135
C₂₀.₆C₂³ = SD₁₆⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.6C2^3	160,136
C₂₀.₇C₂³ = SD₁₆⋊₃D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.7C2^3	160,137
C₂₀.₈C₂³ = D₅×Q₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.8C2^3	160,138
C₂₀.₉C₂³ = Q₁₆⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.9C2^3	160,139
C₂₀.₁₀C₂³ = Q₈.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4+	C20.10C2^3	160,140
C₂₀.₁₁C₂³ = C₂×D₄⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80		C20.11C2^3	160,152
C₂₀.₁₂C₂³ = D₄.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.12C2^3	160,153
C₂₀.₁₃C₂³ = C₂×D₄.D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80		C20.13C2^3	160,154
C₂₀.₁₄C₂³ = C₂×Q₈⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80		C20.14C2^3	160,162
C₂₀.₁₅C₂³ = C₂₀.C₂³	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.15C2^3	160,163
C₂₀.₁₆C₂³ = C₂×C₅⋊Q₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	160		C20.16C2^3	160,164
C₂₀.₁₇C₂³ = D₄⋊D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4+	C20.17C2^3	160,170
C₂₀.₁₈C₂³ = D₄.₈D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.18C2^3	160,171
C₂₀.₁₉C₂³ = D₄.₉D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.19C2^3	160,172
C₂₀.₂₀C₂³ = C₂×D₄⋊₂D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80		C20.20C2^3	160,218
C₂₀.₂₁C₂³ = D₄⋊₆D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.21C2^3	160,219
C₂₀.₂₂C₂³ = C₂×Q₈×D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80		C20.22C2^3	160,220
C₂₀.₂₃C₂³ = C₂×Q₈⋊₂D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80		C20.23C2^3	160,221
C₂₀.₂₄C₂³ = Q₈.₁₀D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.24C2^3	160,222
C₂₀.₂₅C₂³ = D₅×C₄○D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.25C2^3	160,223
C₂₀.₂₆C₂³ = D₄⋊₈D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	40	4+	C20.26C2^3	160,224
C₂₀.₂₇C₂³ = D₄.₁₀D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.27C2^3	160,225
C₂₀.₂₈C₂³ = C₂×C₄₀⋊C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.28C2^3	160,123
C₂₀.₂₉C₂³ = C₂×D₄₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.29C2^3	160,124
C₂₀.₃₀C₂³ = D₄₀⋊₇C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	2	C20.30C2^3	160,125
C₂₀.₃₁C₂³ = C₂×Dic₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	160		C20.31C2^3	160,126
C₂₀.₃₂C₂³ = C₈⋊D₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	40	4+	C20.32C2^3	160,129
C₂₀.₃₃C₂³ = C₈.D₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	4-	C20.33C2^3	160,130
C₂₀.₃₄C₂³ = C₂²×Dic₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	160		C20.34C2^3	160,213
C₂₀.₃₅C₂³ = D₅×C₂×C₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.35C2^3	160,120
C₂₀.₃₆C₂³ = C₂×C₈⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.36C2^3	160,121
C₂₀.₃₇C₂³ = D₂₀.₃C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	2	C20.37C2^3	160,122
C₂₀.₃₈C₂³ = D₅×M₄(2)	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.38C2^3	160,127
C₂₀.₃₉C₂³ = D₂₀.₂C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.39C2^3	160,128
C₂₀.₄₀C₂³ = C₂²×C₅⋊₂C₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	160		C20.40C2^3	160,141
C₂₀.₄₁C₂³ = C₂×C₄.Dic₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.41C2^3	160,142
C₂₀.₄₂C₂³ = D₄.Dic₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.42C2^3	160,169
C₂₀.₄₃C₂³ = C₂×C₄○D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.43C2^3	160,216
C₂₀.₄₄C₂³ = C₁₀×D₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.44C2^3	160,193
C₂₀.₄₅C₂³ = C₁₀×SD₁₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80		C20.45C2^3	160,194
C₂₀.₄₆C₂³ = C₁₀×Q₁₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	160		C20.46C2^3	160,195
C₂₀.₄₇C₂³ = C₅×C₄○D₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	2	C20.47C2^3	160,196
C₂₀.₄₈C₂³ = C₅×C₈⋊C₂²	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.48C2^3	160,197
C₂₀.₄₉C₂³ = C₅×C₈.C₂²	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.49C2^3	160,198
C₂₀.₅₀C₂³ = Q₈×C₂×C₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	160		C20.50C2^3	160,230
C₂₀.₅₁C₂³ = C₅×2₊¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.51C2^3	160,232
C₂₀.₅₂C₂³ = C₅×2_-¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.52C2^3	160,233
C₂₀.₅₃C₂³ = C₁₀×M₄(2)	central extension (φ=1)	80		C20.53C2^3	160,191
C₂₀.₅₄C₂³ = C₅×C₈○D₄	central extension (φ=1)	80	2	C20.54C2^3	160,192
C₂₀.₅₅C₂³ = C₁₀×C₄○D₄	central extension (φ=1)	80		C20.55C2^3	160,231

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Extensions 1→N→G→Q→1 with N=C20 and Q=C23

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂³