Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₄

Direct product G=NxQ with N=C₂₀ and Q=D₄

		d	ρ	Label	ID
D₄xC₂₀		80		D4xC20	160,179

Semidirect products G=N:Q with N=C₂₀ and Q=D₄

extension	φ:Q→Aut N	d	Label	ID
C₂₀:₁D₄ = C₄:D₂₀	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	C20:1D4	160,116
C₂₀:₂D₄ = C₂₀:₂D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	C20:2D4	160,159
C₂₀:₃D₄ = C₂₀:D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	C20:3D4	160,161
C₂₀:₄D₄ = C₂₀:₄D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	C20:4D4	160,95
C₂₀:₅D₄ = C₄xD₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	C20:5D4	160,94
C₂₀:₆D₄ = C₅xC₄:₁D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	C20:6D4	160,188
C₂₀:₇D₄ = C₂₀:₇D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	C20:7D4	160,151
C₂₀:₈D₄ = C₄xC₅:D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	C20:8D4	160,149
C₂₀:₉D₄ = C₅xC₄:D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	C20:9D4	160,182

Non-split extensions G=N.Q with N=C₂₀ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁D₄ = D₂₀:₆C₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.1D4	160,16
C₂₀.₂D₄ = C₁₀.Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	160		C20.2D4	160,17
C₂₀.₃D₄ = C₅:D₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	4+	C20.3D4	160,33
C₂₀.₄D₄ = D₈.D₅	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.4D4	160,34
C₂₀.₅D₄ = C₅:SD₃₂	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	4+	C20.5D4	160,35
C₂₀.₆D₄ = C₅:Q₃₂	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	160	4-	C20.6D4	160,36
C₂₀.₇D₄ = D₄:Dic₅	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.7D4	160,39
C₂₀.₈D₄ = C₂₀.D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.8D4	160,40
C₂₀.₉D₄ = Q₈:Dic₅	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	160		C20.9D4	160,42
C₂₀.₁₀D₄ = C₂₀.₁₀D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.10D4	160,43
C₂₀.₁₁D₄ = D₁₀:₂Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.11D4	160,118
C₂₀.₁₂D₄ = C₈:D₁₀	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	40	4+	C20.12D4	160,129
C₂₀.₁₃D₄ = C₈.D₁₀	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	4-	C20.13D4	160,130
C₂₀.₁₄D₄ = C₂xD₄:D₅	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.14D4	160,152
C₂₀.₁₅D₄ = D₄.D₁₀	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	40	4	C20.15D4	160,153
C₂₀.₁₆D₄ = C₂xD₄.D₅	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.16D4	160,154
C₂₀.₁₇D₄ = C₂₀.₁₇D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.17D4	160,157
C₂₀.₁₈D₄ = C₂xQ₈:D₅	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.18D4	160,162
C₂₀.₁₉D₄ = C₂₀.C₂³	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80	4	C20.19D4	160,163
C₂₀.₂₀D₄ = C₂xC₅:Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	160		C20.20D4	160,164
C₂₀.₂₁D₄ = Dic₅:Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	160		C20.21D4	160,165
C₂₀.₂₂D₄ = D₁₀:₃Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.22D4	160,167
C₂₀.₂₃D₄ = C₂₀.₂₃D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₂₀	80		C20.23D4	160,168
C₂₀.₂₄D₄ = D₈₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2+	C20.24D4	160,6
C₂₀.₂₅D₄ = C₁₆:D₅	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.25D4	160,7
C₂₀.₂₆D₄ = Dic₄₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160	2-	C20.26D4	160,8
C₂₀.₂₇D₄ = C₂₀:₂Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160		C20.27D4	160,90
C₂₀.₂₈D₄ = C₄.D₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.28D4	160,96
C₂₀.₂₉D₄ = C₂xC₄₀:C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.29D4	160,123
C₂₀.₃₀D₄ = C₂xD₄₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.30D4	160,124
C₂₀.₃₁D₄ = C₂xDic₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160		C20.31D4	160,126
C₂₀.₃₂D₄ = C₂₀:₃C₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160		C20.32D4	160,11
C₂₀.₃₃D₄ = D₂₀:₄C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	40	2	C20.33D4	160,12
C₂₀.₃₄D₄ = C₄₀.₆C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.34D4	160,26
C₂₀.₃₅D₄ = D₄₀:₇C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.35D4	160,125
C₂₀.₃₆D₄ = C₅xD₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.36D4	160,61
C₂₀.₃₇D₄ = C₅xSD₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.37D4	160,62
C₂₀.₃₈D₄ = C₅xQ₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160	2	C20.38D4	160,63
C₂₀.₃₉D₄ = C₅xC₄.₄D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.39D4	160,185
C₂₀.₄₀D₄ = C₅xC₄:Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160		C20.40D4	160,189
C₂₀.₄₁D₄ = C₁₀xD₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.41D4	160,193
C₂₀.₄₂D₄ = C₁₀xSD₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.42D4	160,194
C₂₀.₄₃D₄ = C₁₀xQ₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160		C20.43D4	160,195
C₂₀.₄₄D₄ = C₂₀.₄₄D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	160		C20.44D4	160,23
C₂₀.₄₅D₄ = D₂₀:₅C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.45D4	160,28
C₂₀.₄₆D₄ = C₂₀.₄₆D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4+	C20.46D4	160,30
C₂₀.₄₇D₄ = C₄.₁₂D₂₀	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4-	C20.47D4	160,31
C₂₀.₄₈D₄ = C₂₀.₄₈D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.48D4	160,145
C₂₀.₄₉D₄ = D₄:D₁₀	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4+	C20.49D4	160,170
C₂₀.₅₀D₄ = D₄.₉D₁₀	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4-	C20.50D4	160,172
C₂₀.₅₁D₄ = C₂₀.₈Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	160		C20.51D4	160,21
C₂₀.₅₂D₄ = D₁₀:₁C₈	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.52D4	160,27
C₂₀.₅₃D₄ = C₂₀.₅₃D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.53D4	160,29
C₂₀.₅₄D₄ = D₂₀:₇C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.54D4	160,32
C₂₀.₅₅D₄ = C₂₀.₅₅D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.55D4	160,37
C₂₀.₅₆D₄ = D₄:₂Dic₅	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.56D4	160,44
C₂₀.₅₇D₄ = D₄.₈D₁₀	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.57D4	160,171
C₂₀.₅₈D₄ = C₅xC₄.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.58D4	160,50
C₂₀.₅₉D₄ = C₅xC₄.₁₀D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.59D4	160,51
C₂₀.₆₀D₄ = C₅xD₄:C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.60D4	160,52
C₂₀.₆₁D₄ = C₅xQ₈:C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	160		C20.61D4	160,53
C₂₀.₆₂D₄ = C₅xC₂²:Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.62D4	160,183
C₂₀.₆₃D₄ = C₅xC₈:C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.63D4	160,197
C₂₀.₆₄D₄ = C₅xC₈.C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.64D4	160,198
C₂₀.₆₅D₄ = C₅xC₂²:C₈	central extension (φ=1)	80		C20.65D4	160,48
C₂₀.₆₆D₄ = C₅xC₄wrC₂	central extension (φ=1)	40	2	C20.66D4	160,54
C₂₀.₆₇D₄ = C₅xC₄:C₈	central extension (φ=1)	160		C20.67D4	160,55
C₂₀.₆₈D₄ = C₅xC₈.C₄	central extension (φ=1)	80	2	C20.68D4	160,58
C₂₀.₆₉D₄ = C₅xC₄oD₈	central extension (φ=1)	80	2	C20.69D4	160,196

Extensions 1→N→G→Q→1 with N=C20 and Q=D4

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₄