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

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

		d	ρ	Label	ID
D₄×C₂₀		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 = C₄×D₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	C20:5D4	160,94
C₂₀⋊₆D₄ = C₅×C₄⋊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 = C₄×C₅⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	C20:8D4	160,149
C₂₀⋊₉D₄ = C₅×C₄⋊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 = C₂×D₄⋊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 = C₂×D₄.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 = C₂×Q₈⋊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 = C₂×C₅⋊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 = C₂×C₄₀⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.29D4	160,123
C₂₀.₃₀D₄ = C₂×D₄₀	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.30D4	160,124
C₂₀.₃₁D₄ = C₂×Dic₂₀	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 = C₅×D₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.36D4	160,61
C₂₀.₃₇D₄ = C₅×SD₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80	2	C20.37D4	160,62
C₂₀.₃₈D₄ = C₅×Q₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160	2	C20.38D4	160,63
C₂₀.₃₉D₄ = C₅×C₄.₄D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.39D4	160,185
C₂₀.₄₀D₄ = C₅×C₄⋊Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	160		C20.40D4	160,189
C₂₀.₄₁D₄ = C₁₀×D₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.41D4	160,193
C₂₀.₄₂D₄ = C₁₀×SD₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₂₀	80		C20.42D4	160,194
C₂₀.₄₃D₄ = C₁₀×Q₁₆	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 = C₅×C₄.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.58D4	160,50
C₂₀.₅₉D₄ = C₅×C₄.₁₀D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.59D4	160,51
C₂₀.₆₀D₄ = C₅×D₄⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.60D4	160,52
C₂₀.₆₁D₄ = C₅×Q₈⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	160		C20.61D4	160,53
C₂₀.₆₂D₄ = C₅×C₂²⋊Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80		C20.62D4	160,183
C₂₀.₆₃D₄ = C₅×C₈⋊C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	40	4	C20.63D4	160,197
C₂₀.₆₄D₄ = C₅×C₈.C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₂₀	80	4	C20.64D4	160,198
C₂₀.₆₅D₄ = C₅×C₂²⋊C₈	central extension (φ=1)	80		C20.65D4	160,48
C₂₀.₆₆D₄ = C₅×C₄≀C₂	central extension (φ=1)	40	2	C20.66D4	160,54
C₂₀.₆₇D₄ = C₅×C₄⋊C₈	central extension (φ=1)	160		C20.67D4	160,55
C₂₀.₆₈D₄ = C₅×C₈.C₄	central extension (φ=1)	80	2	C20.68D4	160,58
C₂₀.₆₉D₄ = C₅×C₄○D₈	central extension (φ=1)	80	2	C20.69D4	160,196

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

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