Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₈

Direct product G=N×Q with N=C₂₀ and Q=D₈

		d	ρ	Label	ID
D₈×C₂₀		160		D8xC20	320,938

Semidirect products G=N:Q with N=C₂₀ and Q=D₈

extension	φ:Q→Aut N	d	Label	ID
C₂₀⋊₁D₈ = C₄⋊D₄₀	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	C20:1D8	320,470
C₂₀⋊₂D₈ = C₂₀⋊₂D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	C20:2D8	320,699
C₂₀⋊₃D₈ = C₂₀⋊D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	C20:3D8	320,700
C₂₀⋊₄D₈ = C₂₀⋊₄D₈	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	C20:4D8	320,322
C₂₀⋊₅D₈ = C₄×D₄₀	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	C20:5D8	320,319
C₂₀⋊₆D₈ = C₅×C₈⋊₄D₄	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	C20:6D8	320,994
C₂₀⋊₇D₈ = C₂₀⋊₇D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	C20:7D8	320,642
C₂₀⋊₈D₈ = C₄×D₄⋊D₅	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	C20:8D8	320,640
C₂₀⋊₉D₈ = C₅×C₄⋊D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	C20:9D8	320,960

Non-split extensions G=N.Q with N=C₂₀ and Q=D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁D₈ = C₄.D₄₀	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.1D8	320,43
C₂₀.₂D₈ = C₂₀.₂D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	320		C20.2D8	320,44
C₂₀.₃D₈ = D₄₀.₄C₄	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	80	4+	C20.3D8	320,74
C₂₀.₄D₈ = C₂₀.₄D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4-	C20.4D8	320,75
C₂₀.₅D₈ = C₅⋊D₃₂	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4+	C20.5D8	320,77
C₂₀.₆D₈ = D₁₆.D₅	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4-	C20.6D8	320,78
C₂₀.₇D₈ = C₅⋊SD₆₄	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4+	C20.7D8	320,79
C₂₀.₈D₈ = C₅⋊Q₆₄	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	320	4-	C20.8D8	320,80
C₂₀.₉D₈ = C₂₀.₉D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.9D8	320,102
C₂₀.₁₀D₈ = C₂₀.₁₀D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	320		C20.10D8	320,105
C₂₀.₁₁D₈ = D₈.Dic₅	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	80	4	C20.11D8	320,121
C₂₀.₁₂D₈ = Q₁₆.Dic₅	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4	C20.12D8	320,123
C₂₀.₁₃D₈ = D₂₀⋊₄Q₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.13D8	320,473
C₂₀.₁₄D₈ = D₈₀⋊C₂	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	80	4+	C20.14D8	320,535
C₂₀.₁₅D₈ = C₁₆.D₁₀	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4-	C20.15D8	320,536
C₂₀.₁₆D₈ = C₂₀.₁₆D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.16D8	320,697
C₂₀.₁₇D₈ = C₂₀.₁₇D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	320		C20.17D8	320,705
C₂₀.₁₈D₈ = D₂₀⋊₆Q₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.18D8	320,714
C₂₀.₁₉D₈ = C₂₀.D₈	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.19D8	320,715
C₂₀.₂₀D₈ = C₂×C₅⋊D₁₆	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.20D8	320,773
C₂₀.₂₁D₈ = D₈.D₁₀	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	80	4	C20.21D8	320,774
C₂₀.₂₂D₈ = C₂×D₈.D₅	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.22D8	320,775
C₂₀.₂₃D₈ = C₂×C₅⋊SD₃₂	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160		C20.23D8	320,805
C₂₀.₂₄D₈ = Q₁₆.D₁₀	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	160	4	C20.24D8	320,806
C₂₀.₂₅D₈ = C₂×C₅⋊Q₃₂	φ: D₈/C₄ → C₂² ⊆ Aut C₂₀	320		C20.25D8	320,807
C₂₀.₂₆D₈ = D₁₆₀	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2+	C20.26D8	320,6
C₂₀.₂₇D₈ = C₁₆₀⋊C₂	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2	C20.27D8	320,7
C₂₀.₂₈D₈ = Dic₈₀	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320	2-	C20.28D8	320,8
C₂₀.₂₉D₈ = C₄₀⋊₈Q₈	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320		C20.29D8	320,309
C₂₀.₃₀D₈ = C₄.₅D₄₀	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.30D8	320,321
C₂₀.₃₁D₈ = C₂×D₈₀	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.31D8	320,529
C₂₀.₃₂D₈ = C₂×C₁₆⋊D₅	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.32D8	320,530
C₂₀.₃₃D₈ = C₂×Dic₄₀	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320		C20.33D8	320,532
C₂₀.₃₄D₈ = C₄₀⋊₅C₈	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320		C20.34D8	320,16
C₂₀.₃₅D₈ = D₂₀⋊₃C₈	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.35D8	320,17
C₂₀.₃₆D₈ = C₈₀.₆C₄	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2	C20.36D8	320,64
C₂₀.₃₇D₈ = D₄₀.₃C₄	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2	C20.37D8	320,68
C₂₀.₃₈D₈ = D₈₀⋊₇C₂	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2	C20.38D8	320,531
C₂₀.₃₉D₈ = C₅×D₃₂	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2	C20.39D8	320,176
C₂₀.₄₀D₈ = C₅×SD₆₄	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160	2	C20.40D8	320,177
C₂₀.₄₁D₈ = C₅×Q₆₄	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320	2	C20.41D8	320,178
C₂₀.₄₂D₈ = C₅×C₄.₄D₈	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.42D8	320,987
C₂₀.₄₃D₈ = C₅×C₈⋊₂Q₈	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320		C20.43D8	320,1001
C₂₀.₄₄D₈ = C₁₀×D₁₆	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.44D8	320,1006
C₂₀.₄₅D₈ = C₁₀×SD₃₂	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	160		C20.45D8	320,1007
C₂₀.₄₆D₈ = C₁₀×Q₃₂	φ: D₈/C₈ → C₂ ⊆ Aut C₂₀	320		C20.46D8	320,1008
C₂₀.₄₇D₈ = C₂₀.₄₇D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	320		C20.47D8	320,40
C₂₀.₄₈D₈ = D₄₀.₆C₄	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	80	4+	C20.48D8	320,53
C₂₀.₄₉D₈ = C₄₀.₈D₄	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4-	C20.49D8	320,54
C₂₀.₅₀D₈ = C₂₀.₅₀D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160		C20.50D8	320,634
C₂₀.₅₁D₈ = D₈⋊D₁₀	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	80	4+	C20.51D8	320,820
C₂₀.₅₂D₈ = C₄₀.₃₁C₂³	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4-	C20.52D8	320,822
C₂₀.₅₃D₈ = C₂₀.₅₃D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	320		C20.53D8	320,37
C₂₀.₅₄D₈ = D₂₀⋊₄C₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160		C20.54D8	320,41
C₂₀.₅₅D₈ = C₄₀.₇Q₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4	C20.55D8	320,51
C₂₀.₅₆D₈ = D₄₀.₅C₄	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4	C20.56D8	320,55
C₂₀.₅₇D₈ = C₂₀.₅₇D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160		C20.57D8	320,92
C₂₀.₅₈D₈ = C₂₀.₅₈D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4	C20.58D8	320,125
C₂₀.₅₉D₈ = C₄₀.₃₀C₂³	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4	C20.59D8	320,821
C₂₀.₆₀D₈ = C₅×C₄.D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160		C20.60D8	320,136
C₂₀.₆₁D₈ = C₅×C₄.₁₀D₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	320		C20.61D8	320,137
C₂₀.₆₂D₈ = C₅×M₅(2)⋊C₂	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	80	4	C20.62D8	320,166
C₂₀.₆₃D₈ = C₅×C₈.₁₇D₄	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4	C20.63D8	320,167
C₂₀.₆₄D₈ = C₅×D₄⋊Q₈	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160		C20.64D8	320,975
C₂₀.₆₅D₈ = C₅×C₁₆⋊C₂²	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	80	4	C20.65D8	320,1010
C₂₀.₆₆D₈ = C₅×Q₃₂⋊C₂	φ: D₈/D₄ → C₂ ⊆ Aut C₂₀	160	4	C20.66D8	320,1011
C₂₀.₆₇D₈ = C₅×D₄⋊C₈	central extension (φ=1)	160		C20.67D8	320,130
C₂₀.₆₈D₈ = C₅×C₈⋊₁C₈	central extension (φ=1)	320		C20.68D8	320,140
C₂₀.₆₉D₈ = C₅×D₈.C₄	central extension (φ=1)	160	2	C20.69D8	320,164
C₂₀.₇₀D₈ = C₅×C₈.₄Q₈	central extension (φ=1)	160	2	C20.70D8	320,173
C₂₀.₇₁D₈ = C₅×C₄○D₁₆	central extension (φ=1)	160	2	C20.71D8	320,1009

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Extensions 1→N→G→Q→1 with N=C20 and Q=D8

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₈