Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₁₂

Direct product G=N×Q with N=C₂₀ and Q=D₁₂

		d	ρ	Label	ID
C₂₀×D₁₂		240		C20xD12	480,752

Semidirect products G=N:Q with N=C₂₀ and Q=D₁₂

extension	φ:Q→Aut N	d	Label	ID
C₂₀⋊₁D₁₂ = C₂₀⋊D₁₂	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	C20:1D12	480,527
C₂₀⋊₂D₁₂ = C₂₀⋊₂D₁₂	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	C20:2D12	480,542
C₂₀⋊₃D₁₂ = C₄⋊D₆₀	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	C20:3D12	480,860
C₂₀⋊₄D₁₂ = C₄²⋊₆D₁₅	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	C20:4D12	480,839
C₂₀⋊₅D₁₂ = C₄×D₆₀	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	C20:5D12	480,838
C₂₀⋊₆D₁₂ = C₅×C₄⋊D₁₂	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	C20:6D12	480,753
C₂₀⋊₇D₁₂ = C₆₀⋊₆D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	C20:7D12	480,536
C₂₀⋊₈D₁₂ = C₄×C₅⋊D₁₂	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	C20:8D12	480,521
C₂₀⋊₉D₁₂ = C₅×C₁₂⋊D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	C20:9D12	480,774

Non-split extensions G=N.Q with N=C₂₀ and Q=D₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁D₁₂ = C₅⋊D₄₈	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4+	C20.1D12	480,15
C₂₀.₂D₁₂ = D₂₄.D₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4-	C20.2D12	480,20
C₂₀.₃D₁₂ = Dic₁₂⋊D₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4+	C20.3D12	480,21
C₂₀.₄D₁₂ = C₅⋊Dic₂₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	480	4-	C20.4D12	480,24
C₂₀.₅D₁₂ = C₂₀.₅D₁₂	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	120	4	C20.5D12	480,35
C₂₀.₆D₁₂ = C₆₀.₅₄D₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4	C20.6D12	480,38
C₂₀.₇D₁₂ = D₁₂⋊Dic₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.7D12	480,42
C₂₀.₈D₁₂ = Dic₆⋊Dic₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	480		C20.8D12	480,48
C₂₀.₉D₁₂ = D₆₀⋊₉C₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.9D12	480,169
C₂₀.₁₀D₁₂ = Dic₃₀⋊₉C₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	480		C20.10D12	480,170
C₂₀.₁₁D₁₂ = M₄(2)⋊D₁₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	120	4+	C20.11D12	480,183
C₂₀.₁₂D₁₂ = C₄.D₆₀	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4-	C20.12D12	480,184
C₂₀.₁₃D₁₂ = C₂×C₅⋊D₂₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.13D12	480,378
C₂₀.₁₄D₁₂ = D₆₀⋊₃₆C₂²	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	120	4	C20.14D12	480,380
C₂₀.₁₅D₁₂ = C₂×D₁₂.D₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.15D12	480,392
C₂₀.₁₆D₁₂ = C₂×Dic₆⋊D₅	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.16D12	480,393
C₂₀.₁₇D₁₂ = C₂×C₅⋊Dic₁₂	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	480		C20.17D12	480,396
C₂₀.₁₈D₁₂ = C₂₀.D₁₂	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4	C20.18D12	480,397
C₂₀.₁₉D₁₂ = C₆₀.₆₉D₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.19D12	480,449
C₂₀.₂₀D₁₂ = C₆₀.₇₀D₄	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.20D12	480,451
C₂₀.₂₁D₁₂ = Dic₅⋊Dic₆	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	480		C20.21D12	480,452
C₂₀.₂₂D₁₂ = D₃₀⋊₉Q₈	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.22D12	480,459
C₂₀.₂₃D₁₂ = D₃₀⋊₆Q₈	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240		C20.23D12	480,862
C₂₀.₂₄D₁₂ = C₈⋊D₃₀	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	120	4+	C20.24D12	480,873
C₂₀.₂₅D₁₂ = C₈.D₃₀	φ: D₁₂/C₆ → C₂² ⊆ Aut C₂₀	240	4-	C20.25D12	480,874
C₂₀.₂₆D₁₂ = D₂₄₀	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	2+	C20.26D12	480,159
C₂₀.₂₇D₁₂ = C₄₈⋊D₅	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	2	C20.27D12	480,160
C₂₀.₂₈D₁₂ = Dic₁₂₀	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480	2-	C20.28D12	480,161
C₂₀.₂₉D₁₂ = C₆₀⋊₈Q₈	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480		C20.29D12	480,834
C₂₀.₃₀D₁₂ = C₄²⋊₇D₁₅	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.30D12	480,840
C₂₀.₃₁D₁₂ = C₂×C₂₄⋊D₅	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.31D12	480,867
C₂₀.₃₂D₁₂ = C₂×D₁₂₀	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.32D12	480,868
C₂₀.₃₃D₁₂ = C₂×Dic₆₀	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480		C20.33D12	480,870
C₂₀.₃₄D₁₂ = C₆₀⋊₅C₈	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480		C20.34D12	480,164
C₂₀.₃₅D₁₂ = D₆₀⋊₇C₄	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	120	2	C20.35D12	480,165
C₂₀.₃₆D₁₂ = C₄.₁₈D₆₀	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	2	C20.36D12	480,179
C₂₀.₃₇D₁₂ = D₃₀⋊₃C₈	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.37D12	480,180
C₂₀.₃₈D₁₂ = C₄₀.₆₉D₆	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	2	C20.38D12	480,869
C₂₀.₃₉D₁₂ = C₅×D₄₈	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	2	C20.39D12	480,118
C₂₀.₄₀D₁₂ = C₅×C₄₈⋊C₂	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240	2	C20.40D12	480,119
C₂₀.₄₁D₁₂ = C₅×Dic₂₄	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480	2	C20.41D12	480,120
C₂₀.₄₂D₁₂ = C₅×C₁₂⋊₂Q₈	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480		C20.42D12	480,748
C₂₀.₄₃D₁₂ = C₅×C₄²⋊₇S₃	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.43D12	480,754
C₂₀.₄₄D₁₂ = C₁₀×C₂₄⋊C₂	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.44D12	480,781
C₂₀.₄₅D₁₂ = C₁₀×D₂₄	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	240		C20.45D12	480,782
C₂₀.₄₆D₁₂ = C₁₀×Dic₁₂	φ: D₁₂/C₁₂ → C₂ ⊆ Aut C₂₀	480		C20.46D12	480,784
C₂₀.₄₇D₁₂ = C₆₀.₂₉D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	120	4+	C20.47D12	480,36
C₂₀.₄₈D₁₂ = C₆₀.₃₁D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	4-	C20.48D12	480,39
C₂₀.₄₉D₁₂ = D₆₀⋊₁₂C₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240		C20.49D12	480,44
C₂₀.₅₀D₁₂ = Dic₃₀⋊₁₂C₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	480		C20.50D12	480,50
C₂₀.₅₁D₁₂ = C₆₀.₃₈D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	120	4+	C20.51D12	480,381
C₂₀.₅₂D₁₂ = D₁₂.₃₃D₁₀	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	4-	C20.52D12	480,398
C₂₀.₅₃D₁₂ = C₆₀.₄₅D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240		C20.53D12	480,441
C₂₀.₅₄D₁₂ = C₆₀.₉₄D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240		C20.54D12	480,32
C₂₀.₅₅D₁₂ = D₃₀⋊₄C₈	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240		C20.55D12	480,33
C₂₀.₅₆D₁₂ = C₆₀.₉₉D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	120	4	C20.56D12	480,55
C₂₀.₅₇D₁₂ = D₆₀⋊₁₆C₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	120	4	C20.57D12	480,57
C₂₀.₅₈D₁₂ = C₆₀.₁₃Q₈	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	480		C20.58D12	480,58
C₂₀.₅₉D₁₂ = C₆₀.₁₀₅D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	4	C20.59D12	480,67
C₂₀.₆₀D₁₂ = C₂₀.₆₀D₁₂	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	4	C20.60D12	480,379
C₂₀.₆₁D₁₂ = C₅×C₆.D₈	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240		C20.61D12	480,128
C₂₀.₆₂D₁₂ = C₅×C₆.SD₁₆	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	480		C20.62D12	480,129
C₂₀.₆₃D₁₂ = C₅×C₁₂.₄₆D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	120	4	C20.63D12	480,142
C₂₀.₆₄D₁₂ = C₅×C₁₂.₄₇D₄	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	4	C20.64D12	480,143
C₂₀.₆₅D₁₂ = C₅×C₄.D₁₂	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240		C20.65D12	480,776
C₂₀.₆₆D₁₂ = C₅×C₈⋊D₆	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	120	4	C20.66D12	480,787
C₂₀.₆₇D₁₂ = C₅×C₈.D₆	φ: D₁₂/D₆ → C₂ ⊆ Aut C₂₀	240	4	C20.67D12	480,788
C₂₀.₆₈D₁₂ = C₅×C₁₂⋊C₈	central extension (φ=1)	480		C20.68D12	480,123
C₂₀.₆₉D₁₂ = C₅×C₄²⋊₄S₃	central extension (φ=1)	120	2	C20.69D12	480,124
C₂₀.₇₀D₁₂ = C₅×C₂₄.C₄	central extension (φ=1)	240	2	C20.70D12	480,138
C₂₀.₇₁D₁₂ = C₅×D₆⋊C₈	central extension (φ=1)	240		C20.71D12	480,139
C₂₀.₇₂D₁₂ = C₅×C₄○D₂₄	central extension (φ=1)	240	2	C20.72D12	480,783

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Extensions 1→N→G→Q→1 with N=C20 and Q=D12

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₁₂