Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₄²

Direct product G=N×Q with N=C₂₀ and Q=C₄²

		d	ρ	Label	ID
C₄²×C₂₀		320		C4^2xC20	320,875

Semidirect products G=N:Q with N=C₂₀ and Q=C₄²

extension	φ:Q→Aut N	d	Label	ID
C₂₀⋊C₄² = C₄⋊C₄×F₅	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	80	C20:C4^2	320,1048
C₂₀⋊₂C₄² = C₄×C₄⋊F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	C20:2C4^2	320,1025
C₂₀⋊₃C₄² = C₄²×F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	C20:3C4^2	320,1023
C₂₀⋊₄C₄² = C₄⋊C₄×Dic₅	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	320	C20:4C4^2	320,602
C₂₀⋊₅C₄² = C₄×C₄⋊Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320	C20:5C4^2	320,561
C₂₀⋊₆C₄² = C₄²×Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320	C20:6C4^2	320,557
C₂₀⋊₇C₄² = C₄⋊C₄×C₂₀	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320	C20:7C4^2	320,879

Non-split extensions G=N.Q with N=C₂₀ and Q=C₄²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁C₄² = D₁₀.₁₈D₈	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	80		C20.1C4^2	320,212
C₂₀.₂C₄² = C₂₀.C₄²	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	80		C20.2C4^2	320,213
C₂₀.₃C₄² = M₄(2)⋊₃F₅	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	40	8	C20.3C4^2	320,238
C₂₀.₄C₄² = M₄(2).F₅	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	80	8	C20.4C4^2	320,239
C₂₀.₅C₄² = D₁₀.C₄²	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	160		C20.5C4^2	320,1039
C₂₀.₆C₄² = M₄(2)×F₅	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	40	8	C20.6C4^2	320,1064
C₂₀.₇C₄² = M₄(2)⋊₅F₅	φ: C₄²/C₂ → C₂×C₄ ⊆ Aut C₂₀	80	8	C20.7C4^2	320,1066
C₂₀.₈C₄² = C₄²⋊₆F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	40	4	C20.8C4^2	320,200
C₂₀.₉C₄² = D₁₀.₁₀D₈	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80		C20.9C4^2	320,231
C₂₀.₁₀C₄² = C₂₀.₁₀C₄²	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	160		C20.10C4^2	320,234
C₂₀.₁₁C₄² = C₄×C₄.F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	160		C20.11C4^2	320,1015
C₂₀.₁₂C₄² = C₂₀.₁₂C₄²	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.12C4^2	320,1056
C₂₀.₁₃C₄² = C₁₆×F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.13C4^2	320,181
C₂₀.₁₄C₄² = C₁₆⋊₇F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.14C4^2	320,182
C₂₀.₁₅C₄² = C₁₆⋊F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.15C4^2	320,183
C₂₀.₁₆C₄² = C₁₆⋊₄F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.16C4^2	320,184
C₂₀.₁₇C₄² = C₄×C₅⋊C₁₆	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	320		C20.17C4^2	320,195
C₂₀.₁₈C₄² = C₄².₄F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	320		C20.18C4^2	320,197
C₂₀.₁₉C₄² = C₄².₃F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.19C4^2	320,198
C₂₀.₂₀C₄² = C₄²⋊₃F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.20C4^2	320,201
C₂₀.₂₁C₄² = Dic₅⋊C₁₆	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	320		C20.21C4^2	320,223
C₂₀.₂₂C₄² = C₄₀.C₈	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	320		C20.22C4^2	320,224
C₂₀.₂₃C₄² = C₂₀.₂₃C₄²	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.23C4^2	320,228
C₂₀.₂₄C₄² = C₂₀.₂₄C₄²	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.24C4^2	320,233
C₂₀.₂₅C₄² = C₂₀.₂₅C₄²	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.25C4^2	320,235
C₂₀.₂₆C₄² = C₄×D₅⋊C₈	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	160		C20.26C4^2	320,1013
C₂₀.₂₇C₄² = C₄².₅F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	160		C20.27C4^2	320,1014
C₂₀.₂₈C₄² = C₄²⋊₄F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80		C20.28C4^2	320,1024
C₂₀.₂₉C₄² = C₂×C₈×F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80		C20.29C4^2	320,1054
C₂₀.₃₀C₄² = C₂×C₈⋊F₅	φ: C₄²/C₄ → C₄ ⊆ Aut C₂₀	80		C20.30C4^2	320,1055
C₂₀.₃₁C₄² = C₂₀.₃₁C₄²	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	320		C20.31C4^2	320,87
C₂₀.₃₂C₄² = C₂₀.₃₂C₄²	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	80		C20.32C4^2	320,90
C₂₀.₃₃C₄² = C₂₀.₃₃C₄²	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	80		C20.33C4^2	320,113
C₂₀.₃₄C₄² = C₂₀.₃₄C₄²	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	160		C20.34C4^2	320,116
C₂₀.₃₅C₄² = C₂₀.₃₅C₄²	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	160		C20.35C4^2	320,624
C₂₀.₃₆C₄² = M₄(2)×Dic₅	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	160		C20.36C4^2	320,744
C₂₀.₃₇C₄² = C₂₀.₃₇C₄²	φ: C₄²/C₂² → C₂² ⊆ Aut C₂₀	160		C20.37C4^2	320,749
C₂₀.₃₈C₄² = C₄²⋊₆Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80		C20.38C4^2	320,81
C₂₀.₃₉C₄² = C₂₀.₃₉C₄²	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.39C4^2	320,109
C₂₀.₄₀C₄² = C₂₀.₄₀C₄²	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.40C4^2	320,110
C₂₀.₄₁C₄² = C₄×C₄.Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.41C4^2	320,549
C₂₀.₄₂C₄² = C₂₀.₄₂C₄²	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.42C4^2	320,728
C₂₀.₄₃C₄² = C₄×C₅⋊₂C₁₆	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.43C4^2	320,18
C₂₀.₄₄C₄² = C₄₀.₁₀C₈	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.44C4^2	320,19
C₂₀.₄₅C₄² = C₂₀.₄₅C₄²	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.45C4^2	320,24
C₂₀.₄₆C₄² = C₁₆×Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.46C4^2	320,58
C₂₀.₄₇C₄² = C₈₀⋊₁₇C₄	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.47C4^2	320,60
C₂₀.₄₈C₄² = C₈₀⋊C₄	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.48C4^2	320,70
C₂₀.₄₉C₄² = C₄²⋊₁Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.49C4^2	320,89
C₂₀.₅₀C₄² = C₂³.₉D₂₀	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.50C4^2	320,115
C₂₀.₅₁C₄² = C₂₀.₅₁C₄²	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.51C4^2	320,118
C₂₀.₅₂C₄² = C₂×C₄×C₅⋊₂C₈	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.52C4^2	320,547
C₂₀.₅₃C₄² = C₂×C₄².D₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.53C4^2	320,548
C₂₀.₅₄C₄² = C₄²⋊₄Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.54C4^2	320,559
C₂₀.₅₅C₄² = C₂×C₈×Dic₅	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.55C4^2	320,725
C₂₀.₅₆C₄² = C₂×C₄₀⋊₈C₄	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.56C4^2	320,727
C₂₀.₅₇C₄² = C₅×C₄²⋊₆C₄	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	80		C20.57C4^2	320,144
C₂₀.₅₈C₄² = C₅×C₂².₄Q₁₆	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.58C4^2	320,145
C₂₀.₅₉C₄² = C₅×C₄.C₄²	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.59C4^2	320,146
C₂₀.₆₀C₄² = M₄(2)×C₂₀	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.60C4^2	320,905
C₂₀.₆₁C₄² = C₅×C₈○₂M₄(2)	φ: C₄²/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.61C4^2	320,906
C₂₀.₆₂C₄² = C₅×C₄.₉C₄²	central extension (φ=1)	80	4	C20.62C4^2	320,142
C₂₀.₆₃C₄² = C₅×C₄.₁₀C₄²	central extension (φ=1)	80	4	C20.63C4^2	320,143
C₂₀.₆₄C₄² = C₅×C₁₆⋊₅C₄	central extension (φ=1)	320		C20.64C4^2	320,151
C₂₀.₆₅C₄² = C₅×C₁₆⋊C₄	central extension (φ=1)	80	4	C20.65C4^2	320,152
C₂₀.₆₆C₄² = C₅×C₄²⋊₄C₄	central extension (φ=1)	320		C20.66C4^2	320,877
C₂₀.₆₇C₄² = C₁₀×C₈⋊C₄	central extension (φ=1)	320		C20.67C4^2	320,904

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Extensions 1→N→G→Q→1 with N=C20 and Q=C42

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₄²