Extensions 1→N→G→Q→1 with N=C₄ and Q=C₄×F₅

Direct product G=N×Q with N=C₄ and Q=C₄×F₅

		d	ρ	Label	ID
C₄²×F₅		80		C4^2xF5	320,1023

Semidirect products G=N:Q with N=C₄ and Q=C₄×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₄×F₅) = C₄×C₄⋊F₅	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₄	80		C4:1(C4xF5)	320,1025
C₄⋊₂(C₄×F₅) = C₄⋊C₄×F₅	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4:2(C4xF5)	320,1048

Non-split extensions G=N.Q with N=C₄ and Q=C₄×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₄×F₅) = C₄²⋊₆F₅	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₄	40	4	C4.1(C4xF5)	320,200
C₄.₂(C₄×F₅) = D₁₀.₁₀D₈	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₄	80		C4.2(C4xF5)	320,231
C₄.₃(C₄×F₅) = C₂₀.₁₀C₄²	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₄	160		C4.3(C4xF5)	320,234
C₄.₄(C₄×F₅) = C₄×C₄.F₅	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₄	160		C4.4(C4xF5)	320,1015
C₄.₅(C₄×F₅) = C₂₀.₁₂C₄²	φ: C₄×F₅/C₄×D₅ → C₂ ⊆ Aut C₄	80	4	C4.5(C4xF5)	320,1056
C₄.₆(C₄×F₅) = D₁₀.₁₈D₈	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.6(C4xF5)	320,212
C₄.₇(C₄×F₅) = C₂₀.C₄²	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80		C4.7(C4xF5)	320,213
C₄.₈(C₄×F₅) = M₄(2)⋊₃F₅	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.8(C4xF5)	320,238
C₄.₉(C₄×F₅) = M₄(2).F₅	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.9(C4xF5)	320,239
C₄.₁₀(C₄×F₅) = D₁₀.C₄²	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	160		C4.10(C4xF5)	320,1039
C₄.₁₁(C₄×F₅) = M₄(2)×F₅	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	40	8	C4.11(C4xF5)	320,1064
C₄.₁₂(C₄×F₅) = M₄(2)⋊₅F₅	φ: C₄×F₅/C₂×F₅ → C₂ ⊆ Aut C₄	80	8	C4.12(C4xF5)	320,1066
C₄.₁₃(C₄×F₅) = C₁₆×F₅	central extension (φ=1)	80	4	C4.13(C4xF5)	320,181
C₄.₁₄(C₄×F₅) = C₁₆⋊₇F₅	central extension (φ=1)	80	4	C4.14(C4xF5)	320,182
C₄.₁₅(C₄×F₅) = C₄×C₅⋊C₁₆	central extension (φ=1)	320		C4.15(C4xF5)	320,195
C₄.₁₆(C₄×F₅) = C₄².₄F₅	central extension (φ=1)	320		C4.16(C4xF5)	320,197
C₄.₁₇(C₄×F₅) = Dic₅⋊C₁₆	central extension (φ=1)	320		C4.17(C4xF5)	320,223
C₄.₁₈(C₄×F₅) = C₄₀.C₈	central extension (φ=1)	320		C4.18(C4xF5)	320,224
C₄.₁₉(C₄×F₅) = C₄×D₅⋊C₈	central extension (φ=1)	160		C4.19(C4xF5)	320,1013
C₄.₂₀(C₄×F₅) = C₄².₅F₅	central extension (φ=1)	160		C4.20(C4xF5)	320,1014
C₄.₂₁(C₄×F₅) = C₄²⋊₄F₅	central extension (φ=1)	80		C4.21(C4xF5)	320,1024
C₄.₂₂(C₄×F₅) = C₂×C₈×F₅	central extension (φ=1)	80		C4.22(C4xF5)	320,1054
C₄.₂₃(C₄×F₅) = C₂×C₈⋊F₅	central extension (φ=1)	80		C4.23(C4xF5)	320,1055
C₄.₂₄(C₄×F₅) = C₁₆⋊F₅	central stem extension (φ=1)	80	4	C4.24(C4xF5)	320,183
C₄.₂₅(C₄×F₅) = C₁₆⋊₄F₅	central stem extension (φ=1)	80	4	C4.25(C4xF5)	320,184
C₄.₂₆(C₄×F₅) = C₄².₃F₅	central stem extension (φ=1)	80	4	C4.26(C4xF5)	320,198
C₄.₂₇(C₄×F₅) = C₄²⋊₃F₅	central stem extension (φ=1)	80	4	C4.27(C4xF5)	320,201
C₄.₂₈(C₄×F₅) = C₂₀.₂₃C₄²	central stem extension (φ=1)	80	4	C4.28(C4xF5)	320,228
C₄.₂₉(C₄×F₅) = C₂₀.₂₄C₄²	central stem extension (φ=1)	80	4	C4.29(C4xF5)	320,233
C₄.₃₀(C₄×F₅) = C₂₀.₂₅C₄²	central stem extension (φ=1)	80	4	C4.30(C4xF5)	320,235

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Extensions 1→N→G→Q→1 with N=C4 and Q=C4×F5

Extensions 1→N→G→Q→1 with N=C₄ and Q=C₄×F₅