Extensions 1→N→G→Q→1 with N=C₄ and Q=C₄×D₅

Direct product G=N×Q with N=C₄ and Q=C₄×D₅

		d	ρ	Label	ID
D₅×C₄²		80		D5xC4^2	160,92

Semidirect products G=N:Q with N=C₄ and Q=C₄×D₅

extension	φ:Q→Aut N	d	Label	ID
C₄⋊₁(C₄×D₅) = D₂₀⋊₈C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₄	80	C4:1(C4xD5)	160,114
C₄⋊₂(C₄×D₅) = C₄×D₂₀	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₄	80	C4:2(C4xD5)	160,94
C₄⋊₃(C₄×D₅) = D₅×C₄⋊C₄	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₄	80	C4:3(C4xD5)	160,112

Non-split extensions G=N.Q with N=C₄ and Q=C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₄×D₅) = D₂₀⋊₆C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₄	80		C4.1(C4xD5)	160,16
C₄.₂(C₄×D₅) = C₁₀.Q₁₆	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₄	160		C4.2(C4xD5)	160,17
C₄.₃(C₄×D₅) = D₂₀⋊₇C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₄	40	4	C4.3(C4xD5)	160,32
C₄.₄(C₄×D₅) = Dic₅⋊₃Q₈	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₄	160		C4.4(C4xD5)	160,108
C₄.₅(C₄×D₅) = D₂₀.₂C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₄	80	4	C4.5(C4xD5)	160,128
C₄.₆(C₄×D₅) = D₂₀⋊₄C₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₄	40	2	C4.6(C4xD5)	160,12
C₄.₇(C₄×D₅) = C₂₀.₄₄D₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₄	160		C4.7(C4xD5)	160,23
C₄.₈(C₄×D₅) = D₂₀⋊₅C₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₄	80		C4.8(C4xD5)	160,28
C₄.₉(C₄×D₅) = C₄×Dic₁₀	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₄	160		C4.9(C4xD5)	160,89
C₄.₁₀(C₄×D₅) = D₂₀.₃C₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₄	80	2	C4.10(C4xD5)	160,122
C₄.₁₁(C₄×D₅) = C₁₀.D₈	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₄	160		C4.11(C4xD5)	160,14
C₄.₁₂(C₄×D₅) = C₂₀.Q₈	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₄	160		C4.12(C4xD5)	160,15
C₄.₁₃(C₄×D₅) = C₂₀.₅₃D₄	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₄	80	4	C4.13(C4xD5)	160,29
C₄.₁₄(C₄×D₅) = C₄⋊C₄⋊₇D₅	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₄	80		C4.14(C4xD5)	160,113
C₄.₁₅(C₄×D₅) = D₅×M₄(2)	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₄	40	4	C4.15(C4xD5)	160,127
C₄.₁₆(C₄×D₅) = D₅×C₁₆	central extension (φ=1)	80	2	C4.16(C4xD5)	160,4
C₄.₁₇(C₄×D₅) = C₈₀⋊C₂	central extension (φ=1)	80	2	C4.17(C4xD5)	160,5
C₄.₁₈(C₄×D₅) = C₄×C₅⋊₂C₈	central extension (φ=1)	160		C4.18(C4xD5)	160,9
C₄.₁₉(C₄×D₅) = C₄².D₅	central extension (φ=1)	160		C4.19(C4xD5)	160,10
C₄.₂₀(C₄×D₅) = C₈×Dic₅	central extension (φ=1)	160		C4.20(C4xD5)	160,20
C₄.₂₁(C₄×D₅) = C₄₀⋊₈C₄	central extension (φ=1)	160		C4.21(C4xD5)	160,22
C₄.₂₂(C₄×D₅) = C₄²⋊D₅	central extension (φ=1)	80		C4.22(C4xD5)	160,93
C₄.₂₃(C₄×D₅) = D₅×C₂×C₈	central extension (φ=1)	80		C4.23(C4xD5)	160,120
C₄.₂₄(C₄×D₅) = C₂×C₈⋊D₅	central extension (φ=1)	80		C4.24(C4xD5)	160,121

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Extensions 1→N→G→Q→1 with N=C4 and Q=C4×D5

Extensions 1→N→G→Q→1 with N=C₄ and Q=C₄×D₅