Extensions 1→N→G→Q→1 with N=C₄ and Q=C₄×Dic₅

Direct product G=N×Q with N=C₄ and Q=C₄×Dic₅

		d	ρ	Label	ID
C₄²×Dic₅		320		C4^2xDic5	320,557

Semidirect products G=N:Q with N=C₄ and Q=C₄×Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₄×Dic₅) = C₄⋊C₄×Dic₅	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	320		C4:1(C4xDic5)	320,602
C₄⋊₂(C₄×Dic₅) = C₄×C₄⋊Dic₅	φ: C₄×Dic₅/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4:2(C4xDic5)	320,561

Non-split extensions G=N.Q with N=C₄ and Q=C₄×Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₄×Dic₅) = C₂₀.₃₁C₄²	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	320		C4.1(C4xDic5)	320,87
C₄.₂(C₄×Dic₅) = C₂₀.₃₂C₄²	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	80		C4.2(C4xDic5)	320,90
C₄.₃(C₄×Dic₅) = C₂₀.₃₃C₄²	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	80		C4.3(C4xDic5)	320,113
C₄.₄(C₄×Dic₅) = C₂₀.₃₄C₄²	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	160		C4.4(C4xDic5)	320,116
C₄.₅(C₄×Dic₅) = C₂₀.₃₅C₄²	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	160		C4.5(C4xDic5)	320,624
C₄.₆(C₄×Dic₅) = M₄(2)×Dic₅	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	160		C4.6(C4xDic5)	320,744
C₄.₇(C₄×Dic₅) = C₂₀.₃₇C₄²	φ: C₄×Dic₅/C₂×Dic₅ → C₂ ⊆ Aut C₄	160		C4.7(C4xDic5)	320,749
C₄.₈(C₄×Dic₅) = C₄²⋊₆Dic₅	φ: C₄×Dic₅/C₂×C₂₀ → C₂ ⊆ Aut C₄	80		C4.8(C4xDic5)	320,81
C₄.₉(C₄×Dic₅) = C₂₀.₃₉C₄²	φ: C₄×Dic₅/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.9(C4xDic5)	320,109
C₄.₁₀(C₄×Dic₅) = C₂₀.₄₀C₄²	φ: C₄×Dic₅/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.10(C4xDic5)	320,110
C₄.₁₁(C₄×Dic₅) = C₄×C₄.Dic₅	φ: C₄×Dic₅/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.11(C4xDic5)	320,549
C₄.₁₂(C₄×Dic₅) = C₂₀.₄₂C₄²	φ: C₄×Dic₅/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.12(C4xDic5)	320,728
C₄.₁₃(C₄×Dic₅) = C₄×C₅⋊₂C₁₆	central extension (φ=1)	320		C4.13(C4xDic5)	320,18
C₄.₁₄(C₄×Dic₅) = C₄₀.₁₀C₈	central extension (φ=1)	320		C4.14(C4xDic5)	320,19
C₄.₁₅(C₄×Dic₅) = C₁₆×Dic₅	central extension (φ=1)	320		C4.15(C4xDic5)	320,58
C₄.₁₆(C₄×Dic₅) = C₈₀⋊₁₇C₄	central extension (φ=1)	320		C4.16(C4xDic5)	320,60
C₄.₁₇(C₄×Dic₅) = C₂×C₄×C₅⋊₂C₈	central extension (φ=1)	320		C4.17(C4xDic5)	320,547
C₄.₁₈(C₄×Dic₅) = C₂×C₄².D₅	central extension (φ=1)	320		C4.18(C4xDic5)	320,548
C₄.₁₉(C₄×Dic₅) = C₄²⋊₄Dic₅	central extension (φ=1)	320		C4.19(C4xDic5)	320,559
C₄.₂₀(C₄×Dic₅) = C₂×C₈×Dic₅	central extension (φ=1)	320		C4.20(C4xDic5)	320,725
C₄.₂₁(C₄×Dic₅) = C₂×C₄₀⋊₈C₄	central extension (φ=1)	320		C4.21(C4xDic5)	320,727
C₄.₂₂(C₄×Dic₅) = C₂₀.₄₅C₄²	central stem extension (φ=1)	80	4	C4.22(C4xDic5)	320,24
C₄.₂₃(C₄×Dic₅) = C₈₀⋊C₄	central stem extension (φ=1)	80	4	C4.23(C4xDic5)	320,70
C₄.₂₄(C₄×Dic₅) = C₄²⋊₁Dic₅	central stem extension (φ=1)	80	4	C4.24(C4xDic5)	320,89
C₄.₂₅(C₄×Dic₅) = C₂³.₉D₂₀	central stem extension (φ=1)	80	4	C4.25(C4xDic5)	320,115
C₄.₂₆(C₄×Dic₅) = C₂₀.₅₁C₄²	central stem extension (φ=1)	80	4	C4.26(C4xDic5)	320,118

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=C4×Dic5

Extensions 1→N→G→Q→1 with N=C₄ and Q=C₄×Dic₅