Extensions 1→N→G→Q→1 with N=D₄xD₅ and Q=C₄

Direct product G=NxQ with N=D₄xD₅ and Q=C₄

		d	ρ	Label	ID
C₄xD₄xD₅		80		C4xD4xD5	320,1216

Semidirect products G=N:Q with N=D₄xD₅ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄xD₅):₁C₄ = D₅xD₄:C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80		(D4xD5):1C4	320,396
(D₄xD₅):₂C₄ = (D₄xD₅):C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80		(D4xD5):2C4	320,397
(D₄xD₅):₃C₄ = D₅xC₄wrC₂	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	40	4	(D4xD5):3C4	320,447
(D₄xD₅):₄C₄ = C₄²:D₁₀	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80	4	(D4xD5):4C4	320,448
(D₄xD₅):₅C₄ = C₄²:₁₁D₁₀	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80		(D4xD5):5C4	320,1217
(D₄xD₅):₆C₄ = C₂xD₂₀:C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80		(D4xD5):6C4	320,1104
(D₄xD₅):₇C₄ = (D₄xC₁₀):C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	40	8+	(D4xD5):7C4	320,1105
(D₄xD₅):₈C₄ = D₅:C₄wrC₂	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	40	8	(D4xD5):8C4	320,1130
(D₄xD₅):₉C₄ = D₄:F₅:C₂	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80	8	(D4xD5):9C4	320,1133
(D₄xD₅):₁₀C₄ = C₂xD₄xF₅	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	40		(D4xD5):10C4	320,1595
(D₄xD₅):₁₁C₄ = D₁₀.C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	40	8+	(D4xD5):11C4	320,1596

Non-split extensions G=N.Q with N=D₄xD₅ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄xD₅).₁C₄ = C₂₀.₇₂C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80	4	(D4xD5).1C4	320,1422
(D₄xD₅).₂C₄ = Dic₅.₂₁C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80	8	(D4xD5).2C4	320,1601
(D₄xD₅).₃C₄ = Dic₅.₂₂C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄xD₅	80	8	(D4xD5).3C4	320,1602
(D₄xD₅).₄C₄ = D₅xC₈oD₄	φ: trivial image	80	4	(D4xD5).4C4	320,1421

׿

x

:

Z

F

o

wr

Q

<