Question: The Franco-Italian army led by Eugène de Beauharnais was defreated by an Austrian army commanded by a member of what house?

full_context: Document 1: Battle of Piave River (1809): The Battle of Piave River was fought on 8 May 1809 between the Franco-Italian army under the command of Eugène de Beauharnais and an Austrian army led by Archduke John of Austria. The Austrian commander made a stand behind the Piave River but he suffered a defeat at the hands of his numerically superior foes. The combat took place near Nervesa della Battaglia, Italy during the War of the Fifth Coalition, part of the Napoleonic Wars.
Document 2: Archduke John of Austria: Archduke John of Austria (German: "Erzherzog Johann Baptist Joseph Fabian Sebastian von Österreich" ; 20 January 1782 – 11 May 1859), a member of the House of Habsburg-Lorraine, was an Austrian field marshal and Imperial regent ("Reichsverweser") of the short-lived German Empire during the Revolutions of 1848.
Document 3: Piave River 1809 order of battle: The Piave River 1809 Order of Battle shows the units and organization for the Franco-Italian and Austrian Empire armies that fought in the Battle of Piave River on 8 May 1809. Eugène de Beauharnais, the viceroy of the Kingdom of Italy defeated Archduke John of Austria. Eugène's Advance Guard crossed the river first and was assailed by Austrian cavalry and artillery. The French cavalry routed the opposing cavalry and captured 14 enemy guns. A lull followed as John arranged his infantry in a formidable defensive position. Meanwhile, Eugène struggled to pour reinforcements into the bridgehead as the Piave rose dangerously. In the afternoon, the viceroy sent Paul Grenier to drive back the Austrian left while Jacques MacDonald mounted an assault on the center. The attack succeeded in breaking the Austrian line and compelling John to order a retreat.
Document 4: Battle of Tarvis (1809): The Battle of Tarvis from 16 to 17 May 1809, the Storming of the Malborghetto Blockhouse from 15 to 17 May 1809, and the Storming of the Predil Blockhouse from 15 to 18 May saw the Franco-Italian army of Eugène de Beauharnais attacking Austrian Empire forces under Albert Gyulai. Eugène crushed Gyulai's division in a pitched battle near Tarvisio, then an Austrian town known as Tarvis. At nearby Malborghetto Valbruna (Malbotghet Wolfstal) and Predil Pass, small garrisons of Grenz infantry heroically defended two forts before being overwhelmed by sheer numbers. The Franco-Italian capture of the key mountain passes allowed their forces to invade Austrian Kärnten during the War of the Fifth Coalition. Tarvisio is located in far northeast Italy, near the borders of both Austria and Slovenia.
Document 5: Order of battle for the Battle of Caldiero (1805): The armies of the First French Empire and the Austrian Empire fought the Battle of Caldiero from 29 to 31 October 1805 just east of Verona in Italy. Marshal André Masséna led the French Army of Italy while Archduke Charles commanded the Austrian "Armee von Italien". Historians variously call the battle a French victory, an Austrian victory, or indecisive. Austrian losses were over 5,500, while the French suffered at least 5,000 casualties. Archduke Charles began a withdrawal from Italy on 1 November. The retreat ended in early December with Archduke Charles' army intact at Kormend in western Hungary. Unfortunately for Austria, by this time, Emperor Napoleon had decisively defeated the Austro-Russian army at the Battle of Austerlitz.
Document 6: Battle of Caldiero (1813): The Battle of Caldiero on 15 November 1813 saw an army of the First French Empire under Eugène de Beauharnais opposed to an Austrian Empire army led by Johann von Hiller. Eugène, who was the Viceroy of the Napoleonic Kingdom of Italy inflicted a defeat on Hiller's troops, driving them from Caldiero. The action took place during the War of the Sixth Coalition, part of the Napoleonic Wars. Caldiero is located 15 km east of Verona on the Autostrada A4.
Document 7: Archduke Johann Salvator of Austria: Archduke Johann Salvator of Austria (German: "Johann Salvator" , Italian: "Giovanni Salvatore" ; 25 November 1852 – declared dead in absentia 2 February 1911) was a member of the Tuscan branch of the House of Habsburg-Lorraine. He was Archduke and Prince of Austria, Prince of Hungary, Bohemia and Tuscany. After renouncing those titles, he was known as Johann (John) Orth. He disappeared while sailing with his wife in July 1890 and is believed to have died when his ship encountered a storm near Cape Horn. Salvator was declared dead in absentia in February 1911.
Document 8: Archduke Charles, Duke of Teschen: Archduke Charles of Austria, Duke of Teschen (German: Erzherzog Carl Ludwig Johann Joseph Laurentius von Österreich, Herzog von Teschen; 5 September 1771 – 30 April 1847) was an Austrian field-marshal, the third son of Emperor Leopold II and his wife, Maria Luisa of Spain. He was also the younger brother of Francis II, Holy Roman Emperor. Despite being epileptic, Charles achieved respect both as a commander and as a reformer of the Austrian army. He was considered one of Napoleon's most formidable opponents.
Document 9: Battle of Sacile: The Battle of Sacile (also known as the Battle of Fontana Fredda) on 16 April 1809 and its companion Clash at Pordenone on 15 April saw an Austrian army commanded by Archduke John of Austria defeat a Franco-Italian army led by Eugène de Beauharnais and force it to retreat. Sacile proved to be the most notable victory of John's career. The action took place east of the Livenza River near Sacile in modern-day Italy during the War of the Fifth Coalition, part of the Napoleonic Wars.
Document 10: Archduke Franz Ferdinand of Austria: Franz Ferdinand Carl Ludwig Joseph Maria (18 December 1863 – 28 June 1914) was an Archduke of Austria-Este, Austro-Hungarian and Royal Prince of Hungary and of Bohemia and, from 1896 until his death, heir presumptive to the Austro-Hungarian throne.
Document 11: Sacile 1809 order of battle: The Battle of Sacile on 16 April 1809 saw the Franco-Italian Army of Italy commanded by Eugène de Beauharnais attack Archduke John of Austria's Army of Inner Austria. In the morning, the Austrians successfully held off Franco-Italian assaults on their left flank. Later in the day, John counterattacked to drive Eugène's troops from the battlefield. The battle at Sacile was preceded by the action of Pordenone on 15 April in which the Austrian advance guard mauled the French rear guard. The Austrian victory compelled Eugène to withdraw to the Adige River at Verona where he gathered reinforcements and planned a counteroffensive.
Document 12: Battle of Caldiero (1809): In the Battle of Caldiero or Battle of Soave or Battle of Castelcerino from 27 to 30 April 1809, an Austrian army led by Archduke John of Austria defended against a Franco-Italian army headed by Eugène de Beauharnais, the Viceroy of the Kingdom of Italy. The outnumbered Austrians successfully fended off the attacks of their enemies in actions at San Bonifacio, Soave, and Castelcerino before retreating to the east. The clash occurred during the War of the Fifth Coalition, part of the Napoleonic Wars.
Document 13: Franz Stadion, Count von Warthausen: Franz Stadion, Graf von Warthausen (27 July 1806 – 8 June 1853), son of the Austrian diplomat Johann Philipp von Stadion. Born in Vienna, he was a statesman who served the Austrian Empire during the 1840s. From 1841 he was Governor of the Austrian Littoral (with its capital at Trieste), from 1847 to 1848 Governor of Galicia (where he freed the peasants from labor duties), and from 1848 to 1849 he was Interior Minister and Minister of Education. He advocated constitutional government, decreed the Imposed March Constitution in March 1849 which was never enacted, and in 1849 promulgated the "Gemeinde" (municipality) legislation that granted governmental autonomy to all municipalities in the Austrian empire. Lewis Namier, in "1848: The Revolution of the Intellectuals" (p. 18), calls him "one of the most enlightened and efficient Austrian administrators."
Document 14: Archduke Maximilian of Austria-Este: Archduke Maximilian Joseph of Austria-Este (July 14, 1782 – June 1, 1863), the fourth son of Archduke Ferdinand of Austria-Este and younger brother of Francis IV, Duke of Modena. He was grand master of the Teutonic Knights from 1835 to 1863.
Document 15: Archduke Ferdinand Karl Joseph of Austria-Este: Archduke Ferdinand Karl Joseph of Austria-Este (25 April 1781 – 5 November 1850) was the third son of Archduke Ferdinand of Austria-Este and of his wife Princess Maria Beatrice Ricciarda d'Este, last member and heiress of the House of Este. For much of the Napoleonic Wars he was in command of the Austrian army.
ground_truth: House of Habsburg-Lorraine