Batu Khan no relation Eastern Europe
From the 1220s into the 1240s, the Mongols conquered the Turkic states of Volga Bulgaria, Cumania, Alania, and various principalities in Eastern Europe. Following this, they began their invasion into Central Europe by launching a two-pronged invasion of then-fragmented Poland, culminating in the Battle of Legnica (9 April 1241), and the Kingdom of Hungary, culminating in the Battle of Mohi (11 April 1241). Invasions also were launched into the Caucasus against the Kingdom of Georgia and the Chechens and Ingush, as well as into the Southeast Europe against Bulgaria, Croatia, and the Latin Empire. The operations were planned by General Subutai (1175–1248) and commanded by Batu Khan (c. 1207–1255) and Kadan (d. c. 1261), two grandsons of Genghis Khan. Their conquests integrated much of Eastern European territory into the empire of the Golden Horde. Warring European princes realized they had to cooperate in the face of a Mongol invasion, so local wars and conflicts were suspended in parts of central Europe, only to be resumed after the Mongols had withdrawn. 
After the initial invasions, subsequent raids and punitive expeditions continued into the late 13th century.Against Poland (1259 and 1287)
In 1259, eighteen years after the first attack, two tumens (20,000 men) from the Golden Horde, under the leadership of Berke, attacked Poland after raiding Lithuania. This attack was commanded by general Burundai with young princes Nogai and Talabuga. Lublin, Sieradz, Sandomierz, Zawichost, Kraków, and Bytom were ravaged and plundered. Berke had no intention of occupying or conquering Poland. After this raid the Pope Alexander IV tried without success to organize a crusade against the Horde.Against Byzantine Thrace (1265, 1324 and 1337)
During the reign of Berke there was also a raid against Thrace. In the winter of 1265, the Bulgarian czar, Constantine Tych, requested Mongol intervention against the Byzantines in the Balkans. Nogai Khan led a Mongol raid of 20,000 cavalry (two tumens) against the territories of Byzantine eastern Thrace. In early 1265, Michael VIII Palaeologus confronted the Mongols, but his smaller squadron apparently had very low morale and was quickly routed. Most of them were cut down as they fled. Michael was forced to retreat to Constantinople on a Genoese ship while Nogai's army plundered all of Thrace. Following this defeat, the Byzantine emperor made an alliance with the Golden Horde (which was massively beneficial for the latter), giving his daughter Euphrosyne in marriage to Nogai. Michael also sent much valuable fabric to Golden Horde as tribute.Thrace also suffered raids in 1324 and 1337, during the reign of Uzbeg Khan.
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