You are leaving out some old Jewish sects:
Jewish diaspora communities are generally described to have coalesced into three major ethnic subdivisions according to where their ancestors settled: the Ashkenazim (initially in the Rhineland and France), the Sephardim (initially in the Iberian Peninsula), and the Mizrahim (Middle East and North Africa).[148] Romaniote Jews, Tunisian Jews, Yemenite Jews, Egyptian Jews, Ethiopian Jews, Bukharan Jews, Mountain Jews, and other groups also predated the arrival of the Sephardic diaspora.[149]
Despite experiencing repeated waves of persecution, Ashkenazi Jews in Western Europe worked in a variety of fields, making an impact on their communities’ economy and societies. In Francia, for example, figures like Isaac Judaeus and Armentarius occupied prominent social and economic positions. However, Jews were frequently the subjects of discriminatory laws, segregation, blood libels and pogroms, which culminated in events like the Rhineland Massacres (1066) and the expulsion of Jews from England (1290). As a result, Ashkenazi Jews were gradually pushed eastwards to Poland, Lithuania and Russia.
During the same period, Jewish communities in the Middle East thrived under Islamic rule, especially in cities like Baghdad, Cairo, and Damascus. In Babylonia, from the 7th to 11th centuries the Pumbedita and Sura academies led the Arab and to an extant the entire Jewish world. The deans and students of said academies defined the Geonic period in Jewish history.[150] Following this period were the Rishonim who lived from the 11th to 15th centuries. Like their European counterparts, Jews in the Middle East and North Africa also faced periods of persecution and discriminatory policies, with the Almohad Caliphate in North Africa and Iberia issuing forced conversion decrees, causing Jews such as Maimonides to seek safety in other regions.