The 14 Churches
sui iuris which are of the Byzantine Rite are:
Albanian Greek-Catholic
Belarusian Greek-Catholic
Bulgarian Greek-Catholic
Croat Greek-Catholic
Georgian Greek-Catholic
Greek Byzantine Catholic
Hungarian Greek-Catholic
Italo-Greek-Albanian Byzantine Catholic
Melkite Greek-Catholic
Romanian Greek-Catholic
Russian Greek-Catholic
Ruthenian Byzantine Catholic
Slovak Greek-Catholic
Ukrainian Greek-Catholic
Additionally, there are Macedonian (of non-Greek ethnicity), Montenegron, and Serbian Greek-Catholics ascribed to the Croat Greek-Catholic Church and Czech Greek-Catholics ascribed to the Ruthenian Byzantine Church; however, none of those are themselves designated as of a distinct Church
sui iuris
Of the 14, the Italo-Greico-Albanian, Melkite, Romanian, Russian, Ruthenian, and Ukrainian Churches actually have a formal presence (either a canonical jurisdiction or a parish) in the US.
There are ethnically Croat, Hungarian, and Slovak parishes within the Ruthenian Church in the US, as the Ruthenians are charged with the pastoral care of those Greek-Catholics - but I believe that only Saint Nicholas the Wonderworker parish in Cleveland formally descends from a canonical presence in the US of any of those Churches. (It was one of two parishes in the US formally erected by the Eparchy of Krivezci; the other, Ss Peter & Paul in Chicago, memory eternal, was canonically suppressed two decades ago).
The sole Belarusian Greek-Catholic parish in the US (Christ the Redeemer, memory eternal) was in Chicago and was canonically suppressed a few years ago.
For a full schematic and narrative description of the Rites and Churches, formerly available here in the now-archived Reference Threads, see
Eastern & Oriental Catholic Churches and Rites at
OC.net
Many years,
Neil