The indigenous group that was concentrated in Mexico by the time the Spaniards arrived was the Aztecs.
The Aztecs were a Mesoamerican people of Nahua affiliation that founded Mexico-Tenochtitlan and by the 15th century, in the late postclassic period, it became the center of one of the most extensive states known in Mesoamerica, located on an islet west of the lake Texcoco (on the islet sits the current Mexico City). Allied with other peoples of the lake valley basin -Tlacopan and Texcoco-, the Aztecs subdued several indigenous populations that settled in the center and south of the current territory of Mexico.
