1)
The Torah goes on to list the children of Kush, Mitzrayim and Kena'an. Why does it omit the sons of Put?
1.
Ramban, Seforno; Rashbam (to 10:15): Because the Torah is only concerned here with the children that became nations, 1 and all of Put's children combined under the name of their father Put. 2
1
All the seventy nations that were already in existence are listed in this Parshah.
2
As the Pasuk in Yechezkel 38:5 indicates.