Ordination procedure in Theravada Buddhism - What are grievous crimes?
Page 99 of this account of The
Buddhist
Monastic
Code list 11 types who should not be ordained as bhikkhus,


  
  a pandaka (essentially, a eunuch or a person born neuter—see Sanghadisesa
  2),
  a “non-human” being, (this includes nagas, petas, devas, and yakkhas),
  a hermaphrodite,
  a person who poses as a bhikkhu without having been ordained,
  a bhikkhu who has ordained in another religion without first giving up his
  status as a bhikkhu,
  a person who has murdered his father,
  a person who has murdered his mother,
  a person who has murdered an arahant,
  a person who has sexually molested a bhikkhuni,
  a person who has maliciously injured a Buddha to the point of causing him to
  bleed, and
  a person who has dishonestly caused a schism in the Sangha, knowing or
  suspecting that his position was contrary to the Dhamma-Vinaya.
  


Pages 44 through 98 describe just four parajika rules, where if a bhikkhu breaks (or has broken) one of these rules then they are automatically no longer a bhikkhu and cannot ordain again in this life:


Sexual intercourse
Stealing
Killing
Falsely claiming a superior human state