Although the classification of finite abelian groups is straightforward, the classification of finite soluble groups is well beyond mathematicians today and for the foreseeable future. Jordan, however, clearly saw this as an aim of the subject, even if it was not one which might ever be solved.
Kahit na ang pag-uuri ng wakas abelian grupo ay tapat, ang pag-uuri ng wakas matutunaw na grupo ay maayos na lampas mathematicians ngayon at para sa nakikinita hinaharap. Jordan, gayunman, malinaw na nakakita na ito bilang isang layunin ng ang paksa, kahit na ito ay hindi isa na kung saan maaaring kailanman ay malulutas.