The civil service of the city is hereby divided into the unclassified and the classified service.
The unclassified service shall include:
(1) All officers elected by the people.
(2) The Mayor, and all directors of departments.
(3) The members of all boards or commissions appointed by the Council or the Mayor.
(4) The Clerk of Council, and such other offices and positions as may be determined and prescribed by the Council.
The classified service shall consist of the police, sanitary police, and fire forces of the city, and such other offices and positions as shall be determined and prescribed by the Council, except as hereinbefore provided.