The mayor has power to:
(1) nominate and, with the consent of the council, appoint all nonelective officers of the city or town provided for by the council, except as provided in this title;
(2) suspend and, with the consent of the council, remove any nonelective officer, stating in the suspension or removal the cause for the removal;
(3) supervise the discharge of official duty by all subordinate officers;
(4) require of any of the officers of a city or town an exhibit of the officer's books and papers;
(5) request that the governor call out the militia to aid the mayor in suppressing riots or other disorderly conduct, preventing and extinguishing fires, securing the peace and safety of the city or town, or carrying into effect any law or ordinance.