(a) The department shall file each application received for the registration of a vehicle and shall keep a record of each as follows:

1. (1) Under a distinctive registration number assigned to the vehicle.
2. (2) Alphabetically, under the name of the owner.
3. (3) Under the motor or a permanent identifying number of the vehicle as may be determined by the department.
4. (4) In the discretion of the department, in any other manner it may deem desirable.

(b) The department shall file every application for a license to operate a motor vehicle received by it and maintain all of the following:

1. (1) A suitable index containing, in alphabetical order, all applications denied. On the applications shall be noted the reasons for the denial.
2. (2) A suitable index containing, in alphabetical order, all applications granted.
3. (3) A suitable index containing, in alphabetical order, the name of every licensee whose license has been suspended or revoked by the department or by a court and after each name notes the reasons for the action and the period of revocation or suspension.