The department shall file the original of each certificate of registration received by it from the various county clerks, and shall keep a record of all these certificates of registration by registration years for a period of at least five (5) years in suitable books as follows:
(1) Numerically, under the registration number assigned by the county clerk issuing the certificate of registration as provided for in this part, which entry shall show, in addition to the registration number, all the information required to be set out on the face of the certificate of registration; and
(2) Alphabetically, under the name of the registered owner, which entry shall show, in addition to the name of the registered owner, the number of the owner's certificate of registration.