If any registration card or license plate is stolen, lost, mutilated, or illegible, the owner of the vehicle for which the same was issued, as shown by the records of the department, shall immediately make application for and may, upon the applicant furnishing information satisfactory to the department, obtain a duplicate or a substitute or a new registration under a new registration number, as determined to be most advisable by the department. An application for a duplicate registration card is not required in conjunction with any other application.