Currently, only the following fields have the options to sort alphabetically on the Contacts Pages: First Name, Last Name, Company Name, and Email. These fields that are easily sortable without running a filter can be seen and denoted by the up and down arrows highlighted in the image below.
If you are looking to narrow down a certain range of a number or date field properties, or any other property type, you may run an additional filter at the top of your page to narrow down the results that are shown on the page.
For example, if you are trying to search and filter for 'Last Contacted', you may run a filter as shown below!