DAVx⁵
FastMail is an email service offering paid email accounts. It also allows to manage calendars and contacts and provides CalDAV/CardDAV interfaces.
App password
In order to use 3rd-party applications like DAVx⁵ or Thunderbird with FastMail, you need to generate an app password. Choose "Mail, calendars and contacts" access.
DAVx⁵ settings
Choose "Login with email address" and enter your FastMail email address and the generated app password (see above).
Hint: When using fastmail with your own domain without SRV records you can try to use the Login with Base URL method and use https://carddav.fastmail.com as Base URL together with your Email address and app specific password.
Contact group method: groups are separate VCards
WebDAV setup
You can mount your fastmail files using the DAVx⁵ WebDAV mounts feature.
WebDAV URL: https://webdav.fastmail.com
User name: your fastmail email address or username
Password: your password