FastMail is an email service offering paid email accounts. It also allows to manage calendars and contacts and provides CalDAV/CardDAV interfaces.
In order to use 3rd-party applications like DAVdroid or Thunderbird with FastMail, you need to generate an app password. Choose "Mail, calendars and contacts" access.
Choose "Login with email address" and enter your FastMail email address and the generated app password (see above).
Contact group method: groups are separate VCards