Can subfolders be synchronized using the CardDAV protocol?

No, sync.blue® and the CardDAV protocol itself do not support subfolders in the traditional sense.

CardDAV is a protocol for accessing contact information on a server. While it is possible to access multiple address books per user and manage contacts within those address books, the protocol itself does not support a specific subfolder structure as you would know it from a file system.

Some other implementations of CardDAV may allow organizing contacts into groups that can act as a kind of "subfolder." However, sync.blue® does not yet support this group feature. With sync.blue®, the entire primary address book is always synchronized, and there is currently no way to synchronize or select specific groups.

Please vote for this planned feature here.