When I have one group and the other group I leave

Before setting:
http://prntscr.com/fcj2qc

After the command to set a group:

http://prntscr.com/fcj36q

Groups disappear...

Use parent add instead of parent set then.

https://github.com/lucko/LuckPerms/wiki/Command-Usage#lp-usergroup-usergroup-parent-add