Hi @candydrabek,
In order to select a group of students regularly, you would need to create a course section containing those students. (They could still be in the full course section; students can be in multiple sections at once.) Contrary to its name, Groups does not provide this functionality, as it is intended for collaborative work.
Some institutions do not allow users to create sections, so you would need to check with yours. Also, if you use a separate Student Information System and need to sync grades to it, you may not be able to sync the smaller sections. (For example, Aeries does not recognize sections created by the user, only those it created and "pushed" to Cavnas.) If your SIS has this limitation, you would need to input the grades manually in the SIS instead of using the "Sync to SIS" feature.
If you are allowed to add sections and don't need to worry about an SIS, you can create sections and then select an entire section using the method described by @DrNufer .
How do I add a section to a course as an instructor?
How do I assign an assignment to a course section?