Frequently Asked Question
Go to: https://intune.microsoft.com/#home then users on the left, then search for the username you want to add to groups in the right most search box.
click on their name, then go to Groups > add memberships
Then do a search for ULS (assuming your group name starts with ULS) and you should be able to add them to any groups you are the owner of and any groups you aren't the owner of won't have a checkbox next to them.
On the previous page where you are looking at their list of groups you can also remove membership by checking the box next to their name and then clicking remove membership at the top, this will only work for groups that you are the owner of.