Jira (and the other Atlassian applications) don't have "system groups" as I suspect you are imagining them. Jira-users is a group, the same as any other group you choose to add and put people into.
You can grant access and permissions to any group(s) you want. For Jira, look first in "Manage Applications" - this lists the applications you have (Core, Software, Service Manangement) and what group(s) grant access to them. You will find you can add and remove groups from those permissions. These really are just about access to the applications, they don't tell you much more.
The second place to look is in "global permissions". This is a list of things like Administrators, being able to see other users, bulk edit permissions, and so-on. Again, you can add no, one or many groups to these.
My guess is you're thinking Jira-users is a "system group" because it has one or more of the permissions above, and it is a default group, created on installation and set up by default. There isn't actually anything special about it, you can use other groups and drop it completely if you want.
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