Every time you sort a column in CORE, most of the screens remember that last sort order. So if you close the screen, refresh the screen, or log out from CORE and re-visit that screen, CORE remembers your sort order. It is done automatically in most screens.
In some screens, say Activity Items, sorting by the activity's code only sorts the main code, not the sub-codes that are underneath it. You can sort by Code or Sub-Code, but not both at the same time.