mysql, select and sorting by group key + with first row that has that key in another column

I'm trying to make a select that outputs everything, but is sorted by a group column with a "header column" that matches said group column on another column. I have no idea how this type of query should be written. For example, I want the data sorted like this. id, unit, group, col2, col3, col4, col5 --------------------------------------------- 99, ZZX, null, test1, test7, test5, test 6, AAA-B, ZZZ, test1, test7, test5, test8 77, AAA-C, ZZX, test1, test7, test5, test9 101, ZZZ, null, test1, test7, test5, test 122, AAB-A, ZZZ, test1, test7, test5, test11 176, AAB-B, ZZZ, test1, test7, test5, test12 So basically, the unit should be sorted per each group key, but begins with the row that matches the group key. There are also rows with null for group, but are just header rows. You can even just tell me the high level, and I can write the query, I'm just not sure the best way to approach it.