some dummy data:
id group_id name score
1 A Tom 20
2 B Jone 17
3 B Jack 19
4 C Tim 18
select group_id from table order by score
group_id
B
C
B
A
select distinct group_id from (select group_id from table order by score ) t
group_id
A
B
C
select group_id from (select group_id from table order by score ) t group by group_id
group_id
B
C
A
I believe this is what you want:
select group_id
from table
group by group_id
order by min(score);