Use of GROUP BY twice in MySQL

Question

My table looks like this.

Location    Head    Id  IntTime
1           AMD     1   1
2           INTC    3   3
3           AMD     2   2
4           INTC    4   4
5           AMD2    1   0
6           ARMH    5   1
7           ARMH    5   0
8           ARMH    6   1
9           AAPL    7   0
10          AAPL    7   1

Location is the primary key. I need to GROUP BY Head and by Id and when I use GROUP BY, I need to keep the row with the smallest IntTime.

After the first GROUP BY Id, I should get (I keep the smallest IntTime)

Location    Head    Id  IntTime
2           INTC    3   3
3           AMD     2   2
4           INTC    4   4
5           AMD2    1   0
7           ARMH    5   0
8           ARMH    6   1
9           AAPL    7   0

After the second GROUP BY Head, I should get (I keep the smallest IntTime)

Location    Head    Id  IntTime
2           INTC    3   3
3           AMD     2   2
5           AMD2    1   0
7           ARMH    5   0
9           AAPL    7   0

When I run the following command, I keep the smallest IntTime but the rows are not conserved.

SELECT Location, Head, Id, MIN(IntTime) FROM test 
GROUP BY Id

Also, to run the second GROUP BY, I save this table and do again

SELECT Location, Head, Id, MIN(IntTime) FROM test2 
GROUP BY Head

Is there a way to combine both commands?

[Edit: clarification] The result should not contain two Head with the same value or two Id with the same value. When deleting those duplicates, the row with the smallest IntTime should be kept.

Answer 1

This query returns the exact final results you're looking for (example):

SELECT `final`.*
FROM `tableName` AS `final`
JOIN (
    SELECT `thead`.`Id`, `Head`, MIN(`intTime`) AS `min_intTime`
    FROM `tableName` AS `thead`
    JOIN (
        SELECT `Id`, MIN(intTime) as min_intTime
        FROM `tableName` AS `tid`
        GROUP BY `Id`
    ) `tid`
    ON `tid`.`Id` = `thead`.`Id`
    AND `tid`.`min_intTime` = `thead`.`intTime`
    GROUP BY `Head`
) `thead`
ON `thead`.`Head` = `final`.`Head`
AND `thead`.`min_intTime` = `final`.`intTime`
AND `thead`.`Id` = `final`.`Id`

How it works

The innermost query groups by Id, and returns the Id and corresponding MIN(intTime). Then, the middle query groups by Head, and returns the Head and corresponding Id and MIN(intTime). The final query returns all rows, after being narrowed down. You can think of the final (outermost) query as a query on a table with only the rows you want, so you can do additional comparisons (e.g. WHERE final.intTime > 3).