MySQL 5.6

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create table your_table (
 RunNumber int, 
 `Group` varchar(30), 
 Dataset varchar(30), 
 Total int
);
insert into your_table 
(RunNumber, 	`Group`, 	Dataset, 	Total) 
values
(1, 	'Group1', 	'Dataset A', 	10), 
(1, 	'Group1', 	'Dataset A', 	20), 
(2, 	'Group1', 	'Dataset A', 	30), 
(2, 	'Group2', 	'Dataset A', 	15), 
(1, 	'Group1', 	'Dataset B', 	5), 
(1, 	'Group2', 	'Dataset B', 	10), 
(1, 	'Group3', 	'Dataset A', 	30), 
(2, 	'Group3', 	'Dataset A', 	30), 
(1, 	'Group1', 	'Dataset C', 	15),
(1, 	'Group2', 	'Dataset C', 	50), 
(2, 	'Group2', 	'Dataset C', 	70), 
(2, 	'Group2', 	'Dataset C', 	90);

Records: 12  Duplicates: 0  Warnings: 0


--
-- IN with tupple on summary
--
SELECT * 
FROM your_table
WHERE (`Group`, Dataset, RunNumber) IN (
    SELECT `Group`, Dataset, MAX(RunNumber) AS MaxRunNumber
    FROM your_table
    GROUP BY `Group`, Dataset
  )
ORDER BY `Group`, Dataset;


RunNumber
Group
Dataset
Total


2
Group1
Dataset A
30

1
Group1
Dataset B
5

1
Group1
Dataset C
15

2
Group2
Dataset A
15

1
Group2
Dataset B
10

2
Group2
Dataset C
70

2
Group2
Dataset C
90

2
Group3
Dataset A
30


--
-- LEFT JOIN on bigger
--
SELECT t.* 
FROM your_table t
LEFT JOIN your_table t2
  ON t2.`Group` = t.`Group`
 AND t2.Dataset = t.Dataset
 AND t2.RunNumber > t.RunNumber
WHERE t2.RunNumber IS NULL
ORDER BY t.`Group`, t.Dataset;


RunNumber
Group
Dataset
Total


2
Group1
Dataset A
30

1
Group1
Dataset B
5

1
Group1
Dataset C
15

2
Group2
Dataset A
15

1
Group2
Dataset B
10

2
Group2
Dataset C
70

2
Group2
Dataset C
90

2
Group3
Dataset A
30


--
-- where NOT EXISTS on bigger
--
SELECT * 
FROM your_table t
WHERE NOT EXISTS (
  SELECT 1
  FROM your_table t2
  WHERE t2.`Group` = t.`Group`
    AND t2.Dataset = t.Dataset
    AND t2.RunNumber > t.RunNumber
)
ORDER BY `Group`, Dataset;


RunNumber
Group
Dataset
Total


2
Group1
Dataset A
30

1
Group1
Dataset B
5

1
Group1
Dataset C
15

2
Group2
Dataset A
15

1
Group2
Dataset B
10

2
Group2
Dataset C
70

2
Group2
Dataset C
90

2
Group3
Dataset A
30


--
-- Emulating DENSE_RANK = 1 with variables
-- Works also in 5.x
--
SELECT RunNumber, `Group`, Dataset, Total
FROM
(
  SELECT 
    @rnk:=IF(@ds=Dataset AND @grp=`Group`, IF(@run=RunNumber, @rnk, @rnk+1), 1) AS Rnk
  , @grp := `Group` as `Group`
  , @ds := Dataset as Dataset
  , @run := RunNumber as RunNumber
  , Total
  FROM your_table t
  CROSS JOIN (SELECT @grp:=null, @ds:=null, @run:=null, @rnk := 0) var
  ORDER BY `Group`, Dataset, RunNumber DESC
) q
WHERE Rnk = 1
ORDER BY `Group`, Dataset;


RunNumber
Group
Dataset
Total


2
Group1
Dataset A
30

1
Group1
Dataset B
5

1
Group1
Dataset C
15

2
Group2
Dataset A
15

1
Group2
Dataset B
10

2
Group2
Dataset C
70

2
Group2
Dataset C
90

2
Group3
Dataset A
30


--
-- DENSE_RANK = 1
-- MySql 8 and beyond. 
--
SELECT *
FROM
(
  SELECT *
  , DENSE_RANK() OVER (PARTITION BY `Group`, Dataset ORDER BY RunNumber DESC) AS rnk
  FROM your_table
) q
WHERE rnk = 1
ORDER BY `Group`, Dataset;

You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '(PARTITION BY `Group`, Dataset ORDER BY RunNumber DESC) AS rnk
  FROM your_table' at line 9


--
-- ROW_NUMBER = 1
-- MySql 8 and beyond. 
--
SELECT *
FROM
(
  SELECT *
  , ROW_NUMBER() OVER (PARTITION BY `Group`, Dataset ORDER BY RunNumber DESC) AS rn
  FROM your_table
) q
WHERE rn = 1
ORDER BY `Group`, Dataset;

You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '(PARTITION BY `Group`, Dataset ORDER BY RunNumber DESC) AS rn
  FROM your_table
' at line 9


--
-- Group by, order also by RunNumber
-- Won't work when sql_mode has only_full_group_by
-- And gives wrong results anyway
--
SELECT * 
FROM your_table
GROUP BY `Group`, Dataset
ORDER BY `Group`, Dataset, RunNumber DESC;


RunNumber
Group
Dataset
Total


1
Group1
Dataset A
10

1
Group1
Dataset B
5

1
Group1
Dataset C
15

2
Group2
Dataset A
15

1
Group2
Dataset B
10

1
Group2
Dataset C
50

1
Group3
Dataset A
30
RunNumber	Group	Dataset	Total
2	Group1	Dataset A	30
1	Group1	Dataset B	5
1	Group1	Dataset C	15
2	Group2	Dataset A	15
1	Group2	Dataset B	10
2	Group2	Dataset C	70
2	Group2	Dataset C	90
2	Group3	Dataset A	30