Linq order by, group by and order by each group?

Sure:

var query = grades.GroupBy(student => student.Name)
                  .Select(group => 
                        new { Name = group.Key,
                              Students = group.OrderByDescending(x => x.Grade) })
                  .OrderBy(group => group.Students.First().Grade);

Note that you can get away with just taking the first grade within each group after ordering, because you already know the first entry will be have the highest grade.

Then you could display them with:

foreach (var group in query)
{
    Console.WriteLine("Group: {0}", group.Name);
    foreach (var student in group.Students)
    {
        Console.WriteLine("  {0}", student.Grade);
    }
}

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