您可以将GroupBy.agg与DataFrameGroupBy.idxmax和DataFrameGroupBy.idxmin一起用于按最大和最小Score的索引，并使用DataFrame.loc选择匹配行，使用DataFrame.add_prefix将Subject转换为索引，然后连接在一起：

df1 = df.groupby('Subject', sort=False)['Score'].agg(['idxmin','idxmax'])

df11 = df.loc[df1['idxmax']].set_index('Subject').add_prefix('Best')
df22 = df.loc[df1['idxmin']].set_index('Subject').add_prefix('Worst')

df = df11.join(df22).reset_index()
print (df)
   Subject  BestScore  BestName  WorstScore WorstName
0     Math         44  Student3          27  Student1
1  History         50  Student1          10  Student3
2  Science         43  Student2           7  Student1

或者将Name转换为索引，这样您就可以将GroupBy.agg与DataFrameGroupBy.idxmax、DataFrameGroupBy.idxmin以及min一起使用max函数：

df = (df.set_index('Name')
        .groupby('Subject', as_index=False, sort=False)
        .agg(BestScr=('Score', 'max'),
            BestStud= ('Score', 'idxmax'),
            WorstScr=('Score', 'min'),
            WorstStud=('Score', 'idxmax'))
)
print (df)
   Subject  BestScr  BestStud  WorstScr WorstStud
0     Math       44  Student3        27  Student3
1  History       50  Student1        10  Student1
2  Science       43  Student2         7  Student2

您可以使用自定义groupby.agg：

(df.groupby('Subject', as_index=False, sort=False)
    .agg(**{'BestScr': ('Score', 'max'),
            'BestStd': ('Score', lambda s: df.loc[s.idxmax(), 'Name']),
            'WorstScr': ('Score', 'min'),
            'WorstStd': ('Score', lambda s: df.loc[s.idxmin(), 'Name']),
                            })
)

输出：

Subject  BestScr   BestStd  WorstScr  WorstStd
0     Math       44  Student3        27  Student1
1  History       50  Student1        10  Student3
2  Science       43  Student2         7  Student1

另一种可能的解决方案基于pandas.DataFrame.unstack：

out = df.set_index(['Subject', 'Name'])['Score'].unstack()
out['BestScr'], out['BestStud'], out['WorstScr'], out['WorstStud'] = out.max(
    1), out.idxmax(1), out.min(1), out.idxmin(1)
out = out.drop(columns=out.columns[out.columns.str.startswith('Student')])
out = out.rename_axis(None, axis=1).reset_index()

输出：

Subject  BestScr  BestStud  WorstScr WorstStud
0  History     50.0  Student1      10.0  Student3
1     Math     44.0  Student3      27.0  Student1
2  Science     43.0  Student2       7.0  Student1