Oly subset Group if element within a columns are all present within a list and nothing else in pandas

I have a dataframe such as :

The_list=["A","B","D"]

Groups Values
G1     A
G1     B
G1     C
G1     D
G2     A
G2     B
G2     A
G2     D
G3     A
G3     D
G4     Z
G4     D
G4     E
G4     C
G5     A
G5     B
G5     D

And I would like only to subset Groups where Values element are all within The_list, and that not other element are within that group that are not present within The_list.

Here I should only subset then :

Groups Values
G2     A
G2     B
G2     A
G2     D
G5     A
G5     B
G5     D

So far I tried :

df.loc[df.Values.str.contains["A" & "B" & "D"].groupby(df.Groups)]

>Solution :

You can use pandas.groupby on column Groups then check set each values of group with set the_list and return all rows that groups have True values:

The_list=["A","B","D"]
mask_rows = df.groupby('Groups')['Values'].transform(
    lambda x : set(x) == set(The_list)
)
print(df[mask_rows])

Output:

Groups Values
G2     A
G2     B
G2     A
G2     D
G5     A
G5     B
G5     D