Pandas Dataframe Regrouping

I have the following pandas dataframe, it shows the coordinate where there is a step in a tower, including z-min, and z-max:

import pandas as pd

names = ['T1', 'T2', 'T2', 'T1', 'T1']
coord = [0, 0, 5, 50, 70]


df = pd.DataFrame([names , coord ], index=['Name', 'Cord']).T  

Resulting in:

  Name Cord
0    T1   0
1    T2   0
2    T2   5
3    T1   50
4    T1   70

For every unique coordinate, I would like to regroup all towers whose z-max is smaller or equal to that coordinate. Hence:

     Name      Cord
0    T1,T2      0
1    T1,T2      5
2    T1         50
3    T1         70

I was wondering if you see a way of how to do it?

What I have done so far:

1. group by unique coordinate

   import numpy as np
   
   g = df.groupby('Cord')['Name'].apply(lambda x: list(np.unique(x)))
   

I get:

Cord
0     [T1, T2]
5         [T2]
50        [T1]
70        [T1]

... but for the rest, it would be nice to get some hints. Thanks!

EDIT: The proposed answer does not work for the special case that the z-mins of the two towers are not the same:

import pandas as pd

names = ['T1', 'T2', 'T2', 'T1', 'T1']
coord = [0, 5, 10, 50, 70]


df = pd.DataFrame([names , coord ], index=['Name', 'Cord']).T