# Classifying sorted sublists using union

I'm trying to classify a list according to its sorted sublists.

For example:

list = {{1, 1, 1}, {2, 1, 1}, {2, 2, 1}, {3, 2, 1}};
e1 = Table[{}, {i, 1, Length[list]}];
e2 = Table[{}, {i, 1, Length[list]}];
e3 = Table[{}, {i, 1, Length[list]}];
e4 = Table[{}, {i, 1, Length[list]}];
For[j = 1, j < Length[list] + 1, j++, tmp1 = Flatten@list[[j]];
Print[tmp1]
If[Length[Union[tmp1]] == 1, e1[[j]] = tmp1];
If[Length[Union[tmp1]] == 3, e4[[j]] = tmp1];];


In this manner I can classify the sublists of {1,1,1} and {3,2,1}, however it is not sufficient to classify {1,1,2} and {2,2,1}, how can both sublists be distinguished?

The criterion I wish to have is when the larger element in the sublist is larger or smaller than the other two.

Something like this?

list = {{1, 1, 1}, {2, 1, 1}, {2, 2, 1}, {3, 2, 1}};

g = GroupBy[list, {CountDistinct[#], Median[#] > Min[#]} &]
(*    <|{1, False} -> {{1, 1, 1}},
{2, False} -> {{2, 1, 1}},
{2, True}  -> {{2, 2, 1}},
{3, True}  -> {{3, 2, 1}}|>    *)

{e1, e2, e3, e4} = Lookup[g, {{1, False}, {2, False}, {2, True}, {3, True}}, {}];

e1
(*    {{1, 1, 1}}    *)

e2
(*    {{2, 1, 1}}    *)

e3
(*    {{2, 2, 1}}    *)

e4
(*    {{3, 2, 1}}    *)

• it does the job, however I wish to use the classification to separate the values into separate lists. some of the lists hold all the criterions (like this example) and some not. In short, if the list were list={{{1,1,1},{2,1,1},{2,2,1},{3,2,1}},{{1,1,1},{2,1,1}}}, how would you automatically classify the sublists and move them into e1, e2, e3 etc..? May 2, 2021 at 16:25
• see updated answer for assignment to the e1,e2,e3,e4 variables. May 2, 2021 at 16:35