[?] Obtain intersections and delete subset duplicates?

Questions
1

this output is the intersection of pairs of larger subsets:

{{13, 24, 68, 79}, {13, 24, 68, 79, 90}, {13, 24, 44, 48, 68,
79}, {13, 20, 44, 48, 68, 79}, {13, 24, 44, 55, 68, 79, 90}, {13,
24, 44, 68, 79}, {13, 20, 24, 44, 48, 55, 79}, {13, 20, 44, 55, 68,
79}, {13, 20, 44, 68, 79}, {13, 24, 48, 68, 79, 90}, {13, 24, 48,
68, 79}, {13, 24, 48, 55, 79, 90}, {20, 24, 44, 68, 90}, {13, 24,
79, 90}, {13, 20, 48, 68}, {20, 68, 79, 90}, {13, 20, 68}, {20, 24,
68}, {20, 68, 79}, {20, 24, 79}, {13, 20, 24}, {20, 24, 68,
90}, {24, 44, 68, 79}, {13, 24, 68}, {20, 24, 44, 79}, {13, 20, 44,
55, 79}, {13, 20, 79} Β…

now I would like to eliminate the intersections that are already present in other intersections, for example:

{13, 24, 68, 79} is already present in {13, 24, 68, 79, 90} and {13, 24, 44, 48, 68, 79}

{13, 24, 68, 79, 90} is already present in {13, 24, 44, 55, 68, 79, 90} Β…

how to do?

thanks

2

This recent WFR item could be useful:

https://resources.wolframcloud.com/FunctionRepository/resources/MinimalSubsets

It can be accessed as ResourceFunction["MinimalSubsets"]

β€” edit β€”

Actually you seem to want ResourceFunction["MaximalSubsets"]

https://resources.wolframcloud.com/FunctionRepository/resources/MaximalSubsets

β€”end edit β€”

3

For a description of the BCL algorithm used by @Carl Woll in those WFR functions, and other ways to solve the problem, check this MSE post.

4

You can even get a Wolfram Language implementation of BCL in one of the responses here