@vv 

It seems that you misunderstood my question, I just updated my expression.

@mmcdara 

Hello, I don't know if my question is not clear. Maple currently seems to be able to draw only subgroup lattices of Galois groups. I'm more interested in knowing what field extension each subgroup represents rather than the exact appearance of the graph. But I don't know which field extension should be used to rename the vertex. For example, what is the extension relation of x⁵+15x+44?

@acer Elegant solution. Thanks very much。

@vv Confused me some days, It seems to work on Finitely Presented Group. But not for Permutation Groups? This is too obscure for me

@vv Care to elaborate? How can I generate all cosets of S₁₀ by generators? Simple algorithms?

@vv Then I get a different output:

But I don't want to change the original output, I just want to copy the original output normally

@vv Same result:

is(Elements(g1) = Elements(g2))

true

@tomleslie Oh god, I'm in Maple 2021.0

`Standard Worksheet Interface, Maple 2021.0, Windows 10, March 5 2021 Build ID 1523359`

@Carl Love Work now...

@vv I get same result in Worksheet: