Lattice Diagrams of Subgroups Part 1 

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I am in kenya bro please tell address

Depends on whether you are using additive or multiplicative notation. It's confusing with these examples because you have 1 = {0} = in these examples. He does mention at one point that the symbol "1" he is using to denote the trivial group is a "fancy 1" and not the same 1 he is using to denote the member of Z_n that would generate the whole group.

Geometrical intuition. But can you prove geometrical intuition?

Hmm I'm not sure I could do it myself yet but it feels like an important intuition to formalise

U(8) ki latice diagram ela rastaru

In a diagram, you only draw lines between two elements if there is no other element in between them.