1. The problem statement, all variables and given/known data Prove that the octic group [tex] D_4[/tex] has no subgroups of order, 3, 5, 6 and 7. I would appreciate any help on this one. Thanx in advance! 2. Relevant equations 3. The attempt at a solution I usually have at least an idea on how to start about proving things, but lol.. about this one i really have no clue how to start. I think i have to use proof by contradicton, but really don't know how to go about it. I read somewhere that the octic group, since it is of order 8 it has only subgroups of the order of the factors of 8, that is 1,2,4 and 8, but there was not much about it, so i didn't understand a damn thing, there wasn't any proof about it or any further explanation. I also looked at my book, it seems like i can find nothing that would relate somehow to proving this. We haven't worked that much with the order of groups, we havent done yet the lagrange theorem, or how's it called.