Show that a group of order $70$ can not be simple.
I've tried to solve using Sylow theorem. I got $1, 5, 7, 35$ Sylow $2$-subgroups, $1$ sylow $5$-subgroup and $1$ sylow $7$-subgroup. Now the only choice is $35$ Sylow $2$-subgroups which would yield $36$ elements. Now we are left with $34$ elements but we have only one sylow $5$-subgroup and one sylow $7$-subgroup.
Why all the elements of sylow subgroups are not adding up to $70$?