Order of G equal to 2k + 1mod2

Utilizing Theorem 0.3, notice that

202 = 2 * 101; 206 = 2 * 103; 210 = 2 * 105;.....; 398 = 2 * 199

and so all orders n = 2k+1 mod 2 can not be orders of simple groups. This eliminates half of all the even orders between 200 and 400.