I got Four for 196 with
(.).*\1.\1.*\1
and Order for 156 with ^a*b*c*d*e*f*g*h*i*j*k*l*m*n*o*p*q*r*s*t*u*v*w*x*y*z*$ (.).*\1.\1.*\1
and Order for 156 with ^a*b*c*d*e*f*g*h*i*j*k*l*m*n*o*p*q*r*s*t*u*v*w*x*y*z*$ ^[^o].....?$
Probably not what was wanted, but it works (or maybe it was to trick people onto a false path) ^[a-g][^airn]|[fs].*y$|ot$I must say Regex golf is a lot of fun.
^.{5}[^e]?$198 points
^<.*>$|^<<.*>>$|^<<<.*>>>$ ^(<(<(<(<(<(<<>>)*>)*>)*>)*>)*>)*$
If we had named captures: ^(((?<P><)|(?<-P>>))*(?(P)(?!)))$[<>]{28}
(.)(.\1){3}
Order: 168 ^a*b*c*d*e*f*g*h*i*l*m*n*o*p*r*s*t*w*y*z*$
(You just didn't remove unused letters.) ^[a-g]*[^a-g]*$ ^([ab][c-gio][^d]|c[ehlo]|d|f[il]|gh|mo)
Not as clever as you guys though! ^[a-i]*[l-z]*$(.)...\1.\1