We find all primitive subgroups of $GL(8,19)$ with parameters $e=8$, $a=1$. Since in this case $b=2$ does not divide $a=1$, Lemma 5.3 implies that there exists two 
#nonconjugate subgroups $F_1$ and $F_2$ such that $N_{GL(8,19)}(F_1)/F_1\simeq O^+(6,2)$, while $N_{GL(8,19)}(F_2)/F_2\simeq O^-(6,2)$. This log-file contains
#calculations for $F_1$.
#In the notations of Theorem 5.1, if $H$ is a primitive solvable subgroup, then it possesses a series


$$1<U<F<A<G.$$

#$U$ is cyclic of order $18$, $F$ is of type $2^{1+6}$ is such that $N_{GL(8,11)}(F)/F\simeq O^+(6,2)$, and $G=A$. First we take the list of generators of solvable 
#subgroups of $GL(8,19)$, containing all maximal primitive subgroups of $GL(8,19)$ from the file   generators-GL(8,19)+.txt.


#Now we run the following loop. Each entry of the list result has three items: the first is the
#number of the group in the list genS, the second is the order of the group, and the third is the order of the stabilizer of v in H. 
#If the order of the stabilizer is 1, then |v^H=|H| and Corollary 2.5 can be applied.


gap> z:=Z(19);;
gap> v:=[z,z^13,z^2,0*z,z^17,z^5,z^7,z^11];;
gap> result:=[];;
gap> for j in [1..Size(gens)] do
> H:=Subgroup(GL(8,19),gens[j]);;
> n:=Size(H);;
> m:=Size(v^H);
> result[j]:=[j,n,n/m];
> Display(result[j]);
> od;
gap> result;
[ 2, 11520, 1 ]
[ 3, 11520, 1 ]
[ 4, 11520, 1 ]
[ 5, 16128, 1 ]
[ 6, 17280, 1 ]
[ 7, 20736, 1 ]
[ 8, 20736, 1 ]
[ 9, 20736, 1 ]
[ 10, 20736, 1 ]
[ 11, 23040, 1 ]
[ 12, 23040, 1 ]
[ 13, 23040, 1 ]
[ 14, 34560, 1 ]
[ 15, 34560, 1 ]
[ 16, 34560, 1 ]
[ 17, 48384, 1 ]
[ 18, 41472, 1 ]
[ 19, 41472, 1 ]
[ 20, 41472, 1 ]
[ 21, 41472, 1 ]
[ 22, 41472, 1 ]
[ 23, 41472, 1 ]
[ 24, 41472, 1 ]
[ 25, 41472, 1 ]
[ 26, 46080, 1 ]
[ 27, 69120, 1 ]
[ 28, 69120, 1 ]
[ 29, 69120, 1 ]
[ 30, 82944, 1 ]
[ 31, 82944, 1 ]
[ 32, 82944, 1 ]
[ 33, 82944, 1 ]
[ 34, 82944, 1 ]
[ 35, 82944, 1 ]
[ 36, 138240, 1 ]
[ 37, 165888, 1 ]