Standard sequence subgroups in finite fields

In previous work, the authors describe certain configurations which give rise to standard and to non-standard subgroups for linear recurrences of order k=2k=2, while in subsequent work, a number of families of non-standard subgroups for recurrences of order k⩾2k⩾2 are described. Here we exhibit two infinite families of standard groups for k⩾2k⩾2.