  Infinite-component Chern-Simons-Maxwell theories with a periodic $K$ matrix
provide abundant examples of gapped and gapless, foliated and non-foliated
fracton orders. In this paper, we study the ground state degeneracy of these
theories. We show that the ground state degeneracy exhibit various patterns as
a function of the linear system size -- the size of the $K$ matrix. It can grow
exponentially or polynomially, cycle over finitely many values, or fluctuate
erratically inside an exponential envelope. We relate these different patterns
of the ground state degeneracy with the roots of the ``determinant
polynomial'', a Laurent polynomial, associated to the periodic $K$ matrix.
These roots also determine whether the theory is gapped or gapless. Based on
the ground state degeneracy, we formulate a necessary condition for a gapped
theory to be a foliated fracton order.
