Number of maximal cliques in a ($2C_4$, $C_5$, $P_5$)-free graph
The famous graph (the complement of the disjoint union of $n/3$ triangles) with $3^{n/3}$ maximal cliques is $K_1 \cup K_2$-free, and thus has none of $2C_4$, $C_5$, $P_5$ as an induced subgraph.
https://doi.org/10.1007/BF02760024