Many task models have been proposed to express and analyze the behavior of real-time applications at different levels of precision. Most of them target sequential applications with no support for parallelism. The digraph task model is one of the most general ones, as it allows modeling arbitrary directed graphs (digraphs) for sequential job releases. In this paper, we extend the digraph task model to support intra-task parallelism. For the proposed parallel multi-mode digraph model, we derive sufficient schedulability tests and a dichotomic search to improve the test pessimism for a set of n tasks onto a heterogeneous single-ISA multi-core platform. To reduce the computational complexity of the schedulability test, we also propose heuristics for (i) partitioning parallel digraph tasks onto the heterogeneous cores, and (ii) assigning core operating frequencies to reduce the overall energy consumption, while meeting real-time constraints. The effectiveness of the proposed approach is validated with an exhaustive set of simulations.