Compositional generalization–understanding unseen combinations of seen primitives–is an essential reasoning capability in human intelligence.The AI community mainly studies this capability by fine-tuning neural networks on lots of training samples, while it is still unclear whether and how in-context learning–the prevailing few-shot paradigm based on large language models–exhibits compositional generalization.In this paper, we present CoFe, a test suite to investigate in-context compositional generalization.We find that the compositional generalization performance can be easily affected by the selection of in-context examples, thus raising the research question what the key factors are to make good in-context examples for compositional generalization.We study three potential factors: similarity, diversity and complexity. Our systematic experiments indicate that in-context examples should be structurally similar to the test case, diverse from each other, and individually simple.Furthermore, two strong limitations are observed: in-context compositional generalization on fictional words is much weaker than that on commonly used ones; it is still critical that the in-context examples should cover required linguistic structures, even though the backbone model has been pre-trained on large corpus.We hope our analysis would facilitate the understanding and utilization of in-context learning paradigm.