Butterflies are invertebrates, not vertebrates. They are insects in the order Lepidoptera, which sits in phylum Arthropoda—the large group of animals OpenStax Biology 2e describes as invertebrates with a chitinous exoskeleton and jointed appendages rather than a backbone.
OpenStax lists butterflies among everyday Hexapoda (six-legged insects), alongside ants, beetles, and flies. The same classification appears in the U.S. Integrated Taxonomic Information System (ITIS), which places Lepidoptera under Arthropoda and Insecta.
Source: Superphylum Ecdysozoa: Arthropods — OpenStax Biology 2e