What is the list of conjugation forms that occurred to 送る in the sentence
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This 送れて is the te-form of the "potential form" 送れる of 送る.
The potential form is sometimes used to mean that something was done successfully
I (successfully) sent the email (lit. I was able to send the email)
In the sentence
the te-form (which together with いる may be used to express a state) is used to express a state of "not having been sent (successfully)", so
I was under the impression that I replied [to the email], but it hadn't been successfully sent
It's the past-negative-potential-teiru form of 送る. This (て)いる refers to the continuation of state.
The sentence means "I thought I replied, but [I noticed] I hadn't sent [the mail] (successfully)".