For Boards there, you need Jira Software, not just Jira Core.
Sub-tasks are part of the Core of Jira, not Software. You do not need boards to use sub-tasks. Just make sure there is a sub-task type in the project's issue-type scheme
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You can't create sub-tasks without the context of the parent it is going to be part of. So "create" can't do it.
Go to the issue that you want to break down and use "create sub-task" from the tools menu
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