Concerned that subdomain blog.yourdomain.com is an SEO problem? Read this!
This is a bit of a religious debate. You can find many articles for and against. Please look at the year the article was published. The bottom line is Google is smart enough to understand that blog.yourdomain.com is part of yourdomain.com. It will make no difference to SEO for your SEO and is not a immediate concern.
In order to move your blog to a "/blog" directory and keep it on HubSpot, it may require that your website is on HubSpot, e.g. the www. is on HubSpot. Please understand that "www" is also a subdomain. And then you redirect the unqualified domain to the qualified subdomain "www" as part of the implementation. https://app.hubspot.com/settings/domains
Moving blogs to a subdomain is a common concern, and one we've raised ourselves too.
It seems no one is able to agree on whether subdomains are ranked negatively versus your main domain and, if they are, by how much. The consensus among the HubSpot community is that the known benefits outweigh the possible, and mostly unknown, drawbacks.
We do have it on good authority from an SEO expert that any impact is negligible and, if you do want to mitigate it, best practice is to have a single subdomain for your blog, landing pages, and emails. For example:
(This is how we'd set this up for you, though 'info'. can be whatever word you want it to be of course!)
This and obviously setting up all the 301 redirects are key to losing as little SEO juice as possible.
Best article ever, and an excerpt below. The most relevant bit to answer your question is here: https://webmasters.googleblog.com/2011/08/reorganizing-internal-vs-external.html. I'd tend to believe Google!
Myth: Using Subdomains is Bad
HubSpot blogs are hosted on subdomains (blog.example.com), which can be a concern for some marketers. But in 2011, Google reorganised its interpretation of internal and external links and announced that subdomains (previously categorised as external links, and which weren’t providing any SEO benefits to your website) would be categorised as internal links. Today, this means believing that using a subdomain for your blog is bad for SEO is nothing more than SEO myth. Google is smart enough to know both www.strategic-ic.co.uk and blog.strategic-ic.co.uk are tied to the same site.