When looking into the popup in the breadcrumb of the lastBuild of a particular job, there is a link to the console of the last build (GOOD). See for example, the popup of the breadcrumb in https://buildhive.cloudbees.com/job/cgeo/job/c-geo-opensource/lastBuild/

And there is also a link to the lastBuild console in the popup of the lastBuild permalink in this job page (GOOD).
See for example, the "good.png" attached screenshot.

But in some other job (log file larger than 200000 probably), there is no link to the console of the last build in the breadcrumb of the lastBuild page (BAD).
See for example, the popup of the breadcrumb in https://buildhive.cloudbees.com/job/Atmosphere/job/atmosphere/lastBuild/

And in the job page of the same job, there is no link to the lastBuild console in the popup of the lastBuild permalink in the same job page (BAD).
See for exampe, the "BAD.png" attached screenshot.