  Measurements of the substructure of top-quark jets are presented, using 140
fb$^{-1}$ of 13 TeV $pp$ collision data recorded with the ATLAS detector at the
LHC. Top-quark jets reconstructed with the anti-$k_{t}$ algorithm with a radius
parameter $R=1.0$ are selected in top-quark pair ($t\bar{t}$) events where one
top quark decays semileptonically and the other hadronically, or where both top
quarks decay hadronically. The top-quark jets are required to have transverse
momentum $p_\mathrm{T} > 350$ GeV, yielding large samples of data events with
jet $p_\mathrm{T}$ values between 350 and 600 GeV. One- and two-dimensional
differential cross-sections for eight substructure variables, defined using
only the charged components of the jets, are measured in a particle-level phase
space by correcting for the smearing and acceptance effects induced by the
detector. The differential cross-sections are compared with the predictions of
several Monte Carlo simulations in which top-quark pair-production quantum
chromodynamic matrix-element calculations at next-to-leading-order precision in
the strong coupling constant $\alpha_\mathrm{S}$ are passed to leading-order
parton shower and hadronization generators. The Monte Carlo predictions for
measures of the broadness, and also the two-body structure, of the top-quark
jets are found to be in good agreement with the measurements, while variables
sensitive to the three-body structure of the top-quark jets exhibit some
tension with the measured distributions.
