  Adinkras are graphs that encode a supersymmetric representation's
transformation laws that have been reduced to one dimension, that of time. A
goal of the supersymmetry ``genomics'' project is to classify all 4D,
$\mathcal{N}=1$ off-shell supermultiplets in terms of their adinkras.
In~previous works, the genomics project uncovered two fundamental isomer
adinkras, the cis- and trans-adinkras, into which all multiplets investigated
to date can be decomposed. The number of cis- and trans-adinkras describing a
given multiplet define the isomer-equivalence class to which the multiplet
belongs. A further refining classification is that of a supersymmetric
multiplet's holoraumy: the commutator of the supercharges acting on the
representation. The one-dimensionally reduced, matrix representation of a
multiplet's holoraumy defines the multiplet's holoraumy-equivalence class.
Together, a multiplet's isomer-equivalence and holoraumy-equivalence classes
are two of the main characteristics used to distinguish the adinkras associated
with different supersymmetry multiplets in higher dimensions. This paper
focuses on two matter gravitino formulations, each with 20 bosonic and 20
fermionic off-shell degrees of freedom, analyzes them in terms of their isomer-
and holoraumy-equivalence classes, and compares with non-minimal supergravity
which is also a 20x20 multiplet. This analysis fills a missing piece in the
supersymmetry genomics project, as now the isomer-equivalence and
holoraumy-equivalence for representations up to spin two in component fields
have been analyzed for 4D, $\mathcal{N}=1$ supersymmetry. To handle the
calculations of this research effort, we have used the Mathematica software
package called Adinkra.m. This package is open-source and available for
download at a GitHub Repository. Data files associated with this paper are also
published open-source at a Data Repository also on GitHub.
