  By using a relativistic linear augmented-plane-wave method with the
one-electron potential in the local-density approximation, we investigate
energy band structures and the Fermi surfaces of transuranium compounds
NpTGa$_5$, PuTGa$_5$, and AmCoGa$_5$ with transition metal atoms T. It is found
in common that the energy bands in the vicinity of the Fermi level are mainly
due to the large hybridization between $5f$ and Ga $4p$ electrons. For
PuTGa$_5$, we observe several cylindrical sheets of Fermi surfaces with large
volume for T=Co, Rh, and Ir. The de Haas-van Alphen (dHvA) frequencies are
theoretically estimated for PuCoGa$_5$. It is also found that the Fermi
surfaces of NpFeGa$_5$, NpCoGa$_5$, and NpNiGa$_5$ are similar to those of
UCoGa$_5$, UNiGa$_5$, and PuCoGa$_5$, respectively, except for small details.
For AmCoGa$_5$, the Fermi surfaces are found to consist of large cylindrical
electron sheets and small closed hole sheets, similar to PuCoGa$_5$. The
similarity is basically understood by the change of electron numbers inside the
Fermi surfaces on the basis of a rigid-band picture. We discuss our theoretical
Fermi surfaces with the dHvA experimental results on NpTGa$_5$.
