  We have studied the positive-parity states of $^{40}$Ca using antisymmetrized
molecular dynamics (AMD) and the generator coordinate method (GCM). Imposing
two different kinds of constraints on the variational calculation, we have
found various kinds of $^{40}{\rm Ca}$ structures such as a deformed-shell
structure, as well as $\alpha$-$^{36}$Ar and $^{12}$C-$^{28}$Si cluster
structures. After the GCM calculation, we obtained a normal-deformed band and a
superdeformed band together with their side bands associated with triaxial
deformation. The calculated $B(E2)$ values agreed well with empirical data. It
was also found that the normal-deformed and superdeformed bands have a
non-negligible $\alpha$-$^{36}$Ar cluster component and $^{12}$C-$^{28}$Si
cluster component, respectively. This leads to the presence of an
$\alpha$-$^{36}$Ar higher-nodal band occurring above the normal-deformed band.
