  We study supersymmetric $AdS_n\times \Sigma^{7-n}$, $n=2,3,4,5$ solutions in
seven-dimensional maximal gauged supergravity with $CSO(p,q,5-p-q)$ and
$CSO(p,q,4-p-q)$ gauge groups. These gauged supergravities are consistent
truncations of eleven-dimensional supergravity and type IIB theory on
$H^{p,q}\circ T^{5-p-q}$ and $H^{p,q}\circ T^{4-p-q}$, respectively. Apart from
recovering the previously known $AdS_n\times \Sigma^{7-n}$ solutions in $SO(5)$
gauge group, we find novel classes of $AdS_5\times S^2$, $AdS_3\times S^2\times
\Sigma^2$ and $AdS_3\times CP^2$ solutions in non-compact $SO(3,2)$ gauge group
together with a class of $AdS_3\times CP^2$ solutions in $SO(4,1)$ gauge group.
In $SO(5)$ gauge group, we extensively study holographic RG flow solutions
interpolating from the $SO(5)$ supersymmetric $AdS_7$ vacuum to the
$AdS_n\times \Sigma^{7-n}$ fixed points and singular geometries in the form of
curved domain walls with $Mkw_{n-1}\times \Sigma^{7-n}$ slices. In many cases,
the singularities are physically acceptable and can be interpreted as
non-conformal phases of $(n-1)$-dimensional SCFTs obtained from twisted
compactifications of $N=(2,0)$ SCFT in six dimensions. In $SO(3,2)$ and
$SO(4,1)$ gauge groups, we give a large number of RG flows between the new
$AdS_n\times \Sigma^{7-n}$ fixed points and curved domain walls while, in
$CSO(p,q,4-p-q)$ gauge group, RG flows interpolating between asymptotically
locally flat domain walls and curved domain walls are given.
