Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #91992 | C2 | direct (N × H) |
| 3. C2×#6758 | C2 | semidirect |
| 4. C2×D5⋊(C3⋊C8) | C2 | semidirect |
| 13. #6758 | C22 | semidirect |
| 14. D5⋊(C3⋊C8) | C22 | semidirect |
| 71. C2×C3×C5 | #131 | semidirect |
| 98. C3×C5 | C2×#131 | semidirect |
| 105. C2×C5 | #948 | semidirect |
| 118. C2×C3 | #4133 | semidirect |
| 120. C5 | C2×#948 | semidirect |
| 127. C3 | C2×#4133 | semidirect |
| 129. C2 | #91992 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| #91992 | 2 |
| C2×#6758 | 2 |
| C2×D5⋊(C3⋊C8) | 2 |
| C2×#4133 | 3 |
| C2×#948 | 5 |