Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. C5×#819 | C2 | semidirect |
| 11. #5125 | C5 | direct (N × H) |
| 24. #819 | C2×C5 | semidirect |
| 76. C3×C5 | #430 | semidirect |
| 96. C5 | #5125 | direct (N × H) |
| 103. C3 | C5×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M16 | 2 |
| C2×C5×#208 | 2 |
| C5×#819 | 2 |
| C5×#430 | 3 |
| #5125 | 5 |