Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C5×C4⋊Dic3 | C2 | semidirect |
| 3. C5×#832 | C2 | semidirect |
| 4. C5×#830 | C2 | semidirect |
| 5. C5×#808 | C2 | semidirect |
| 16. #5034 | C5 | direct (N × H) |
| 34. C2×C4⋊Dic3 | C2×C5 | semidirect |
| 35. #832 | C2×C5 | semidirect |
| 36. #830 | C2×C5 | semidirect |
| 37. #808 | C2×C5 | semidirect |
| 120. C3×C5 | #481 | semidirect |
| 153. C5 | #5034 | direct (N × H) |
| 165. C3 | C5×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#121 | 2 |
| C2×C5×C4⋊Dic3 | 2 |
| C5×#832 | 2 |
| C5×#830 | 2 |
| C5×#808 | 2 |
| C5×#481 | 3 |
| #5034 | 5 |