Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. D8×D15 | C2 | semidirect |
| 2. C3×C5×D16 | C2 | semidirect |
| 3. #91110 | C2 | semidirect |
| 4. D240 | C2 | semidirect |
| 5. C16×D15 | C2 | semidirect |
| 8. C3×C5×D8 | C22 | semidirect |
| 10. D120 | C22 | semidirect |
| 12. C3×C5×C16 | C22 | semidirect |
| 13. C3⋊#672 | C22 | semidirect |
| 16. C5×D16 | D3 | semidirect |
| 28. C3×D16 | D5 | semidirect |
| 33. C5×D8 | C2×D3 | semidirect |
| 37. C5×C16 | C2×D3 | semidirect |
| 47. C3×D8 | C2×D5 | semidirect |
| 51. C3×C16 | C2×D5 | semidirect |
| 63. D16 | D15 | direct (N × H) |
| 68. D15 | D16 | direct (N × H) |
| 85. D8 | C2×D15 | semidirect |
| 88. C16 | C2×D15 | semidirect |
| 89. C3×C5 | C2×D16 | semidirect |
| 111. C5 | D3×D16 | semidirect |
| 118. C3 | D5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D15 | 2 |
| C3×C5×D16 | 2 |
| #91110 | 2 |
| D240 | 2 |
| C16×D15 | 2 |
| D5×D16 | 3 |
| D3×D16 | 5 |