Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 110 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×C3×C8×D5 | C2 | semidirect |
| 3. C3×#4038 | C2 | semidirect |
| 4. C3×C5×#102 | C2 | semidirect |
| 5. C3×#3964 | C2 | semidirect |
| 6. C3×#3948 | C2 | semidirect |
| 7. C3×#3942 | C2 | semidirect |
| 8. #65061 | C3 | direct (N × H) |
| 13. C3×#711 | C4 | semidirect |
| 25. C2×C8×D5 | C2×C3 | semidirect |
| 26. #4038 | C2×C3 | semidirect |
| 27. C5×#102 | C2×C3 | semidirect |
| 28. #3964 | C2×C3 | semidirect |
| 29. #3948 | C2×C3 | semidirect |
| 30. #3942 | C2×C3 | semidirect |
| 54. C3×#102 | D5 | semidirect |
| 59. #711 | C3×C4 | semidirect |
| 120. #102 | C3×D5 | semidirect |
| 170. C3×C5 | #416 | semidirect |
| 211. C5 | C3×#416 | semidirect |
| 225. C3 | #65061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#711 | 2 |
| C2×C3×C8×D5 | 2 |
| C3×#4038 | 2 |
| C3×C5×#102 | 2 |
| C3×#3964 | 2 |
| C3×#3948 | 2 |
| C3×#3942 | 2 |
| #65061 | 3 |
| C3×#416 | 5 |