Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
594 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×A4×M16 | C2 | semidirect |
| 3. C5×#5409 | C2 | semidirect |
| 4. C5×#5400 | C2 | semidirect |
| 5. C5×C8×S4 | C2 | semidirect |
| 15. C5×C8×A4 | C22 | semidirect |
| 16. C5×A4⋊C8 | C22 | semidirect |
| 17. M16×S4 | C5 | direct (N × H) |
| 19. C22×C5×M16 | D3 | semidirect |
| 43. A4×M16 | C2×C5 | semidirect |
| 44. #5409 | C2×C5 | semidirect |
| 45. #5400 | C2×C5 | semidirect |
| 46. C8×S4 | C2×C5 | semidirect |
| 60. C22×C5×C8 | C2×D3 | semidirect |
| 86. C5×S4 | M16 | direct (N × H) |
| 103. C8×A4 | C22×C5 | semidirect |
| 104. A4⋊C8 | C22×C5 | semidirect |
| 139. C5×M16 | S4 | direct (N × H) |
| 163. C22×M16 | C5×D3 | semidirect |
| 177. C5×A4 | C2×M16 | semidirect |
| 242. C5×C8 | C2×S4 | semidirect |
| 256. C22×C8 | C2×C5×D3 | semidirect |
| 285. S4 | C5×M16 | direct (N × H) |
| 309. C22×C5 | D3×M16 | semidirect |
| 355. M16 | C5×S4 | direct (N × H) |
| 383. A4 | C2×C5×M16 | semidirect |
| 442. C8 | C2×C5×S4 | semidirect |
| 447. C5 | M16×S4 | direct (N × H) |
| 463. C22 | C5×D3×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×S4 | 2 |
| C5×A4×M16 | 2 |
| C5×#5409 | 2 |
| C5×#5400 | 2 |
| C5×C8×S4 | 2 |
| C5×D4×M16 | 3 |
| C5×D3×M16 | 4 |
| M16×S4 | 5 |