Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
714 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 88 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×A4⋊Q8 | C2 | semidirect |
| 3. C5×#5414 | C2 | direct (N × H) |
| 4. C2×C5×A4⋊C8 | C2 | semidirect |
| 12. C5×A4⋊Q8 | C22 | semidirect |
| 14. C5×A4⋊C8 | C22 | semidirect |
| 15. C2×#5414 | C5 | direct (N × H) |
| 36. C2×A4⋊Q8 | C2×C5 | semidirect |
| 37. #5414 | C2×C5 | direct (N × H) |
| 38. C2×A4⋊C8 | C2×C5 | semidirect |
| 72. C2×C5×A4 | SD16 | semidirect |
| 87. A4⋊Q8 | C22×C5 | semidirect |
| 89. A4⋊C8 | C22×C5 | semidirect |
| 153. C5×A4 | C2×SD16 | semidirect |
| 184. C23×C5 | #214 | semidirect |
| 249. C2×A4 | C5×SD16 | semidirect |
| 275. C22×C5 | C2×#214 | semidirect |
| 338. A4 | C2×C5×SD16 | semidirect |
| 347. C2×C5 | #5414 | direct (N × H) |
| 366. C23 | C5×#214 | semidirect |
| 399. C5 | C2×#5414 | direct (N × H) |
| 417. C22 | C2×C5×#214 | semidirect |
| 431. C2 | C5×#5414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×A4 | 2 |
| C2×C5×A4⋊Q8 | 2 |
| C5×#5414 | 2 |
| C2×C5×A4⋊C8 | 2 |
| C2×C5×#450 | 3 |
| C2×C5×#214 | 4 |
| C2×#5414 | 5 |