Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
726 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 136 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×#5409 | C2 | direct (N × H) |
| 3. C2×C5×A4⋊C8 | C2 | semidirect |
| 11. C5×A4⋊C8 | C22 | semidirect |
| 12. C2×#5409 | C5 | direct (N × H) |
| 30. #5409 | C2×C5 | direct (N × H) |
| 31. C2×A4⋊C8 | C2×C5 | semidirect |
| 59. C2×C5×A4 | M16 | semidirect |
| 72. A4⋊C8 | C22×C5 | semidirect |
| 129. C5×A4 | C2×M16 | semidirect |
| 158. C23×C5 | #208 | semidirect |
| 217. C2×A4 | C5×M16 | semidirect |
| 240. C22×C5 | C2×#208 | semidirect |
| 299. A4 | C2×C5×M16 | semidirect |
| 308. C2×C5 | #5409 | direct (N × H) |
| 326. C23 | C5×#208 | semidirect |
| 359. C5 | C2×#5409 | direct (N × H) |
| 376. C22 | C2×C5×#208 | semidirect |
| 391. C2 | C5×#5409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×A4 | 2 |
| C5×#5409 | 2 |
| C2×C5×A4⋊C8 | 2 |
| C2×C5×#407 | 3 |
| C2×C5×#208 | 4 |
| C2×#5409 | 5 |