Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
580 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 16. #69536 | C5 | direct (N × H) |
| 29. C22×C3×C4×C5 | Q8 | semidirect |
| 94. C22×C4×C5 | Dic6 | semidirect |
| 131. C22×C3×C4 | C5×Q8 | semidirect |
| 222. C22×C4 | C5×Dic6 | semidirect |
| 232. C3×C5 | #2030 | semidirect |
| 280. C5 | #69536 | direct (N × H) |
| 296. C3 | C5×#2030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5483 | 2 |
| C3×C5×#381 | 2 |
| C5×#5211 | 2 |
| C5×#4527 | 2 |
| C5×#4526 | 2 |
| C5×#2030 | 3 |
| #69536 | 5 |