Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
932 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 932 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 |
|---|---|---|
| 1. C5×#5483 | C2 | semidirect |
| 4. C5×#4527 | C2 | semidirect |
| 5. C5×#4526 | C2 | semidirect |
| 16. #69497 | C5 | direct (N × H) |
| 27. C24×C3×C5 | Q8 | semidirect |
| 44. #5483 | C2×C5 | semidirect |
| 47. #4527 | C2×C5 | semidirect |
| 48. #4526 | C2×C5 | semidirect |
| 100. C24×C5 | Dic6 | semidirect |
| 149. C24×C3 | C5×Q8 | semidirect |
| 263. C24 | C5×Dic6 | semidirect |
| 280. C3×C5 | #2029 | semidirect |
| 344. C5 | #69497 | direct (N × H) |
| 367. C3 | C5×#2029 | 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×#379 | 2 |
| C5×#5247 | 2 |
| C5×#4527 | 2 |
| C5×#4526 | 2 |
| C5×#2029 | 3 |
| #69497 | 5 |