Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5602 | C2 | semidirect |
| 3. C5×#4731 | C2 | semidirect |
| 4. C5×#4672 | C2 | semidirect |
| 5. C3×C5×#327 | C2 | semidirect |
| 6. C5×#4469 | C2 | semidirect |
| 7. C5×#4452 | C2 | semidirect |
| 28. #68292 | C5 | direct (N × H) |
| 34. C5×#327 | D3 | semidirect |
| 68. #5602 | C2×C5 | semidirect |
| 70. #4731 | C2×C5 | semidirect |
| 71. #4672 | C2×C5 | semidirect |
| 72. C3×#327 | C2×C5 | semidirect |
| 73. #4469 | C2×C5 | semidirect |
| 74. #4452 | C2×C5 | semidirect |
| 185. #327 | C5×D3 | semidirect |
| 391. C3×C5 | #1597 | semidirect |
| 463. C5 | #68292 | direct (N × H) |
| 487. C3 | C5×#1597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5602 | 2 |
| C5×#5036 | 2 |
| C5×#4731 | 2 |
| C5×#4672 | 2 |
| C3×C5×#327 | 2 |
| C5×#4469 | 2 |
| C5×#4452 | 2 |
| C5×#1597 | 3 |
| #68292 | 5 |