Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 110 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×#5075 | C2 | semidirect |
| 3. C5×#4679 | C2 | semidirect |
| 4. C5×#4544 | C2 | semidirect |
| 5. C5×#4457 | C2 | semidirect |
| 18. #71287 | C5 | direct (N × H) |
| 40. #5075 | C2×C5 | semidirect |
| 41. #4679 | C2×C5 | semidirect |
| 42. #4544 | C2×C5 | semidirect |
| 43. #4457 | C2×C5 | semidirect |
| 69. C3×C5×C8 | SD16 | semidirect |
| 143. C5×C8 | #214 | semidirect |
| 172. C3×C8 | C5×SD16 | semidirect |
| 200. C3×C5 | #1688 | semidirect |
| 230. C8 | C5×#214 | semidirect |
| 235. C5 | #71287 | direct (N × H) |
| 246. C3 | C5×#1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| C5×#5075 | 2 |
| C5×#4679 | 2 |
| C5×#4544 | 2 |
| C5×#4457 | 2 |
| C5×#1688 | 3 |
| #71287 | 5 |