Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5196 | C2 | semidirect |
| 3. C5×#5195 | C2 | semidirect |
| 4. C5×#5155 | C2 | semidirect |
| 5. C5×#4563 | C2 | semidirect |
| 6. C5×#4517 | C2 | semidirect |
| 7. C5×#4511 | C2 | semidirect |
| 24. #71513 | C5 | direct (N × H) |
| 54. #5196 | C2×C5 | semidirect |
| 55. #5195 | C2×C5 | semidirect |
| 56. #5155 | C2×C5 | semidirect |
| 57. #4563 | C2×C5 | semidirect |
| 58. #4517 | C2×C5 | semidirect |
| 59. #4511 | C2×C5 | semidirect |
| 249. C3×C5 | #2212 | semidirect |
| 284. C5 | #71513 | direct (N × H) |
| 294. C3 | C5×#2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#509 | 2 |
| C5×#5196 | 2 |
| C5×#5195 | 2 |
| C5×#5155 | 2 |
| C5×#4563 | 2 |
| C5×#4517 | 2 |
| C5×#4511 | 2 |
| C5×#2212 | 3 |
| #71513 | 5 |