Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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×#5155 | C2 | semidirect |
| 3. C5×#4909 | C2 | semidirect |
| 4. C5×#4895 | C2 | semidirect |
| 5. C3×C5×#361 | C2 | semidirect |
| 6. C5×#4511 | C2 | semidirect |
| 7. C5×#4496 | C2 | semidirect |
| 24. #69262 | C5 | direct (N × H) |
| 31. C5×#361 | D3 | semidirect |
| 53. #5155 | C2×C5 | semidirect |
| 55. #4909 | C2×C5 | semidirect |
| 56. #4895 | C2×C5 | semidirect |
| 57. C3×#361 | C2×C5 | semidirect |
| 58. #4511 | C2×C5 | semidirect |
| 59. #4496 | C2×C5 | semidirect |
| 135. #361 | C5×D3 | semidirect |
| 249. C3×C5 | #2212 | semidirect |
| 284. C5 | #69262 | 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 |
|---|---|
| C5×#5155 | 2 |
| C5×#5147 | 2 |
| C5×#4909 | 2 |
| C5×#4895 | 2 |
| C3×C5×#361 | 2 |
| C5×#4511 | 2 |
| C5×#4496 | 2 |
| C5×#2212 | 3 |
| #69262 | 5 |