Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C5×#5069 | C2 | semidirect |
| 3. C5×#5064 | C2 | semidirect |
| 5. C5×#4543 | C2 | semidirect |
| 6. C5×#4543 | C2 | semidirect |
| 28. #71957 | C5 | direct (N × H) |
| 64. #5069 | C2×C5 | semidirect |
| 65. #5064 | C2×C5 | semidirect |
| 67. #4543 | C2×C5 | semidirect |
| 68. #4543 | C2×C5 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | #71957 | direct (N × H) |
| 354. C3 | C5×#1664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#563 | 2 |
| C5×#5069 | 2 |
| C5×#5064 | 2 |
| C5×#5055 | 2 |
| C5×#4543 | 2 |
| C5×#4540 | 2 |
| C5×#1664 | 3 |
| #71957 | 5 |