Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 94 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×#5771 | C2 | semidirect |
| 2. C3×C5×#509 | C2 | semidirect |
| 3. C5×#5160 | C2 | semidirect |
| 4. C2×C5×#827 | C2 | semidirect |
| 5. C5×#4567 | C2 | semidirect |
| 6. C5×#4517 | C2 | semidirect |
| 7. C5×#4515 | C2 | semidirect |
| 26. #71518 | C5 | direct (N × H) |
| 28. C5×#509 | D3 | semidirect |
| 61. #5771 | C2×C5 | semidirect |
| 62. C3×#509 | C2×C5 | semidirect |
| 63. #5160 | C2×C5 | semidirect |
| 64. C2×#827 | C2×C5 | semidirect |
| 65. #4567 | C2×C5 | semidirect |
| 66. #4517 | C2×C5 | semidirect |
| 67. #4515 | C2×C5 | semidirect |
| 154. #509 | C5×D3 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #71518 | direct (N × H) |
| 357. C3 | C5×#2193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5771 | 2 |
| C3×C5×#509 | 2 |
| C5×#5160 | 2 |
| C2×C5×#827 | 2 |
| C5×#4567 | 2 |
| C5×#4517 | 2 |
| C5×#4515 | 2 |
| C5×#2193 | 3 |
| #71518 | 5 |