Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 520 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. C3×C5×#448 | C2 | semidirect |
| 3. C5×#5231 | C2 | semidirect |
| 4. C5×#5228 | C2 | semidirect |
| 5. C5×#4537 | C2 | semidirect |
| 6. C5×#4468 | C2 | semidirect |
| 7. C5×#4467 | C2 | semidirect |
| 28. #70973 | C5 | direct (N × H) |
| 31. C5×#448 | D3 | semidirect |
| 68. C3×#448 | C2×C5 | semidirect |
| 69. #5231 | C2×C5 | semidirect |
| 70. #5228 | C2×C5 | semidirect |
| 71. #4537 | C2×C5 | semidirect |
| 72. #4468 | C2×C5 | semidirect |
| 73. #4467 | C2×C5 | semidirect |
| 180. #448 | C5×D3 | semidirect |
| 383. C3×C5 | #1606 | semidirect |
| 453. C5 | #70973 | direct (N × H) |
| 475. C3 | C5×#1606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5617 | 2 |
| C3×C5×#448 | 2 |
| C5×#5231 | 2 |
| C5×#5228 | 2 |
| C5×#4537 | 2 |
| C5×#4468 | 2 |
| C5×#4467 | 2 |
| C5×#1606 | 3 |
| #70973 | 5 |