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. C5×#5040 | C2 | semidirect |
| 3. C5×#4739 | C2 | semidirect |
| 4. C5×#4673 | C2 | semidirect |
| 5. C3×C5×#327 | C2 | semidirect |
| 6. C5×#4468 | C2 | semidirect |
| 7. C5×#4452 | C2 | semidirect |
| 28. #68287 | C5 | direct (N × H) |
| 34. C5×#327 | D3 | semidirect |
| 68. #5040 | C2×C5 | semidirect |
| 69. #4739 | C2×C5 | semidirect |
| 70. #4673 | C2×C5 | semidirect |
| 71. C3×#327 | C2×C5 | semidirect |
| 72. #4468 | C2×C5 | semidirect |
| 73. #4452 | C2×C5 | semidirect |
| 183. #327 | C5×D3 | semidirect |
| 383. C3×C5 | #1606 | semidirect |
| 453. C5 | #68287 | 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 |
| C5×#5040 | 2 |
| C5×#4739 | 2 |
| C5×#4673 | 2 |
| C3×C5×#327 | 2 |
| C5×#4468 | 2 |
| C5×#4452 | 2 |
| C5×#1606 | 3 |
| #68287 | 5 |