Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 5. C2×C3×C5×M16 | C4 | semidirect |
| 6. C22×C3×C5×C8 | C4 | semidirect |
| 10. C5×#834 | C4 | semidirect |
| 11. #67691 | C5 | direct (N × H) |
| 31. C2×C5×M16 | Dic3 | semidirect |
| 32. C22×C5×C8 | Dic3 | semidirect |
| 54. C2×C3×M16 | C4×C5 | semidirect |
| 55. C22×C3×C8 | C4×C5 | semidirect |
| 59. #834 | C4×C5 | semidirect |
| 116. C2×M16 | C5×Dic3 | semidirect |
| 117. C22×C8 | C5×Dic3 | semidirect |
| 165. C3×C5 | #1391 | semidirect |
| 199. C5 | #67691 | direct (N × H) |
| 210. C3 | C5×#1391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#408 | 2 |
| C5×#5240 | 2 |
| C5×#1391 | 3 |
| #67691 | 5 |