Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
428 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 146 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. C3×C5×#498 | C2 | semidirect |
| 3. C3×#65368 | C2 | semidirect |
| 5. C3×C8×#168 | C2 | semidirect |
| 6. #10602125 | C3 | direct (N × H) |
| 17. C5×#498 | C2×C3 | semidirect |
| 19. #65368 | C2×C3 | semidirect |
| 21. C8×#168 | C2×C3 | semidirect |
| 35. C3×#498 | D5 | semidirect |
| 58. C3×C5×C8 | SD16 | semidirect |
| 59. C3×#168 | SD16 | semidirect |
| 82. #498 | C3×D5 | semidirect |
| 114. C5×C8 | C3×SD16 | semidirect |
| 115. #168 | C3×SD16 | semidirect |
| 138. C3×C8 | #688 | semidirect |
| 158. C3×C5 | #1705 | semidirect |
| 179. C8 | C3×#688 | semidirect |
| 183. C5 | C3×#1705 | semidirect |
| 191. C3 | #10602125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#498 | 2 |
| C3×#65374 | 2 |
| C3×#65368 | 2 |
| C3×#64982 | 2 |
| C3×C8×#168 | 2 |
| #10602125 | 3 |
| C3×#1705 | 5 |