Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5184 | C2 | semidirect |
| 4. #11746386 | C2 | semidirect |
| 5. #11745933 | C2 | semidirect |
| 7. #11745877 | C2 | semidirect |
| 18. C3×#3961 | C4 | semidirect |
| 19. C3×#3960 | C4 | semidirect |
| 50. #5184 | D5 | semidirect |
| 62. #3961 | Dic3 | semidirect |
| 63. #3960 | Dic3 | semidirect |
| 217. C3×C5 | #2180 | semidirect |
| 246. C5 | #71521 | semidirect |
| 255. C3 | #10601710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5184 | 2 |
| C3×#65468 | 2 |
| #11748067 | 2 |
| #11746386 | 2 |
| #11745933 | 2 |
| #11745909 | 2 |
| #11745877 | 2 |
| #10601710 | 3 |
| #71521 | 5 |