Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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×#508 | C2 | semidirect |
| 2. #11751005 | C2 | semidirect |
| 3. #11746343 | C2 | semidirect |
| 4. #11746342 | C2 | semidirect |
| 5. #11746341 | C2 | semidirect |
| 6. #11746340 | C2 | semidirect |
| 7. C2×C3⋊#3926 | C2 | semidirect |
| 21. C5×#508 | D3 | semidirect |
| 39. C3×#508 | D5 | semidirect |
| 92. #508 | D15 | semidirect |
| 171. C3×C5 | #2262 | semidirect |
| 198. C5 | #71508 | semidirect |
| 206. C3 | #10602301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| #11751005 | 2 |
| #11746343 | 2 |
| #11746342 | 2 |
| #11746341 | 2 |
| #11746340 | 2 |
| C2×C3⋊#3926 | 2 |
| #10602301 | 3 |
| #71508 | 5 |