Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C3×C5×#135 | C2 | semidirect |
| 2. C2×#91112 | C2 | semidirect |
| 3. C2×#91110 | C2 | semidirect |
| 4. #11751216 | C2 | semidirect |
| 5. #11746385 | C2 | semidirect |
| 6. #11746383 | C2 | semidirect |
| 7. #11746370 | C2 | semidirect |
| 25. C2×C5×#135 | D3 | semidirect |
| 42. C3×C5×Q16 | D4 | semidirect |
| 45. C3×C5×D8 | D4 | semidirect |
| 56. C2×C3×#135 | D5 | semidirect |
| 125. C5×Q16 | #67 | semidirect |
| 128. C5×D8 | #67 | semidirect |
| 139. C2×#135 | D15 | semidirect |
| 171. C3×Q16 | C22⋊D5 | semidirect |
| 174. C3×D8 | C22⋊D5 | semidirect |
| 273. Q16 | #1220 | semidirect |
| 278. D8 | #1220 | semidirect |
| 287. C3×C5 | #2186 | semidirect |
| 336. C5 | #72082 | semidirect |
| 352. C3 | #10602875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#135 | 2 |
| C2×#91112 | 2 |
| C2×#91110 | 2 |
| #11751216 | 2 |
| #11746385 | 2 |
| #11746383 | 2 |
| #11746370 | 2 |
| #10602875 | 3 |
| #72082 | 5 |