Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 101 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. Q8×D60 | C2 | semidirect |
| 2. C3×C5×#460 | C2 | semidirect |
| 4. #11751171 | C2 | semidirect |
| 5. #11746356 | C2 | semidirect |
| 6. #11746304 | C2 | semidirect |
| 7. #11746303 | C2 | semidirect |
| 28. C5×#460 | D3 | semidirect |
| 61. C3×#460 | D5 | semidirect |
| 88. C3×C5×Q8 | D8 | semidirect |
| 102. D60 | SD16 | semidirect |
| 157. #460 | D15 | semidirect |
| 207. C5×Q8 | #213 | semidirect |
| 256. C3×Q8 | #686 | semidirect |
| 322. C3×C5 | #1627 | semidirect |
| 350. Q8 | #6715 | semidirect |
| 376. C5 | #71035 | semidirect |
| 393. C3 | #10601828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D60 | 2 |
| C3×C5×#460 | 2 |
| #11751173 | 2 |
| #11751171 | 2 |
| #11746356 | 2 |
| #11746304 | 2 |
| #11746303 | 2 |
| #10601828 | 3 |
| #71035 | 5 |