Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5577 | C2 | semidirect |
| 2. C3×#65316 | C2 | semidirect |
| 3. #11747039 | C2 | semidirect |
| 4. #11747033 | C2 | semidirect |
| 5. #11746356 | C2 | semidirect |
| 6. #11745853 | C2 | semidirect |
| 7. #11745836 | C2 | semidirect |
| 29. #65316 | D3 | semidirect |
| 61. #5577 | D5 | semidirect |
| 90. C3×C5×Q8 | D8 | semidirect |
| 217. C5×Q8 | #213 | semidirect |
| 271. C3×Q8 | #686 | semidirect |
| 343. C3×C5 | #1621 | semidirect |
| 372. Q8 | #6652 | semidirect |
| 405. C5 | #71032 | semidirect |
| 424. C3 | #10602711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5577 | 2 |
| C3×#65316 | 2 |
| #11747039 | 2 |
| #11747033 | 2 |
| #11746356 | 2 |
| #11745853 | 2 |
| #11745836 | 2 |
| #10602711 | 3 |
| #71032 | 5 |