Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 80 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×#5757 | C2 | semidirect |
| 2. C2×#91110 | C2 | semidirect |
| 3. #11748086 | C2 | semidirect |
| 4. #11747548 | C2 | semidirect |
| 5. C3×#64783 | C2 | semidirect |
| 6. #11745905 | C2 | semidirect |
| 7. #11745887 | C2 | semidirect |
| 11. C2×D120 | C22 | semidirect |
| 20. C2×C3⋊#672 | C22 | semidirect |
| 21. C3×#3951 | C22 | semidirect |
| 22. C3×#3944 | C22 | semidirect |
| 32. #64783 | D3 | semidirect |
| 61. #5757 | D5 | semidirect |
| 82. #3951 | C2×D3 | semidirect |
| 83. #3944 | C2×D3 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #69258 | semidirect |
| 368. C3 | #10602915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5757 | 2 |
| C2×#91110 | 2 |
| #11748086 | 2 |
| #11747548 | 2 |
| C3×#64783 | 2 |
| #11745905 | 2 |
| #11745887 | 2 |
| #10602915 | 3 |
| #69258 | 5 |