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. #11756511 | C2 | semidirect |
| 2. C5×#5142 | C2 | semidirect |
| 3. #11747547 | C2 | semidirect |
| 4. C2×#90939 | C2 | semidirect |
| 5. C3×#64781 | C2 | semidirect |
| 6. #11745920 | C2 | semidirect |
| 7. #11745908 | C2 | semidirect |
| 18. C2×C5×D24 | C22 | semidirect |
| 20. C5×#819 | C22 | semidirect |
| 21. C3×#3944 | C22 | semidirect |
| 22. C2×C3×#672 | C22 | semidirect |
| 31. #64781 | D3 | semidirect |
| 62. #5142 | D5 | semidirect |
| 83. #3944 | C2×D3 | semidirect |
| 84. C2×#672 | C2×D3 | semidirect |
| 118. C2×D24 | C2×D5 | semidirect |
| 122. #819 | C2×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #69126 | semidirect |
| 368. C3 | #10601887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756511 | 2 |
| C5×#5142 | 2 |
| #11747547 | 2 |
| C2×#90939 | 2 |
| C3×#64781 | 2 |
| #11745920 | 2 |
| #11745908 | 2 |
| #10601887 | 3 |
| #69126 | 5 |