Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11753981 | C2 | semidirect |
| 2. C5×#4908 | C2 | semidirect |
| 3. #11748090 | C2 | semidirect |
| 4. C2×#90937 | C2 | semidirect |
| 5. #11746336 | C2 | semidirect |
| 6. C3×#64736 | C2 | semidirect |
| 7. #11745905 | C2 | semidirect |
| 12. C2×C5×D24 | C22 | semidirect |
| 19. C3×C5×M32 | C22 | semidirect |
| 20. C2×C3⋊#672 | C22 | semidirect |
| 23. C3×#3951 | C22 | semidirect |
| 32. #64736 | D3 | semidirect |
| 63. #4908 | D5 | semidirect |
| 80. C5×M32 | C2×D3 | semidirect |
| 83. #3951 | C2×D3 | semidirect |
| 117. C2×D24 | C2×D5 | semidirect |
| 119. C3×M32 | C2×D5 | semidirect |
| 235. M32 | D3×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #69258 | semidirect |
| 368. C3 | #10602310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753981 | 2 |
| C5×#4908 | 2 |
| #11748090 | 2 |
| C2×#90937 | 2 |
| #11746336 | 2 |
| C3×#64736 | 2 |
| #11745905 | 2 |
| #10602310 | 3 |
| #69258 | 5 |