Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 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. Q16×Dic15 | C2 | semidirect |
| 4. C3×#64784 | C2 | semidirect |
| 5. #11745944 | C2 | semidirect |
| 7. #11745872 | C2 | semidirect |
| 16. C5×#828 | C4 | semidirect |
| 25. #64784 | D3 | semidirect |
| 33. C3×C5×Q16 | C2×C4 | semidirect |
| 45. C5×C3⋊C16 | C2×C4 | semidirect |
| 88. #828 | Dic5 | semidirect |
| 97. C5×Q16 | C4×D3 | semidirect |
| 126. Dic15 | SD32 | semidirect |
| 132. C3×Q16 | C2×Dic5 | semidirect |
| 144. C3⋊C16 | C2×Dic5 | semidirect |
| 206. Q16 | D3×Dic5 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 254. C5 | #69206 | semidirect |
| 266. C3 | Dic5×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic15 | 2 |
| C2×C5×#828 | 2 |
| #11747810 | 2 |
| C3×#64784 | 2 |
| #11745944 | 2 |
| #11745894 | 2 |
| #11745872 | 2 |
| Dic5×SD32 | 3 |
| #69206 | 5 |