Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 66 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. D3×Dic30 | C2 | semidirect |
| 3. #10623902 | C2 | semidirect |
| 4. C3×#6706 | C2 | semidirect |
| 5. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 6. #10623808 | C2 | semidirect |
| 7. #10623803 | C2 | semidirect |
| 32. #6706 | D3 | semidirect |
| 33. C5×ΓL(1,𝔽25) | D3 | semidirect |
| 49. C3×ΓL(1,𝔽25) | D5 | semidirect |
| 131. ΓL(1,𝔽25) | D15 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #909 | semidirect |
| 203. C3×C5 | #915 | semidirect |
| 224. C32 | #4055 | semidirect |
| 243. C5 | #63800 | semidirect |
| 252. C3 | #91274 | semidirect |
| 253. C3 | #91798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Dic30 | 2 |
| #10624193 | 2 |
| #10623902 | 2 |
| C3×#6706 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| #10623808 | 2 |
| #10623803 | 2 |
| #91798 | 3 |
| #91274 | 3 |
| #63800 | 5 |