Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. D5⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 3. C3×D5⋊(C3⋊C8) | C2 | semidirect |
| 4. #10623976 | C2 | semidirect |
| 5. #10623975 | C2 | semidirect |
| 15. C3⋊(C3⋊#170) | C22 | semidirect |
| 16. C3×C3⋊#170 | C22 | semidirect |
| 25. D5⋊(C3⋊C8) | D3 | semidirect |
| 61. C3⋊#170 | C2×D3 | semidirect |
| 68. C32×D5 | M16 | semidirect |
| 113. C32×C5 | C2×M16 | semidirect |
| 139. C3×D5 | ΓL(1,𝔽25) | semidirect |
| 140. C3×D5 | #208 | semidirect |
| 180. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 181. C3×C5 | C2×#208 | semidirect |
| 204. D5 | #3711 | semidirect |
| 205. C32 | D5⋊M16 | semidirect |
| 225. C5 | C2×#3711 | semidirect |
| 235. C3 | D5⋊ΓL(1,𝔽25) | semidirect |
| 236. C3 | D5⋊#208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D3×D5 | 2 |
| D5⋊(C3⋊(C3⋊C8)) | 2 |
| C3×D5⋊(C3⋊C8) | 2 |
| #10623976 | 2 |
| #10623975 | 2 |
| D5⋊#208 | 3 |
| D5⋊ΓL(1,𝔽25) | 3 |
| C2×#3711 | 5 |