Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 310 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. C5×Q8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×#215 | C2 | semidirect |
| 4. C5×#3716 | C2 | semidirect |
| 5. C5×#3710 | C2 | semidirect |
| 8. C32×C5×Q8 | C22 | semidirect |
| 12. C5×#634 | C22 | semidirect |
| 15. C3×C5×C3⋊C8 | C22 | semidirect |
| 16. #63940 | C5 | direct (N × H) |
| 21. C5×#215 | D3 | semidirect |
| 33. Q8×C3⋊D3 | C2×C5 | semidirect |
| 35. C3×#215 | C2×C5 | semidirect |
| 36. #3716 | C2×C5 | semidirect |
| 37. #3710 | C2×C5 | semidirect |
| 40. C3×C5×Q8 | C2×D3 | semidirect |
| 53. C5×C3⋊C8 | C2×D3 | semidirect |
| 56. C5×C3⋊D3 | SD16 | semidirect |
| 64. C32×Q8 | C22×C5 | semidirect |
| 68. #634 | C22×C5 | semidirect |
| 71. C3×C3⋊C8 | C22×C5 | semidirect |
| 89. #215 | C5×D3 | semidirect |
| 93. C32×C5 | C2×SD16 | semidirect |
| 97. C5×Q8 | D32 | semidirect |
| 119. C3×Q8 | C2×C5×D3 | semidirect |
| 132. C3⋊C8 | C2×C5×D3 | semidirect |
| 141. C3⋊D3 | C5×SD16 | semidirect |
| 149. C3×C5 | D3×SD16 | semidirect |
| 166. C32 | C2×C5×SD16 | semidirect |
| 170. Q8 | C5×D32 | semidirect |
| 182. C5 | #63940 | direct (N × H) |
| 191. C3 | C5×D3×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| C5×#3802 | 2 |
| C3×C5×#215 | 2 |
| C5×#3716 | 2 |
| C5×#3710 | 2 |
| C5×D3×SD16 | 3 |
| #63940 | 5 |