Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 136 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 |
|---|---|---|
| 2. C3×#704 | C2 | semidirect |
| 3. C3×#700 | C2 | semidirect |
| 4. C3×D5⋊C8 | C2 | semidirect |
| 5. D5⋊M16 | C3 | direct (N × H) |
| 13. C3×#170 | C22 | semidirect |
| 16. #704 | C2×C3 | semidirect |
| 17. #700 | C2×C3 | semidirect |
| 18. D5⋊C8 | C2×C3 | semidirect |
| 38. #170 | C22×C3 | semidirect |
| 43. C3×D5 | M16 | semidirect |
| 64. C3×C5 | C2×M16 | semidirect |
| 76. D5 | C3×M16 | semidirect |
| 89. C5 | C2×C3×M16 | semidirect |
| 98. C3 | D5⋊M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D5 | 2 |
| C3×#704 | 2 |
| C3×#700 | 2 |
| C3×D5⋊C8 | 2 |
| D5⋊M16 | 3 |
| C2×C3×M16 | 5 |