Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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×D3×Q8 | C2 | semidirect |
| 3. C3×C5×SD16 | C2 | semidirect |
| 4. C5×#216 | C2 | semidirect |
| 5. C5×#214 | C2 | semidirect |
| 6. C5×Dic12 | C2 | semidirect |
| 7. C5×ΓL(1,𝔽25) | C2 | semidirect |
| 20. #915 | C5 | direct (N × H) |
| 26. C5×SD16 | D3 | semidirect |
| 35. D3×Q8 | C2×C5 | semidirect |
| 37. C3×SD16 | C2×C5 | semidirect |
| 38. #216 | C2×C5 | semidirect |
| 39. #214 | C2×C5 | semidirect |
| 40. Dic12 | C2×C5 | semidirect |
| 41. ΓL(1,𝔽25) | C2×C5 | semidirect |
| 80. SD16 | C5×D3 | semidirect |
| 82. C3×C5 | #137 | semidirect |
| 107. C5 | #915 | direct (N × H) |
| 115. C3 | C5×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q8 | 2 |
| C5×#237 | 2 |
| C3×C5×SD16 | 2 |
| C5×#216 | 2 |
| C5×#214 | 2 |
| C5×Dic12 | 2 |
| C5×ΓL(1,𝔽25) | 2 |
| C5×#137 | 3 |
| #915 | 5 |