Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
558 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 214 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×#4150 | C2 | semidirect |
| 2. C52×#131 | C2 | semidirect |
| 3. C5×#4055 | C2 | semidirect |
| 4. C2×C5×Dic20 | C2 | semidirect |
| 5. C5×#4050 | C2 | semidirect |
| 18. #66087 | C5 | direct (N × H) |
| 31. #4150 | C2×C5 | semidirect |
| 36. C5×#131 | D5 | semidirect |
| 37. C5×#131 | C2×C5 | semidirect |
| 38. #4055 | C2×C5 | semidirect |
| 39. C2×Dic20 | C2×C5 | semidirect |
| 40. #4050 | C2×C5 | semidirect |
| 106. #131 | C5×D5 | semidirect |
| 107. C52 | #578 | semidirect |
| 152. C5 | #66087 | direct (N × H) |
| 153. C5 | C5×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4150 | 2 |
| C52×#131 | 2 |
| C5×#4055 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#4050 | 2 |
| C5×#578 | 5 |
| #66087 | 5 |