Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. C2×C5×Dic20 | C2 | semidirect |
| 4. C5×#3950 | C2 | semidirect |
| 5. C5×#3948 | C2 | semidirect |
| 16. #65405 | C5 | direct (N × H) |
| 34. C2×Dic20 | C2×C5 | semidirect |
| 37. #3950 | C2×C5 | semidirect |
| 38. #3948 | C2×C5 | semidirect |
| 41. C22×C52 | Q16 | semidirect |
| 109. C52 | #467 | semidirect |
| 118. C22×C5 | Dic20 | semidirect |
| 119. C22×C5 | C5×Q16 | semidirect |
| 168. C5 | #65405 | direct (N × H) |
| 169. C5 | C5×#467 | semidirect |
| 172. C22 | C5×Dic20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| C5×#4070 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#3950 | 2 |
| C5×#3948 | 2 |
| C5×#467 | 5 |
| #65405 | 5 |