Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
792 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 4. C2×#87780 | C2 | semidirect |
| 5. #11717073 | C2 | direct (N × H) |
| 6. C2×Dic52 | C2 | semidirect |
| 9. C22×C5×Dic5 | C4 | semidirect |
| 16. #87780 | C22 | semidirect |
| 17. Dic52 | C22 | semidirect |
| 29. C2×C5×Dic5 | C2×C4 | semidirect |
| 67. C22×Dic5 | Dic5 | semidirect |
| 83. C2×C52 | #117 | semidirect |
| 114. C2×Dic5 | C2×Dic5 | semidirect |
| 124. C52 | C2×#117 | semidirect |
| 169. C2×C5 | #4023 | semidirect |
| 170. C2×C5 | #4072 | semidirect |
| 189. C5 | C2×#4023 | semidirect |
| 190. C5 | C2×#4072 | semidirect |
| 202. C2 | #11717073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Dic5 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×#87780 | 2 |
| #11717073 | 2 |
| C2×Dic52 | 2 |
| C2×#4072 | 5 |
| C2×#4023 | 5 |