Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 136 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. #11716595 | C2 | semidirect |
| 5. Dic5×#168 | C2 | semidirect |
| 7. #87804 | C4 | semidirect |
| 12. C2×C5×#168 | C4 | semidirect |
| 62. C2×#168 | Dic5 | semidirect |
| 98. C52 | #405 | semidirect |
| 147. C5 | #65286 | semidirect |
| 148. C5 | #65390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87804 | 2 |
| C5×#4072 | 2 |
| C22×C5×#168 | 2 |
| #11716595 | 2 |
| Dic5×#168 | 2 |
| #65390 | 5 |
| #65286 | 5 |