Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
274 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 64 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. Dic5×Dic10 | C2 | semidirect |
| 4. C2×#87775 | C2 | semidirect |
| 6. #11716612 | C2 | semidirect |
| 7. #11716607 | C2 | semidirect |
| 141. C52 | #464 | semidirect |
| 212. C5 | #65343 | semidirect |
| 213. C5 | #65455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4082 | 2 |
| C2×C5×#687 | 2 |
| Dic5×Dic10 | 2 |
| C2×#87775 | 2 |
| #11716699 | 2 |
| #11716612 | 2 |
| #11716607 | 2 |
| #65455 | 5 |
| #65343 | 5 |