Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
292 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. C5×Q8×Dic5 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 41. Q8×Dic5 | D5 | semidirect |
| 42. C2×#689 | D5 | semidirect |
| 144. C52 | #464 | semidirect |
| 215. C5 | #65317 | semidirect |
| 216. C5 | #65474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87811 | 2 |
| C5×Q8×Dic5 | 2 |
| C2×C5×#689 | 2 |
| #11716982 | 2 |
| #11716612 | 2 |
| #11716606 | 2 |
| #11716605 | 2 |
| #65474 | 5 |
| #65317 | 5 |