Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
512 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 128 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. #11716698 | C2 | semidirect |
| 4. C5×#3963 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 12. C2×C4×C5×D5 | C4 | semidirect |
| 43. #3963 | D5 | semidirect |
| 73. C2×C4×D5 | Dic5 | semidirect |
| 128. C52 | #381 | semidirect |
| 207. C5 | #64953 | semidirect |
| 208. C5 | #65500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×#87778 | 2 |
| #11716698 | 2 |
| C5×#3963 | 2 |
| #11716620 | 2 |
| #65500 | 5 |
| #64953 | 5 |