Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
190 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 44 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. #11716920 | C2 | semidirect |
| 3. #11716665 | C2 | semidirect |
| 4. C5×Dic40 | C2 | semidirect |
| 5. C5×#3932 | C2 | semidirect |
| 6. #11716591 | C2 | semidirect |
| 7. #11716588 | C2 | semidirect |
| 42. Dic40 | D5 | semidirect |
| 43. #3932 | D5 | semidirect |
| 115. C52 | #510 | semidirect |
| 164. C5 | #65204 | semidirect |
| 165. C5 | #65207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716928 | 2 |
| #11716920 | 2 |
| #11716665 | 2 |
| C5×Dic40 | 2 |
| C5×#3932 | 2 |
| #11716591 | 2 |
| #11716588 | 2 |
| #65207 | 5 |
| #65204 | 5 |