Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C2×#87870 | C2 | semidirect |
| 2. C2×#87810 | C2 | semidirect |
| 3. C5×#4084 | C2 | semidirect |
| 4. C2×C5×#686 | C2 | semidirect |
| 5. #11716608 | C2 | semidirect |
| 6. #11716603 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 33. #6045 | D4 | semidirect |
| 38. C5×D20 | D4 | semidirect |
| 49. #4084 | D5 | semidirect |
| 53. C2×#686 | D5 | semidirect |
| 149. D20 | C22⋊D5 | semidirect |
| 171. C52 | #449 | semidirect |
| 261. C5 | #65326 | semidirect |
| 262. C5 | #65447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| C2×#87810 | 2 |
| C5×#4084 | 2 |
| C2×C5×#686 | 2 |
| #11716608 | 2 |
| #11716603 | 2 |
| #11716597 | 2 |
| #65447 | 5 |
| #65326 | 5 |