Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
374 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 72 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×C5×#709 | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C2×#87772 | C2 | semidirect |
| 4. C2×#87770 | C2 | semidirect |
| 5. C22⋊#6029 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 39. C5×D20 | D4 | semidirect |
| 42. C5×Dic10 | D4 | semidirect |
| 46. C2×#709 | D5 | semidirect |
| 52. #4076 | D5 | semidirect |
| 152. D20 | C22⋊D5 | semidirect |
| 155. Dic10 | C22⋊D5 | semidirect |
| 169. C52 | #449 | semidirect |
| 259. C5 | #65326 | semidirect |
| 260. C5 | #65527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C5×#4076 | 2 |
| C2×#87772 | 2 |
| C2×#87770 | 2 |
| C22⋊#6029 | 2 |
| #11716606 | 2 |
| #11716603 | 2 |
| #65527 | 5 |
| #65326 | 5 |