Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 74 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×#87811 | C2 | semidirect |
| 2. C5×#4090 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 5. C2×#87774 | C2 | semidirect |
| 6. C2×#87772 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 38. #6029 | D4 | semidirect |
| 39. C5×#168 | D4 | semidirect |
| 42. #4090 | D5 | semidirect |
| 48. C2×#688 | D5 | semidirect |
| 64. C5×Dic5 | SD16 | semidirect |
| 141. #168 | C22⋊D5 | semidirect |
| 149. C52 | #492 | semidirect |
| 175. Dic5 | #688 | semidirect |
| 218. C5 | #65374 | semidirect |
| 219. C5 | #65464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87811 | 2 |
| C5×#4090 | 2 |
| C2×C5×#688 | 2 |
| #11717029 | 2 |
| C2×#87774 | 2 |
| C2×#87772 | 2 |
| Dic5×#168 | 2 |
| #65464 | 5 |
| #65374 | 5 |