Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
308 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 4. #11716983 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 7. #11716606 | C2 | semidirect |
| 64. C5×Dic5 | SD16 | semidirect |
| 147. C52 | #461 | semidirect |
| 176. Dic5 | #687 | semidirect |
| 219. C5 | #65308 | semidirect |
| 220. C5 | #65451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87810 | 2 |
| C5×D4×Dic5 | 2 |
| C2×C5×#687 | 2 |
| #11716983 | 2 |
| #11716612 | 2 |
| #11716608 | 2 |
| #11716606 | 2 |
| #65451 | 5 |
| #65308 | 5 |