Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
300 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 116 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. #11716670 | C2 | semidirect |
| 5. C4×C5×#168 | C2 | semidirect |
| 6. #11716595 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 17. #87768 | C4 | semidirect |
| 18. D5×#168 | C4 | semidirect |
| 46. C4×#168 | D5 | semidirect |
| 117. C52 | #405 | semidirect |
| 169. C5 | #64978 | semidirect |
| 170. C5 | #65286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4018 | 2 |
| C2×#87768 | 2 |
| C2×D5×#168 | 2 |
| #11716670 | 2 |
| C4×C5×#168 | 2 |
| #11716595 | 2 |
| Dic5×#168 | 2 |
| #65286 | 5 |
| #64978 | 5 |