Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 102 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. #11716733 | C2 | semidirect |
| 5. #11716731 | C2 | semidirect |
| 10. C5×#704 | C4 | semidirect |
| 11. C5×#700 | C4 | semidirect |
| 13. C2×#6029 | C4 | semidirect |
| 14. C2×C5×#168 | C4 | semidirect |
| 15. D5×#168 | C4 | semidirect |
| 16. D5×#168 | C4 | semidirect |
| 56. #704 | Dic5 | semidirect |
| 59. #700 | Dic5 | semidirect |
| 75. C2×#168 | AGL(1,𝔽5) | semidirect |
| 119. C52 | #405 | semidirect |
| 178. C5 | #65411 | semidirect |
| 179. C5 | #65718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C5×D5⋊M16 | 2 |
| C2×D5×#168 | 2 |
| #11716733 | 2 |
| #11716731 | 2 |
| #65718 | 5 |
| #65411 | 5 |