Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
239 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11716743 | C2 | semidirect |
| 5. #11716742 | C2 | semidirect |
| 13. C2×#6029 | C4 | semidirect |
| 14. C2×C5×#168 | C4 | semidirect |
| 15. D5×#168 | C4 | semidirect |
| 16. D5×#168 | C4 | semidirect |
| 76. C2×#168 | AGL(1,𝔽5) | semidirect |
| 120. C52 | #427 | semidirect |
| 181. C5 | #65287 | semidirect |
| 182. C5 | #65721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C5×#4130 | 2 |
| C2×D5×#168 | 2 |
| #11716743 | 2 |
| #11716742 | 2 |
| #65721 | 5 |
| #65287 | 5 |