Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 275 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. C52×H(5,𝔽2) | C2 | semidirect |
| 2. #11717523 | C2 | semidirect |
| 3. #11717271 | C2 | semidirect |
| 4. #11717270 | C2 | semidirect |
| 5. #11717268 | C2 | semidirect |
| 6. C2×#87810 | C2 | semidirect |
| 7. #11717252 | C2 | semidirect |
| 15. #87900 | C22 | semidirect |
| 16. C2×#6045 | C22 | semidirect |
| 17. #87812 | C22 | semidirect |
| 18. #87811 | C22 | semidirect |
| 19. #87810 | C22 | semidirect |
| 20. #87810 | C22 | semidirect |
| 21. #87809 | C22 | semidirect |
| 22. #87804 | C22 | semidirect |
| 23. C2×#6029 | C22 | semidirect |
| 42. C5×H(5,𝔽2) | D5 | semidirect |
| 96. H(5,𝔽2) | C5⋊D5 | semidirect |
| 102. C52 | #577 | semidirect |
| 148. C5 | #66170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×H(5,𝔽2) | 2 |
| #11717523 | 2 |
| #11717271 | 2 |
| #11717270 | 2 |
| #11717268 | 2 |
| C2×#87810 | 2 |
| #11717252 | 2 |
| #66170 | 5 |