Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. #11717425 | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. #11716740 | C2 | semidirect |
| 5. #11716738 | C2 | semidirect |
| 6. #87900 | C4 | semidirect |
| 7. C5×#709 | C4 | semidirect |
| 11. D5×D20 | C4 | semidirect |
| 16. D5×Dic10 | C4 | semidirect |
| 19. C4×#1042 | C22 | semidirect |
| 22. C5×#700 | C22 | semidirect |
| 53. C2×#700 | D5 | semidirect |
| 91. #709 | AGL(1,𝔽5) | semidirect |
| 102. #700 | C2×D5 | semidirect |
| 176. C52 | #421 | semidirect |
| 268. C5 | #65428 | semidirect |
| 269. C5 | #65795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#709 | 2 |
| #11717425 | 2 |
| C2×C5×#700 | 2 |
| #11716740 | 2 |
| #11716738 | 2 |
| #65795 | 5 |
| #65428 | 5 |