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. C2×#87849 | C2 | semidirect |
| 3. C5×#4130 | C2 | semidirect |
| 4. #11716741 | C2 | semidirect |
| 5. #11716739 | C2 | semidirect |
| 6. #87900 | C4 | semidirect |
| 7. C5×#709 | C4 | semidirect |
| 11. D5×D20 | C4 | semidirect |
| 16. D5×Dic10 | C4 | semidirect |
| 19. #87849 | C22 | semidirect |
| 22. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 52. #4130 | D5 | semidirect |
| 91. #709 | AGL(1,𝔽5) | semidirect |
| 100. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 176. C52 | #421 | semidirect |
| 268. C5 | #65294 | 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 |
| C2×#87849 | 2 |
| C5×#4130 | 2 |
| #11716741 | 2 |
| #11716739 | 2 |
| #65795 | 5 |
| #65294 | 5 |