Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 68 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. D5×D5⋊C8 | C2 | semidirect |
| 3. #11717323 | C2 | semidirect |
| 4. #11716852 | C2 | semidirect |
| 5. C5×#4009 | C2 | semidirect |
| 6. #11716735 | C2 | semidirect |
| 7. #11716734 | C2 | semidirect |
| 8. #87904 | C4 | semidirect |
| 9. C5×#713 | C4 | semidirect |
| 16. #87874 | C4 | semidirect |
| 18. #87871 | C4 | semidirect |
| 63. #4009 | D5 | semidirect |
| 96. #713 | AGL(1,𝔽5) | semidirect |
| 200. C52 | #416 | semidirect |
| 304. C5 | #65093 | semidirect |
| 305. C5 | #65794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#713 | 2 |
| D5×D5⋊C8 | 2 |
| #11717323 | 2 |
| #11716852 | 2 |
| C5×#4009 | 2 |
| #11716735 | 2 |
| #11716734 | 2 |
| #65794 | 5 |
| #65093 | 5 |