Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
300 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 79 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. C8×#1044 | C2 | semidirect |
| 5. #11716860 | C2 | semidirect |
| 6. #11716764 | C2 | semidirect |
| 7. #11716761 | C2 | semidirect |
| 13. D5⋊#170 | C4 | semidirect |
| 17. C5×#676 | C4 | semidirect |
| 18. #87768 | C4 | semidirect |
| 63. #676 | AGL(1,𝔽5) | semidirect |
| 98. C52 | #405 | semidirect |
| 144. C5 | #65728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊(D5⋊C8) | 2 |
| #11717356 | 2 |
| #11716909 | 2 |
| C8×#1044 | 2 |
| #11716860 | 2 |
| #11716764 | 2 |
| #11716761 | 2 |
| #65728 | 5 |