Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11717523 | C2 | semidirect |
| 2. C52×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #11717256 | C2 | semidirect |
| 4. #11717252 | C2 | semidirect |
| 5. #11716704 | C2 | semidirect |
| 6. #11716692 | C2 | semidirect |
| 7. #11716691 | C2 | semidirect |
| 49. C5×AGL(1,ℤ/8) | D5 | semidirect |
| 113. AGL(1,ℤ/8) | C5⋊D5 | semidirect |
| 118. C52 | #454 | semidirect |
| 174. C5 | #65490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717523 | 2 |
| C52×AGL(1,ℤ/8) | 2 |
| #11717256 | 2 |
| #11717252 | 2 |
| #11716704 | 2 |
| #11716692 | 2 |
| #11716691 | 2 |
| #65490 | 5 |