Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 109 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. C52×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11717269 | C2 | semidirect |
| 3. #11717268 | C2 | semidirect |
| 4. C2×#87809 | C2 | semidirect |
| 5. #11716700 | C2 | semidirect |
| 6. #11716690 | C2 | semidirect |
| 7. #11716689 | C2 | semidirect |
| 40. C5×AGL(1,ℤ/8) | D5 | semidirect |
| 94. AGL(1,ℤ/8) | C5⋊D5 | semidirect |
| 100. C52 | #472 | semidirect |
| 146. C5 | #65488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×AGL(1,ℤ/8) | 2 |
| #11717269 | 2 |
| #11717268 | 2 |
| C2×#87809 | 2 |
| #11716700 | 2 |
| #11716690 | 2 |
| #11716689 | 2 |
| #65488 | 5 |