Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11717246 | C2 | semidirect |
| 3. C52×C22⋊C8 | C2 | semidirect |
| 4. #11716688 | C2 | semidirect |
| 5. #11716688 | C2 | semidirect |
| 6. #11716685 | C2 | semidirect |
| 7. #11716684 | C2 | semidirect |
| 36. C5×C22⋊C8 | D5 | semidirect |
| 91. C22⋊C8 | C5⋊D5 | semidirect |
| 92. C52 | #482 | semidirect |
| 136. C5 | #65026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717250 | 2 |
| #11717246 | 2 |
| C52×C22⋊C8 | 2 |
| #11716688 | 2 |
| #11716685 | 2 |
| #11716684 | 2 |
| #65026 | 5 |