Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 127 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. #11717244 | C2 | semidirect |
| 3. C2×#87802 | C2 | semidirect |
| 4. C2×#87800 | C2 | semidirect |
| 5. C52×C22⋊C8 | C2 | semidirect |
| 6. #11716688 | C2 | semidirect |
| 7. #11716683 | C2 | semidirect |
| 47. C5×C22⋊C8 | D5 | semidirect |
| 109. C22⋊C8 | C5⋊D5 | semidirect |
| 110. C52 | #452 | semidirect |
| 163. C5 | #65022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| #11717244 | 2 |
| C2×#87802 | 2 |
| C2×#87800 | 2 |
| C52×C22⋊C8 | 2 |
| #11716688 | 2 |
| #11716683 | 2 |
| #65022 | 5 |