Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
576 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 138 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. C2×C4×#1039 | C2 | semidirect |
| 2. C4×C5×C22⋊D5 | C2 | semidirect |
| 3. #11717100 | C2 | semidirect |
| 5. #11717080 | C2 | semidirect |
| 6. C4×#6039 | C2 | semidirect |
| 7. #11717033 | C2 | semidirect |
| 8. C4×#6037 | C2 | semidirect |
| 9. #11716989 | C2 | semidirect |
| 10. #11716980 | C2 | semidirect |
| 11. #11716973 | C2 | semidirect |
| 58. C4×C22⋊D5 | D5 | semidirect |
| 179. C52 | #529 | semidirect |
| 264. C5 | #65872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C4×C5×C22⋊D5 | 2 |
| #11717100 | 2 |
| #11717098 | 2 |
| #11717080 | 2 |
| C4×#6039 | 2 |
| #11717033 | 2 |
| C4×#6037 | 2 |
| #11716989 | 2 |
| #11716980 | 2 |
| #11716973 | 2 |
| #65872 | 5 |