Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
816 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 168 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. C22×#6045 | C2 | semidirect |
| 3. C2×C5×#685 | C2 | semidirect |
| 4. C2×#87778 | C2 | semidirect |
| 5. C2×Dic52 | C2 | semidirect |
| 6. #11717031 | C2 | direct (N × H) |
| 12. C2×#6045 | C22 | semidirect |
| 16. C5×#685 | C22 | semidirect |
| 17. #87778 | C22 | semidirect |
| 18. Dic52 | C22 | semidirect |
| 41. C2×#685 | D5 | semidirect |
| 74. #685 | C2×D5 | semidirect |
| 77. C2×C52 | #124 | semidirect |
| 116. C52 | C2×#124 | semidirect |
| 156. C2×C5 | #4031 | semidirect |
| 177. C5 | C2×#4031 | semidirect |
| 190. C2 | #11717031 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C22×#6037 | 2 |
| C2×C5×#685 | 2 |
| C2×#87778 | 2 |
| C2×Dic52 | 2 |
| #11717031 | 2 |
| C2×#4031 | 5 |