Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 144 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×C5×#713 | C2 | semidirect |
| 2. C2×#87874 | C2 | semidirect |
| 3. C2×#87811 | C2 | semidirect |
| 4. C2×C5×#689 | C2 | semidirect |
| 5. #11717067 | C2 | direct (N × H) |
| 6. C2×#87772 | C2 | semidirect |
| 7. C2×#87771 | C2 | semidirect |
| 8. C2×D5×#168 | C2 | semidirect |
| 12. C5×#713 | C22 | semidirect |
| 21. #87874 | C22 | semidirect |
| 22. #87811 | C22 | semidirect |
| 24. C5×#689 | C22 | semidirect |
| 26. #87772 | C22 | semidirect |
| 27. #87771 | C22 | semidirect |
| 28. D5×#168 | C22 | semidirect |
| 56. C2×#713 | D5 | semidirect |
| 60. C2×#689 | D5 | semidirect |
| 97. #713 | C2×D5 | semidirect |
| 113. #689 | C2×D5 | semidirect |
| 128. C2×C52 | #135 | semidirect |
| 195. C52 | C2×#135 | semidirect |
| 250. C2×C5 | #4065 | semidirect |
| 251. C2×C5 | #4096 | semidirect |
| 283. C5 | C2×#4065 | semidirect |
| 284. C5 | C2×#4096 | semidirect |
| 300. C2 | #11717067 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×#87874 | 2 |
| C2×#87811 | 2 |
| C2×C5×#689 | 2 |
| #11717067 | 2 |
| C2×#87772 | 2 |
| C2×#87771 | 2 |
| C2×D5×#168 | 2 |
| C2×#4096 | 5 |
| C2×#4065 | 5 |