Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
776 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 176 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×C4×C5×D5 | C2 | semidirect |
| 3. C2×#87806 | C2 | semidirect |
| 4. C2×C5×#685 | C2 | semidirect |
| 5. C2×#87780 | C2 | semidirect |
| 6. C2×#87778 | C2 | semidirect |
| 7. C2×#87778 | C2 | semidirect |
| 8. #11717023 | C2 | direct (N × H) |
| 17. C2×C4×C5×D5 | C22 | semidirect |
| 20. #87806 | C22 | semidirect |
| 21. C5×#685 | C22 | semidirect |
| 22. #87780 | C22 | semidirect |
| 23. #87778 | C22 | semidirect |
| 24. #87778 | C22 | semidirect |
| 51. C22×C4×D5 | D5 | semidirect |
| 58. C2×#685 | D5 | semidirect |
| 106. C2×C4×D5 | C2×D5 | semidirect |
| 112. #685 | C2×D5 | semidirect |
| 119. C2×C52 | #123 | semidirect |
| 182. C52 | C2×#123 | semidirect |
| 246. C2×C5 | #4029 | semidirect |
| 247. C2×C5 | #4075 | semidirect |
| 278. C5 | C2×#4029 | semidirect |
| 279. C5 | C2×#4075 | semidirect |
| 299. C2 | #11717023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C22×#6037 | 2 |
| C2×#87806 | 2 |
| C2×C5×#685 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| #11717023 | 2 |
| C2×#4075 | 5 |
| C2×#4029 | 5 |