Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 192 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. #11717197 | C2 | semidirect |
| 3. C5×D5×C22⋊C4 | C2 | semidirect |
| 4. D5×C22⋊Dic5 | C2 | semidirect |
| 5. #11717075 | C2 | semidirect |
| 6. #11717020 | C2 | semidirect |
| 7. C4×#6037 | C2 | semidirect |
| 8. #11716997 | C2 | semidirect |
| 11. C2×C4×C5×D5 | C22 | semidirect |
| 12. C2×#6037 | C4 | semidirect |
| 16. C2×D5×Dic5 | C22 | semidirect |
| 19. #87806 | C22 | semidirect |
| 20. C4×#1039 | C22 | semidirect |
| 22. C5×#685 | C22 | semidirect |
| 23. #87781 | C22 | semidirect |
| 24. #87778 | C22 | semidirect |
| 25. Dic52 | C22 | semidirect |
| 29. C22×C5×D5 | C2×C4 | semidirect |
| 33. C2×#1039 | C2×C4 | semidirect |
| 39. #6037 | C2×C4 | semidirect |
| 40. #6037 | C2×C4 | semidirect |
| 41. #6037 | C2×C4 | semidirect |
| 51. D5×C22⋊C4 | D5 | semidirect |
| 80. C2×C4×D5 | C2×D5 | semidirect |
| 90. #685 | C2×D5 | semidirect |
| 110. C22×D5 | C4×D5 | semidirect |
| 141. C52 | #518 | semidirect |
| 212. C5 | #65820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6037 | 2 |
| #11717197 | 2 |
| C5×D5×C22⋊C4 | 2 |
| D5×C22⋊Dic5 | 2 |
| #11717075 | 2 |
| #11717020 | 2 |
| C4×#6037 | 2 |
| #11716997 | 2 |
| #65820 | 5 |