Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
551 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 172 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. #11717428 | C2 | semidirect |
| 3. C5×#4133 | C2 | semidirect |
| 4. #11717331 | C2 | semidirect |
| 5. #11717329 | C2 | semidirect |
| 6. #11717327 | C2 | semidirect |
| 7. D5×D5⋊C8 | C2 | semidirect |
| 15. #87849 | C22 | semidirect |
| 16. D5⋊#168 | C22 | semidirect |
| 17. C5×#700 | C22 | semidirect |
| 18. C5×D5⋊C8 | C22 | semidirect |
| 19. #87828 | C22 | semidirect |
| 22. D5×#170 | C22 | semidirect |
| 23. D5×#170 | C22 | semidirect |
| 45. #4133 | D5 | semidirect |
| 83. #700 | C2×D5 | semidirect |
| 87. D5⋊C8 | C2×D5 | semidirect |
| 99. C5⋊D5 | #131 | semidirect |
| 144. C52 | C2×#131 | semidirect |
| 207. C5 | D5×#131 | semidirect |
| 208. C5 | D5⋊#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717484 | 2 |
| #11717428 | 2 |
| C5×#4133 | 2 |
| #11717331 | 2 |
| #11717329 | 2 |
| #11717327 | 2 |
| D5×D5⋊C8 | 2 |
| D5⋊#131 | 5 |
| D5×#131 | 5 |