Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
552 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 174 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. #11717332 | C2 | semidirect |
| 5. #11717330 | C2 | semidirect |
| 6. D5×#700 | 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. #87829 | C22 | semidirect |
| 20. #87827 | C22 | semidirect |
| 21. #87827 | C22 | semidirect |
| 47. #4133 | D5 | direct (N × H) |
| 83. #700 | C2×D5 | semidirect |
| 87. D5⋊C8 | C2×D5 | semidirect |
| 101. C5×D5 | #131 | semidirect |
| 144. C52 | C2×#131 | semidirect |
| 189. D5 | #4133 | direct (N × H) |
| 207. C5 | D5×#131 | semidirect |
| 208. C5 | C2×#4133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#713 | 2 |
| #11717428 | 2 |
| C5×#4133 | 2 |
| #11717332 | 2 |
| #11717330 | 2 |
| D5×#700 | 2 |
| D5×D5⋊C8 | 2 |
| C2×#4133 | 5 |
| D5×#131 | 5 |