Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
664 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 183 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. C2×#87863 | C2 | semidirect |
| 3. C2×#87856 | C2 | semidirect |
| 4. C2×#87834 | C2 | semidirect |
| 5. C2×D5⋊#170 | C2 | semidirect |
| 6. D5⋊#700 | C2 | direct (N × H) |
| 16. C2×#6034 | C22 | semidirect |
| 17. #87863 | C22 | semidirect |
| 18. C2×#6033 | C22 | semidirect |
| 19. #87856 | C22 | semidirect |
| 20. #87834 | C22 | semidirect |
| 21. D5⋊#170 | C22 | semidirect |
| 42. #6034 | C23 | semidirect |
| 43. #6033 | C23 | semidirect |
| 61. C2×C5×D5 | M16 | semidirect |
| 104. C2×C52 | C2×M16 | semidirect |
| 108. C5×D5 | C2×M16 | semidirect |
| 161. C52 | C22×M16 | semidirect |
| 178. C2×D5 | #700 | semidirect |
| 213. C2×C5 | C2×#700 | semidirect |
| 214. C2×C5 | D5⋊M16 | semidirect |
| 221. D5 | C2×#700 | semidirect |
| 243. C5 | C22×#700 | semidirect |
| 244. C5 | C2×D5⋊M16 | semidirect |
| 261. C2 | D5⋊#700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×#87863 | 2 |
| C2×#87856 | 2 |
| C2×#87834 | 2 |
| C2×D5⋊#170 | 2 |
| D5⋊#700 | 2 |
| C2×D5⋊M16 | 5 |
| C22×#700 | 5 |