Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
623 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 623 conjugacy classes of subgroups — too many to draw. Only its 194 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×#87849 | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. C2×#87829 | C2 | semidirect |
| 5. C2×D5×#170 | C2 | semidirect |
| 6. D5×#700 | C2 | direct (N × H) |
| 16. C2×#6032 | C22 | semidirect |
| 17. #87849 | C22 | semidirect |
| 18. C2×C5×#170 | C22 | semidirect |
| 19. C5×#700 | C22 | semidirect |
| 20. #87829 | C22 | semidirect |
| 21. D5×#170 | C22 | semidirect |
| 42. #6032 | C23 | semidirect |
| 43. C5×#170 | C23 | semidirect |
| 50. C2×#700 | D5 | direct (N × H) |
| 60. C2×C5×D5 | M16 | semidirect |
| 90. C2×#170 | C2×D5 | semidirect |
| 93. #700 | C2×D5 | direct (N × H) |
| 101. C2×C52 | C2×M16 | semidirect |
| 105. C5×D5 | C2×M16 | semidirect |
| 147. #170 | C22×D5 | semidirect |
| 156. C52 | C22×M16 | semidirect |
| 173. C2×D5 | #700 | direct (N × H) |
| 207. C2×C5 | D5×M16 | semidirect |
| 208. C2×C5 | C2×#700 | semidirect |
| 215. D5 | C2×#700 | direct (N × H) |
| 237. C5 | C2×D5×M16 | semidirect |
| 238. C5 | C22×#700 | semidirect |
| 255. 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×#87849 | 2 |
| C2×C5×#700 | 2 |
| C2×#87829 | 2 |
| C2×D5×#170 | 2 |
| D5×#700 | 2 |
| C22×#700 | 5 |
| C2×D5×M16 | 5 |