Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 68 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. C4×D5×AGL(1,𝔽5) | C2 | semidirect |
| 3. D5×#700 | C2 | semidirect |
| 4. #11716851 | C2 | semidirect |
| 5. C5×#4008 | C2 | semidirect |
| 6. #11716739 | C2 | semidirect |
| 7. #11716738 | C2 | semidirect |
| 9. #87902 | C4 | semidirect |
| 11. C5×D4×D5 | C4 | semidirect |
| 17. #87871 | C4 | semidirect |
| 19. D5×Dic10 | C4 | semidirect |
| 20. C4×#1042 | C22 | semidirect |
| 21. #87849 | C22 | semidirect |
| 22. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 23. C5×#700 | C22 | semidirect |
| 34. C52×D4 | C2×C4 | semidirect |
| 38. #6045 | C2×C4 | semidirect |
| 42. C5×D20 | C2×C4 | semidirect |
| 45. C5×Dic10 | C2×C4 | semidirect |
| 66. #4008 | D5 | direct (N × H) |
| 103. D4×D5 | AGL(1,𝔽5) | semidirect |
| 114. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 117. #700 | C2×D5 | semidirect |
| 131. C5×D5 | #104 | semidirect |
| 144. C5×D4 | C4×D5 | semidirect |
| 145. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 169. D20 | C2×AGL(1,𝔽5) | semidirect |
| 188. Dic10 | C4×D5 | semidirect |
| 200. C52 | C2×#104 | semidirect |
| 269. D5 | #4008 | direct (N × H) |
| 281. D4 | D5×AGL(1,𝔽5) | semidirect |
| 299. C5 | D5×#104 | semidirect |
| 300. C5 | C2×#4008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#711 | 2 |
| C4×D5×AGL(1,𝔽5) | 2 |
| D5×#700 | 2 |
| #11716851 | 2 |
| C5×#4008 | 2 |
| #11716739 | 2 |
| #11716738 | 2 |
| C2×#4008 | 5 |
| D5×#104 | 5 |