Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 608 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. Q8×#1042 | C2 | semidirect |
| 3. C5×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. #11717337 | C2 | semidirect |
| 5. D5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 6. AGL(1,𝔽5)×D20 | C2 | semidirect |
| 7. #11717325 | C2 | semidirect |
| 9. #87904 | C4 | semidirect |
| 10. C5×#713 | C4 | semidirect |
| 14. #87874 | C4 | semidirect |
| 15. #87871 | C4 | semidirect |
| 32. C52×Q8 | C2×C4 | semidirect |
| 33. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 34. C4×C5⋊D5 | C2×C4 | semidirect |
| 35. C5×D20 | C2×C4 | semidirect |
| 36. C4×C5×D5 | C2×C4 | semidirect |
| 38. C5×Dic10 | C2×C4 | semidirect |
| 39. #6038 | C2×C4 | semidirect |
| 40. #6036 | C2×C4 | semidirect |
| 41. D5×Dic5 | C2×C4 | semidirect |
| 46. Q8×AGL(1,𝔽5) | D5 | semidirect |
| 78. #713 | AGL(1,𝔽5) | semidirect |
| 118. C5×Q8 | C4×D5 | semidirect |
| 119. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 134. D20 | C2×AGL(1,𝔽5) | semidirect |
| 143. C4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 145. Dic10 | C4×D5 | semidirect |
| 153. C52 | #520 | semidirect |
| 213. Q8 | D5×AGL(1,𝔽5) | semidirect |
| 229. C5 | #65908 | semidirect |
| 230. C5 | #66266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#713 | 2 |
| Q8×#1042 | 2 |
| C5×Q8×AGL(1,𝔽5) | 2 |
| #11717337 | 2 |
| D5×C4⋊AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×D20 | 2 |
| #11717325 | 2 |
| #66266 | 5 |
| #65908 | 5 |