Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
551 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 551 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 |
| 5. #1042⋊Q8 | C2 | semidirect |
| 7. AGL(1,𝔽5)×Dic10 | C2 | semidirect |
| 8. Q8×C5⋊D5 | C4 | semidirect |
| 9. C5×Q8×D5 | C4 | semidirect |
| 12. #87872 | C4 | semidirect |
| 13. D5×Dic10 | C4 | semidirect |
| 47. Q8×AGL(1,𝔽5) | D5 | semidirect |
| 78. Q8×D5 | AGL(1,𝔽5) | semidirect |
| 150. C52 | #519 | semidirect |
| 225. C5 | #65906 | semidirect |
| 226. C5 | #66262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| Q8×#1042 | 2 |
| C5×Q8×AGL(1,𝔽5) | 2 |
| #11717325 | 2 |
| #1042⋊Q8 | 2 |
| #11717323 | 2 |
| AGL(1,𝔽5)×Dic10 | 2 |
| #66262 | 5 |
| #65906 | 5 |