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 |
|---|---|---|
| 5. #1042⋊Q8 | C2 | semidirect |
| 6. AGL(1,𝔽5)×Dic10 | C2 | semidirect |
| 7. C2×#6045 | C4 | semidirect |
| 9. C2×C5×Dic10 | C4 | semidirect |
| 10. C2×#6039 | C4 | semidirect |
| 12. D5×Dic10 | C4 | semidirect |
| 13. D5×Dic10 | C4 | semidirect |
| 87. C2×Dic10 | AGL(1,𝔽5) | semidirect |
| 157. C52 | #519 | semidirect |
| 233. C5 | #65850 | semidirect |
| 234. C5 | #66262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| #11717425 | 2 |
| C5×#4130 | 2 |
| #11717339 | 2 |
| #1042⋊Q8 | 2 |
| AGL(1,𝔽5)×Dic10 | 2 |
| #66262 | 5 |
| #65850 | 5 |