Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
335 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11717425 | C2 | semidirect |
| 3. D5⋊#681 | C2 | semidirect |
| 4. #11716851 | C2 | semidirect |
| 5. C2×C52×D4 | C4 | semidirect |
| 10. C5×#711 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 17. C4×#1042 | C22 | semidirect |
| 18. #87849 | C22 | semidirect |
| 68. C2×C5×D4 | Dic5 | semidirect |
| 69. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 76. #711 | Dic5 | semidirect |
| 79. C2×Dic10 | Dic5 | semidirect |
| 144. C52 | #421 | semidirect |
| 180. C2×D4 | #1042 | semidirect |
| 222. C5 | #65525 | semidirect |
| 223. C5 | #65769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| #11717425 | 2 |
| D5⋊#681 | 2 |
| #11716851 | 2 |
| #65769 | 5 |
| #65525 | 5 |