Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
470 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 60 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. C5×#4082 | C2 | semidirect |
| 3. #11716951 | C2 | semidirect |
| 4. C5×#3965 | C2 | semidirect |
| 5. #11716611 | C2 | semidirect |
| 11. C2×C5×Dic10 | C22 | semidirect |
| 13. C4×C5×Dic5 | C22 | semidirect |
| 14. C5×#681 | C22 | semidirect |
| 38. #4082 | D5 | semidirect |
| 41. #3965 | D5 | semidirect |
| 69. C2×Dic10 | C2×D5 | semidirect |
| 76. C4×Dic5 | C2×D5 | semidirect |
| 77. #681 | C2×D5 | semidirect |
| 128. C52 | #455 | semidirect |
| 192. C5 | #65035 | semidirect |
| 193. C5 | #65350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717517 | 2 |
| C5×#4082 | 2 |
| #11716951 | 2 |
| C5×#3965 | 2 |
| #11716611 | 2 |
| #65350 | 5 |
| #65035 | 5 |