Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
338 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 78 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×D5×M16 | C2 | semidirect |
| 3. D5×#681 | C2 | semidirect |
| 4. #11716691 | C2 | semidirect |
| 5. C5×#3955 | C2 | semidirect |
| 6. #11716602 | C2 | semidirect |
| 7. #11716599 | C2 | semidirect |
| 53. D5×M16 | D5 | semidirect |
| 62. #3955 | D5 | semidirect |
| 172. C52 | #413 | semidirect |
| 250. C5 | #65034 | semidirect |
| 251. C5 | #65421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| C5×D5×M16 | 2 |
| D5×#681 | 2 |
| #11716691 | 2 |
| C5×#3955 | 2 |
| #11716602 | 2 |
| #11716599 | 2 |
| #65421 | 5 |
| #65034 | 5 |