Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 346 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. #11716690 | C2 | semidirect |
| 5. C5×#3956 | C2 | semidirect |
| 6. #11716601 | C2 | semidirect |
| 7. #11716600 | C2 | semidirect |
| 53. D5×M16 | D5 | semidirect |
| 57. #3956 | D5 | semidirect |
| 172. C52 | #413 | semidirect |
| 252. C5 | #65040 | semidirect |
| 253. C5 | #65421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C5×D5×M16 | 2 |
| D5×#681 | 2 |
| #11716690 | 2 |
| C5×#3956 | 2 |
| #11716601 | 2 |
| #11716600 | 2 |
| #65421 | 5 |
| #65040 | 5 |