Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
418 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3955 | C2 | semidirect |
| 6. #11716600 | C2 | semidirect |
| 7. #11716599 | C2 | semidirect |
| 17. C52×M16 | C22 | semidirect |
| 18. #87804 | C22 | semidirect |
| 19. C5×#681 | C22 | semidirect |
| 20. C5×#681 | C22 | semidirect |
| 54. D5×M16 | D5 | semidirect |
| 63. #3955 | D5 | direct (N × H) |
| 101. C5×M16 | C2×D5 | semidirect |
| 102. C5×M16 | C2×D5 | semidirect |
| 108. #681 | C2×D5 | semidirect |
| 109. #681 | C2×D5 | semidirect |
| 121. C5×D5 | #100 | semidirect |
| 179. C52 | C2×#100 | semidirect |
| 227. M16 | D52 | semidirect |
| 244. D5 | #3955 | direct (N × H) |
| 268. C5 | D5×#100 | semidirect |
| 269. C5 | C2×#3955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| C5×D5×M16 | 2 |
| D5×#681 | 2 |
| #11716690 | 2 |
| C5×#3955 | 2 |
| #11716600 | 2 |
| #11716599 | 2 |
| C2×#3955 | 5 |
| D5×#100 | 5 |