Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 352 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. #11716973 | C2 | semidirect |
| 4. #11716692 | C2 | semidirect |
| 5. C5×#3957 | C2 | semidirect |
| 6. #11716611 | C2 | semidirect |
| 7. #11716609 | C2 | semidirect |
| 13. D5×D20 | C4 | semidirect |
| 15. #87874 | C4 | semidirect |
| 17. #87870 | C4 | semidirect |
| 18. D5×Dic10 | C4 | semidirect |
| 19. C52×M16 | C22 | semidirect |
| 20. C4×#1039 | C22 | semidirect |
| 21. C4×C5×Dic5 | C22 | semidirect |
| 22. C5×#681 | C22 | semidirect |
| 60. D5×M16 | D5 | semidirect |
| 69. #3957 | D5 | semidirect |
| 112. C5×M16 | C2×D5 | semidirect |
| 113. C5×M16 | C2×D5 | semidirect |
| 123. C4×Dic5 | C2×D5 | semidirect |
| 124. #681 | C2×D5 | semidirect |
| 202. C52 | #421 | semidirect |
| 252. M16 | D52 | semidirect |
| 301. C5 | #65110 | semidirect |
| 302. C5 | #65428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#709 | 2 |
| C5×D5×M16 | 2 |
| #11716973 | 2 |
| #11716692 | 2 |
| C5×#3957 | 2 |
| #11716611 | 2 |
| #11716609 | 2 |
| #65428 | 5 |
| #65110 | 5 |