Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1048 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 1. C2×#87900 | C2 | semidirect |
| 2. C2×C52×M16 | C2 | semidirect |
| 3. #11717229 | C2 | semidirect |
| 4. #11717228 | C2 | semidirect |
| 5. #11717224 | C2 | semidirect |
| 11. #87900 | C22 | semidirect |
| 12. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 14. C2×#6045 | C22 | semidirect |
| 15. C52×M16 | C22 | semidirect |
| 16. C2×C52×C8 | C22 | semidirect |
| 17. #87802 | C22 | semidirect |
| 18. #87801 | C22 | semidirect |
| 19. #87800 | C22 | semidirect |
| 38. C2×C5×M16 | D5 | semidirect |
| 60. C5×M16 | C2×D5 | semidirect |
| 61. C2×C5×C8 | C2×D5 | semidirect |
| 90. C2×M16 | C5⋊D5 | semidirect |
| 91. C52 | #575 | semidirect |
| 113. M16 | C2×C5⋊D5 | semidirect |
| 114. C2×C8 | C2×C5⋊D5 | semidirect |
| 135. C5 | #66082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C52×M16 | 2 |
| #11717229 | 2 |
| #11717228 | 2 |
| #11717224 | 2 |
| #66082 | 5 |