Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2096 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 2096 conjugacy classes of subgroups — too many to draw. Only its 272 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. C22×#6036 | C2 | semidirect |
| 3. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 4. #11717092 | C2 | direct (N × H) |
| 5. C2×#87779 | C2 | semidirect |
| 8. C23×C5⋊D5 | C4 | semidirect |
| 12. C22×C5×Dic5 | C22 | semidirect |
| 14. C2×#6036 | C22 | semidirect |
| 15. C5×C22⋊Dic5 | C22 | semidirect |
| 16. #87779 | C22 | semidirect |
| 19. C23×C52 | C2×C4 | semidirect |
| 26. C22×C5⋊D5 | C2×C4 | semidirect |
| 27. C22×C5⋊D5 | C2×C4 | semidirect |
| 32. C2×C5×Dic5 | C23 | semidirect |
| 38. C2×C22⋊Dic5 | D5 | semidirect |
| 44. C22×C52 | C22×C4 | semidirect |
| 50. C2×C5⋊D5 | C22⋊C4 | semidirect |
| 52. C2×C5⋊D5 | C22×C4 | semidirect |
| 68. C22×Dic5 | C2×D5 | semidirect |
| 72. C22⋊Dic5 | C2×D5 | semidirect |
| 76. C2×C52 | C2×C22⋊C4 | semidirect |
| 80. C5⋊D5 | C2×C22⋊C4 | semidirect |
| 86. C23×C5 | C4×D5 | semidirect |
| 110. C2×Dic5 | C22×D5 | semidirect |
| 117. C52 | C22×C22⋊C4 | semidirect |
| 127. C22×C5 | C2×C4×D5 | semidirect |
| 162. C2×C5 | D5×C22⋊C4 | semidirect |
| 179. C23 | #6036 | semidirect |
| 186. C5 | C2×D5×C22⋊C4 | semidirect |
| 197. C22 | C2×#6036 | semidirect |
| 204. C2 | #11717092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5⋊D5 | 2 |
| C22×#6036 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| #11717092 | 2 |
| C2×#87779 | 2 |
| C2×D5×C22⋊C4 | 5 |