Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1600 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 1600 conjugacy classes of subgroups — too many to draw. Only its 379 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×C52×#135 | C2 | semidirect |
| 2. C22×#87801 | C2 | semidirect |
| 3. #13103058 | C2 | direct (N × H) |
| 4. C2×#11716695 | C2 | semidirect |
| 5. C2×#11716693 | C2 | semidirect |
| 6. C2×#11716679 | C2 | semidirect |
| 10. C52×#135 | C22 | semidirect |
| 11. C2×C52×Q16 | C22 | semidirect |
| 13. C2×C52×D8 | C22 | semidirect |
| 18. C2×#87801 | C22 | semidirect |
| 19. #11716695 | C22 | semidirect |
| 20. #11716693 | C22 | semidirect |
| 21. #11716679 | C22 | semidirect |
| 22. C2×#87756 | C22 | semidirect |
| 37. C52×Q16 | C23 | semidirect |
| 40. C52×D8 | C23 | semidirect |
| 48. #87756 | C23 | semidirect |
| 49. C2×C5×#135 | D5 | semidirect |
| 80. C5×#135 | C2×D5 | semidirect |
| 81. C2×C5×Q16 | C2×D5 | semidirect |
| 83. C2×C5×D8 | C2×D5 | semidirect |
| 119. C5×Q16 | C22×D5 | semidirect |
| 122. C5×D8 | C22×D5 | semidirect |
| 131. C2×#135 | C5⋊D5 | semidirect |
| 139. C2×C52 | #509 | semidirect |
| 167. #135 | C2×C5⋊D5 | semidirect |
| 168. C2×Q16 | C2×C5⋊D5 | semidirect |
| 174. C2×D8 | C2×C5⋊D5 | semidirect |
| 180. C52 | C2×#509 | semidirect |
| 206. Q16 | C22×C5⋊D5 | semidirect |
| 212. D8 | C22×C5⋊D5 | semidirect |
| 220. C2×C5 | #65482 | semidirect |
| 245. C5 | C2×#65482 | semidirect |
| 261. C2 | #13103058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#135 | 2 |
| C22×#87801 | 2 |
| #13103058 | 2 |
| C2×#11716695 | 2 |
| C2×#11716693 | 2 |
| C2×#11716679 | 2 |
| C2×#65482 | 5 |