Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1192 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C2×C52×M16 | C2 | semidirect |
| 4. #11717228 | C2 | direct (N × H) |
| 5. C2×#87801 | C2 | semidirect |
| 6. C2×#87800 | C2 | semidirect |
| 11. #87900 | C22 | semidirect |
| 15. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 16. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 18. C2×#6045 | C22 | semidirect |
| 19. C52×M16 | C22 | semidirect |
| 20. C2×C52×C8 | C22 | semidirect |
| 21. #87801 | C22 | semidirect |
| 22. #87800 | C22 | semidirect |
| 39. C4⋊(C5⋊D5) | C23 | semidirect |
| 42. #6045 | C23 | semidirect |
| 43. C52×C8 | C23 | semidirect |
| 46. C2×C5×M16 | D5 | semidirect |
| 74. C5×M16 | C2×D5 | semidirect |
| 75. C2×C5×C8 | C2×D5 | semidirect |
| 80. C2×C52 | AGL(1,ℤ/8) | semidirect |
| 103. C5×C8 | C22×D5 | semidirect |
| 109. C2×M16 | C5⋊D5 | semidirect |
| 110. C52 | C2×AGL(1,ℤ/8) | semidirect |
| 137. M16 | C2×C5⋊D5 | semidirect |
| 138. C2×C8 | C2×C5⋊D5 | semidirect |
| 140. C2×C5 | #4054 | semidirect |
| 163. C8 | C22×C5⋊D5 | semidirect |
| 164. C5 | C2×#4054 | semidirect |
| 180. C2 | #11717228 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| C2×C52×M16 | 2 |
| #11717228 | 2 |
| C2×#87801 | 2 |
| C2×#87800 | 2 |
| C2×#4054 | 5 |