Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2648 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2648 conjugacy classes of subgroups — too many to draw. Only its 371 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. C24×C5⋊D5 | C2 | semidirect |
| 2. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 4. C2×C52×C22⋊C4 | C2 | semidirect |
| 5. C2×#87808 | C2 | semidirect |
| 6. #11717202 | C2 | direct (N × H) |
| 11. C23×C5⋊D5 | C22 | semidirect |
| 12. C23×C5⋊D5 | C22 | semidirect |
| 13. C22×C4×C52 | C22 | semidirect |
| 15. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 16. C22×#1039 | C22 | semidirect |
| 18. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 19. C52×C22⋊C4 | C22 | semidirect |
| 20. #87808 | C22 | semidirect |
| 23. C23×C52 | D4 | semidirect |
| 33. C22×C5⋊D5 | D4 | semidirect |
| 35. C22×C5⋊D5 | C23 | semidirect |
| 37. C2×C4×C52 | C23 | semidirect |
| 40. C2×#1039 | C23 | semidirect |
| 45. C2×C5×C22⋊C4 | D5 | semidirect |
| 52. C22×C52 | C2×D4 | semidirect |
| 61. C2×C5⋊D5 | C2×D4 | semidirect |
| 70. C22×C4×C5 | C2×D5 | semidirect |
| 76. C5×C22⋊C4 | C2×D5 | semidirect |
| 80. C2×C52 | #120 | semidirect |
| 86. C23×C5 | D20 | semidirect |
| 100. C2×C4×C5 | C22×D5 | semidirect |
| 110. C2×C22⋊C4 | C5⋊D5 | semidirect |
| 111. C52 | C2×#120 | semidirect |
| 115. C22×C5 | C2×D20 | semidirect |
| 139. C22×C4 | C2×C5⋊D5 | semidirect |
| 141. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 143. C2×C5 | #4028 | semidirect |
| 159. C23 | C4⋊(C5⋊D5) | semidirect |
| 167. C2×C4 | C22×C5⋊D5 | semidirect |
| 168. C5 | C2×#4028 | semidirect |
| 180. C22 | C2×C4⋊(C5⋊D5) | semidirect |
| 188. C2 | #11717202 | 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×C22⋊(C5⋊D5) | 2 |
| C22×C4⋊(C5⋊D5) | 2 |
| C2×C52×C22⋊C4 | 2 |
| C2×#87808 | 2 |
| #11717202 | 2 |
| C2×#4028 | 5 |