Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 70 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. C52×#135 | C2 | semidirect |
| 2. C2×C5×D40 | C2 | semidirect |
| 3. C5×#3960 | C2 | semidirect |
| 4. C5×#3958 | C2 | semidirect |
| 5. C5×#3944 | C2 | semidirect |
| 8. C52×Q16 | C22 | semidirect |
| 10. C52×D8 | C22 | semidirect |
| 14. C5×#672 | C22 | semidirect |
| 16. #65482 | C5 | direct (N × H) |
| 28. C5×#135 | D5 | semidirect |
| 29. C5×#135 | C2×C5 | semidirect |
| 31. C2×D40 | C2×C5 | semidirect |
| 35. #3960 | C2×C5 | semidirect |
| 36. #3958 | C2×C5 | semidirect |
| 37. #3944 | C2×C5 | semidirect |
| 51. C5×Q16 | C2×D5 | semidirect |
| 52. C5×Q16 | C22×C5 | semidirect |
| 59. C5×D8 | C2×D5 | semidirect |
| 60. C5×D8 | C22×C5 | semidirect |
| 67. #672 | C22×C5 | semidirect |
| 100. #135 | C5×D5 | semidirect |
| 105. C52 | #509 | semidirect |
| 127. Q16 | C2×C5×D5 | semidirect |
| 131. D8 | C2×C5×D5 | semidirect |
| 156. C5 | #65482 | direct (N × H) |
| 157. C5 | C5×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| C2×C5×D40 | 2 |
| C5×#3960 | 2 |
| C5×#3958 | 2 |
| C5×#3944 | 2 |
| C5×#509 | 5 |
| #65482 | 5 |