Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
448 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C52×M16 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 9. C2×C5×D20 | C4 | semidirect |
| 12. C2×C52×C8 | C22 | semidirect |
| 14. C5×C4⋊Dic5 | C22 | semidirect |
| 17. #65420 | C5 | direct (N × H) |
| 34. C2×C5×M16 | D5 | semidirect |
| 35. C2×C5×M16 | C2×C5 | semidirect |
| 37. #4072 | C2×C5 | semidirect |
| 39. #3953 | C2×C5 | semidirect |
| 61. C2×D20 | C4×C5 | semidirect |
| 67. C2×C5×C8 | C2×D5 | semidirect |
| 68. C2×C5×C8 | C22×C5 | semidirect |
| 73. C4⋊Dic5 | C22×C5 | semidirect |
| 113. C2×M16 | C5×D5 | semidirect |
| 116. C52 | #418 | semidirect |
| 150. C2×C8 | C2×C5×D5 | semidirect |
| 179. C5 | #65420 | direct (N × H) |
| 180. C5 | C5×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C2×C52×M16 | 2 |
| C5×#4072 | 2 |
| C5×#3953 | 2 |
| C5×#418 | 5 |
| #65420 | 5 |