Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 142 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. C5×#4072 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 12. C5×C4⋊Dic5 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 17. #65504 | C5 | direct (N × H) |
| 36. #4072 | C2×C5 | semidirect |
| 37. C2×#681 | C2×C5 | semidirect |
| 39. #3964 | C2×C5 | semidirect |
| 61. C2×C5×D4 | Dic5 | semidirect |
| 62. C2×C5×D4 | C4×C5 | semidirect |
| 74. C4⋊Dic5 | C22×C5 | semidirect |
| 77. C2×#168 | C22×C5 | semidirect |
| 124. C52 | #418 | semidirect |
| 157. C2×D4 | C5×Dic5 | semidirect |
| 191. C5 | #65504 | direct (N × H) |
| 192. C5 | C5×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C5×#4072 | 2 |
| C2×C5×#681 | 2 |
| C5×#3964 | 2 |
| C5×#418 | 5 |
| #65504 | 5 |