Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 94 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×C5×Dic20 | C2 | semidirect |
| 4. C5×#4015 | C2 | semidirect |
| 5. C52×#97 | C2 | semidirect |
| 16. #65004 | C5 | direct (N × H) |
| 31. C2×Dic20 | C2×C5 | semidirect |
| 34. #4015 | C2×C5 | semidirect |
| 36. C5×#97 | D5 | semidirect |
| 37. C5×#97 | C2×C5 | semidirect |
| 96. #97 | C5×D5 | semidirect |
| 97. C52 | #497 | semidirect |
| 143. C5 | #65004 | direct (N × H) |
| 144. C5 | C5×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C2×C5×#677 | 2 |
| C5×#4021 | 2 |
| C5×#4015 | 2 |
| C52×#97 | 2 |
| C5×#497 | 5 |
| #65004 | 5 |