Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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×#124 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 3. C2×C5×#686 | C2 | semidirect |
| 4. C5×#4020 | C2 | semidirect |
| 5. C5×#3935 | C2 | semidirect |
| 16. #65347 | C5 | direct (N × H) |
| 27. C5×#168 | D4 | semidirect |
| 32. C5×#124 | D5 | semidirect |
| 33. C5×#124 | C2×C5 | semidirect |
| 34. C2×#688 | C2×C5 | semidirect |
| 35. C2×#686 | C2×C5 | semidirect |
| 36. #4020 | C2×C5 | semidirect |
| 38. #3935 | C2×C5 | semidirect |
| 101. #168 | C5×D4 | semidirect |
| 105. #124 | C5×D5 | semidirect |
| 107. C52 | #496 | semidirect |
| 162. C5 | #65347 | direct (N × H) |
| 163. C5 | C5×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×#686 | 2 |
| C5×#4020 | 2 |
| C5×#3935 | 2 |
| C5×#496 | 5 |
| #65347 | 5 |