Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
127 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 127 conjugacy classes of subgroups — too many to draw. Only its 37 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. #11716836 | C2 | semidirect |
| 3. #11716833 | C2 | semidirect |
| 6. C52×D8 | C4 | semidirect |
| 8. C5×Dic20 | C4 | semidirect |
| 39. C5×D8 | Dic5 | semidirect |
| 40. C5×D8 | AGL(1,𝔽5) | semidirect |
| 44. Dic20 | Dic5 | semidirect |
| 73. C52 | #360 | semidirect |
| 91. D8 | #1042 | semidirect |
| 112. C5 | #64786 | semidirect |
| 113. C5 | #64903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4058 | 2 |
| #11716836 | 2 |
| #11716833 | 2 |
| #64903 | 5 |
| #64786 | 5 |