Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
551 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 225 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. Q8×#1042 | C2 | semidirect |
| 4. C2×C52×Q8 | C4 | semidirect |
| 5. C5×Q8×D5 | C4 | semidirect |
| 8. C2×C5×Dic10 | C4 | semidirect |
| 39. C2×C5×Q8 | Dic5 | semidirect |
| 40. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 42. Q8×D5 | Dic5 | semidirect |
| 45. C2×Dic10 | Dic5 | semidirect |
| 78. C52 | #519 | semidirect |
| 98. C2×Q8 | #1042 | semidirect |
| 122. C5 | #66146 | semidirect |
| 123. C5 | #66262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| Q8×#1042 | 2 |
| #11717425 | 2 |
| #66262 | 5 |
| #66146 | 5 |