Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
326 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 68 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. Q8×#1039 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. #11716613 | C2 | semidirect |
| 5. #11716604 | C2 | semidirect |
| 19. C52×Q8 | D4 | semidirect |
| 33. C2×#688 | D5 | semidirect |
| 47. #1039 | SD16 | semidirect |
| 76. C5×Q8 | C22⋊D5 | semidirect |
| 100. C52 | #460 | semidirect |
| 141. Q8 | #6037 | semidirect |
| 153. C5 | #65452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1039 | 2 |
| C2×C5×#688 | 2 |
| #11717032 | 2 |
| #11716613 | 2 |
| #11716604 | 2 |
| #65452 | 5 |