Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 136 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. C2×#87872 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 4. #11717063 | C2 | direct (N × H) |
| 5. C2×#87774 | C2 | semidirect |
| 6. C2×#87769 | C2 | semidirect |
| 18. #87872 | C22 | semidirect |
| 19. C5×#689 | C22 | semidirect |
| 21. #87774 | C22 | semidirect |
| 22. #87769 | C22 | semidirect |
| 47. C2×#689 | D5 | semidirect |
| 84. #689 | C2×D5 | semidirect |
| 90. C2×C52 | #137 | semidirect |
| 136. C52 | C2×#137 | semidirect |
| 175. C2×C5 | #4064 | semidirect |
| 201. C5 | C2×#4064 | semidirect |
| 214. C2 | #11717063 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×#87872 | 2 |
| C2×C5×#689 | 2 |
| #11717063 | 2 |
| C2×#87774 | 2 |
| C2×#87769 | 2 |
| C2×#4064 | 5 |