Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
666 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 266 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×#1039 | C2 | semidirect |
| 3. C5×Q8×Dic5 | C2 | semidirect |
| 6. #11716961 | C2 | semidirect |
| 7. Dic5×Dic10 | C2 | semidirect |
| 9. C5×Q8×D5 | C4 | semidirect |
| 24. C52×Q8 | C2×C4 | semidirect |
| 32. C5×Dic10 | C2×C4 | semidirect |
| 34. D5×Dic5 | Q8 | direct (N × H) |
| 43. Q8×Dic5 | D5 | direct (N × H) |
| 56. #1039 | C2×Q8 | semidirect |
| 59. C5×Dic5 | C2×Q8 | semidirect |
| 68. Q8×D5 | Dic5 | direct (N × H) |
| 93. C5×D5 | C4×Q8 | semidirect |
| 98. C5×Q8 | C4×D5 | semidirect |
| 99. C5×Q8 | C2×Dic5 | semidirect |
| 121. Dic10 | C2×Dic5 | semidirect |
| 129. C52 | C2×C4×Q8 | semidirect |
| 152. Dic5 | Q8×D5 | direct (N × H) |
| 177. D5 | Q8×Dic5 | direct (N × H) |
| 180. Q8 | D5×Dic5 | direct (N × H) |
| 191. C5 | C4×Q8×D5 | semidirect |
| 192. C5 | C2×Q8×Dic5 | 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×#1039 | 2 |
| C5×Q8×Dic5 | 2 |
| D5×C4⋊Dic5 | 2 |
| C4×D5×Dic5 | 2 |
| #11716961 | 2 |
| Dic5×Dic10 | 2 |
| C2×Q8×Dic5 | 5 |
| C4×Q8×D5 | 5 |