Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
690 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
| 4. #11717017 | C2 | semidirect |
| 5. Dic5×D20 | C2 | semidirect |
| 6. C4×D5×Dic5 | C2 | semidirect |
| 7. #11716959 | C2 | semidirect |
| 9. C5×#713 | C4 | semidirect |
| 24. C52×Q8 | C2×C4 | semidirect |
| 31. C5×D20 | C2×C4 | semidirect |
| 32. C4×C5×D5 | C2×C4 | semidirect |
| 41. Q8×Dic5 | D5 | semidirect |
| 56. #1039 | #41 | semidirect |
| 59. C5×Dic5 | #41 | semidirect |
| 68. #713 | Dic5 | direct (N × H) |
| 97. C5×Q8 | C4×D5 | semidirect |
| 98. C5×Q8 | C2×Dic5 | semidirect |
| 118. D20 | C2×Dic5 | semidirect |
| 121. C4×D5 | C2×Dic5 | semidirect |
| 129. C52 | C4×#41 | semidirect |
| 152. Dic5 | #713 | direct (N × H) |
| 179. Q8 | D5×Dic5 | semidirect |
| 191. C5 | C4×#713 | semidirect |
| 192. C5 | #41×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| Q8×#1039 | 2 |
| C5×Q8×Dic5 | 2 |
| #11717017 | 2 |
| Dic5×D20 | 2 |
| C4×D5×Dic5 | 2 |
| #11716959 | 2 |
| #41×Dic5 | 5 |
| C4×#713 | 5 |