Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
576 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 222 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×C52×Q16 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 4. C5×D5×Q16 | C2 | direct (N × H) |
| 5. C2×C5×Dic20 | C2 | semidirect |
| 14. C52×Q16 | C22 | semidirect |
| 16. C5×#689 | C22 | semidirect |
| 18. C5×Dic20 | C22 | semidirect |
| 21. C2×D5×Q16 | C5 | direct (N × H) |
| 43. C2×C5×Q16 | D5 | direct (N × H) |
| 44. C2×C5×Q16 | C2×C5 | semidirect |
| 46. C2×#689 | C2×C5 | semidirect |
| 47. D5×Q16 | C2×C5 | direct (N × H) |
| 48. C2×Dic20 | C2×C5 | semidirect |
| 51. C2×C5×D5 | Q16 | direct (N × H) |
| 76. C5×Q16 | C2×D5 | direct (N × H) |
| 77. C5×Q16 | C22×C5 | semidirect |
| 83. #689 | C22×C5 | semidirect |
| 85. Dic20 | C22×C5 | semidirect |
| 88. C2×C52 | C2×Q16 | semidirect |
| 90. C5×D5 | C2×Q16 | direct (N × H) |
| 130. C2×Q16 | C5×D5 | direct (N × H) |
| 132. C52 | C22×Q16 | semidirect |
| 138. C2×D5 | C5×Q16 | direct (N × H) |
| 162. Q16 | C2×C5×D5 | direct (N × H) |
| 169. C2×C5 | D5×Q16 | direct (N × H) |
| 170. C2×C5 | C2×C5×Q16 | semidirect |
| 173. D5 | C2×C5×Q16 | direct (N × H) |
| 190. C5 | C2×D5×Q16 | direct (N × H) |
| 191. C5 | C22×C5×Q16 | semidirect |
| 201. C2 | C5×D5×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C52×Q16 | 2 |
| C2×C5×#689 | 2 |
| C5×D5×Q16 | 2 |
| C2×C5×Dic20 | 2 |
| C2×C5×C8×D5 | 2 |
| C22×C5×Q16 | 5 |
| C2×D5×Q16 | 5 |