Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
816 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C52×Q8 | C2 | semidirect |
| 3. C5×#4093 | C2 | direct (N × H) |
| 4. C2×C5×#685 | C2 | semidirect |
| 5. C2×C4×C5×Dic5 | C2 | semidirect |
| 8. C2×C52×Q8 | C22 | semidirect |
| 14. C5×#685 | C22 | semidirect |
| 15. C4×C5×Dic5 | C22 | semidirect |
| 17. C2×#4093 | C5 | direct (N × H) |
| 31. C22×C5×Q8 | D5 | semidirect |
| 32. C22×C5×Q8 | C2×C5 | semidirect |
| 38. #4093 | C2×C5 | direct (N × H) |
| 39. C2×#685 | C2×C5 | semidirect |
| 40. C2×C4×Dic5 | C2×C5 | semidirect |
| 56. C2×C5×Q8 | C2×D5 | semidirect |
| 57. C2×C5×Q8 | C22×C5 | semidirect |
| 72. #685 | C22×C5 | semidirect |
| 73. C4×Dic5 | C22×C5 | semidirect |
| 75. C2×C52 | #124 | semidirect |
| 109. C22×Q8 | C5×D5 | semidirect |
| 114. C52 | C2×#124 | semidirect |
| 140. C2×Q8 | C2×C5×D5 | semidirect |
| 152. C2×C5 | #4093 | direct (N × H) |
| 153. C2×C5 | C5×#124 | semidirect |
| 172. C5 | C2×#4093 | direct (N × H) |
| 173. C5 | C2×C5×#124 | semidirect |
| 184. C2 | C5×#4093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C22×C5×D20 | 2 |
| C5×#4093 | 2 |
| C2×C5×#685 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×#124 | 5 |
| C2×#4093 | 5 |