Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 94 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. C52×C22⋊Q8 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 7. C2×C52×Q8 | C22 | semidirect |
| 13. C52×C4⋊C4 | C22 | semidirect |
| 16. C2×C5×#168 | C22 | semidirect |
| 18. #65335 | C5 | direct (N × H) |
| 38. C5×C22⋊Q8 | D5 | semidirect |
| 39. C5×C22⋊Q8 | C2×C5 | semidirect |
| 40. C2×#688 | C2×C5 | semidirect |
| 43. C22⋊#168 | C2×C5 | semidirect |
| 44. #3941 | C2×C5 | semidirect |
| 47. C22×C52 | SD16 | semidirect |
| 60. C2×C5×Q8 | C2×D5 | semidirect |
| 61. C2×C5×Q8 | C22×C5 | semidirect |
| 77. C5×C4⋊C4 | C2×D5 | semidirect |
| 78. C5×C4⋊C4 | C22×C5 | semidirect |
| 83. C2×#168 | C22×C5 | semidirect |
| 129. C22⋊Q8 | C5×D5 | semidirect |
| 132. C52 | #450 | semidirect |
| 145. C22×C5 | #688 | semidirect |
| 146. C22×C5 | C5×SD16 | semidirect |
| 166. C2×Q8 | C2×C5×D5 | semidirect |
| 174. C4⋊C4 | C2×C5×D5 | semidirect |
| 206. C5 | #65335 | direct (N × H) |
| 207. C5 | C5×#450 | semidirect |
| 214. C22 | C5×#688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C52×C22⋊Q8 | 2 |
| C2×C5×#688 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#3941 | 2 |
| C5×#450 | 5 |
| #65335 | 5 |