Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
426 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 426 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. C5×#4070 | C2 | semidirect |
| 3. C2×C5×#677 | C2 | semidirect |
| 4. C52×C22⋊C8 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 11. C2×C5×Dic10 | C22 | semidirect |
| 12. C2×C52×C8 | C22 | semidirect |
| 14. C5×C4⋊Dic5 | C22 | semidirect |
| 18. #65020 | C5 | direct (N × H) |
| 38. #4070 | C2×C5 | semidirect |
| 39. C2×#677 | C2×C5 | semidirect |
| 42. C5×C22⋊C8 | D5 | semidirect |
| 43. C5×C22⋊C8 | C2×C5 | semidirect |
| 44. #3953 | C2×C5 | semidirect |
| 47. C22×C52 | SD16 | semidirect |
| 69. C2×Dic10 | C22×C5 | semidirect |
| 72. C2×C5×C8 | C2×D5 | semidirect |
| 73. C2×C5×C8 | C22×C5 | semidirect |
| 78. C4⋊Dic5 | C22×C5 | semidirect |
| 126. C22⋊C8 | C5×D5 | semidirect |
| 127. C52 | #450 | semidirect |
| 140. C22×C5 | #677 | semidirect |
| 141. C22×C5 | C5×SD16 | semidirect |
| 165. C2×C8 | C2×C5×D5 | semidirect |
| 199. C5 | #65020 | direct (N × H) |
| 200. C5 | C5×#450 | semidirect |
| 207. C22 | C5×#677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C5×#4070 | 2 |
| C2×C5×#677 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#450 | 5 |
| #65020 | 5 |