Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
418 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 106 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×D5×M16 | C2 | semidirect |
| 3. C52×#100 | C2 | semidirect |
| 4. C5×#3965 | C2 | semidirect |
| 5. C5×#3955 | C2 | semidirect |
| 13. C52×M16 | C22 | semidirect |
| 14. C5×#681 | C22 | semidirect |
| 18. D5×#100 | C5 | direct (N × H) |
| 37. D5×M16 | C2×C5 | semidirect |
| 41. C5×#100 | D5 | direct (N × H) |
| 42. C5×#100 | C2×C5 | semidirect |
| 43. #3965 | C2×C5 | semidirect |
| 44. #3955 | C2×C5 | semidirect |
| 75. C5×M16 | C2×D5 | semidirect |
| 76. C5×M16 | C22×C5 | semidirect |
| 78. #681 | C22×C5 | semidirect |
| 87. C5×D5 | #100 | direct (N × H) |
| 126. #100 | C5×D5 | direct (N × H) |
| 127. C52 | C2×#100 | semidirect |
| 165. M16 | C2×C5×D5 | semidirect |
| 181. D5 | C5×#100 | direct (N × H) |
| 198. C5 | D5×#100 | direct (N × H) |
| 199. C5 | C2×C5×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C5×D5×M16 | 2 |
| C52×#100 | 2 |
| C5×#3965 | 2 |
| C5×#3955 | 2 |
| C2×C5×#100 | 5 |
| D5×#100 | 5 |