Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
382 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#4144 | C2 | semidirect |
| 2. C5×#4086 | C2 | semidirect |
| 3. C5×#4054 | C2 | semidirect |
| 4. C52×#100 | C2 | semidirect |
| 5. C5×#3957 | C2 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 13. C52×M16 | C22 | semidirect |
| 14. C4×C5×Dic5 | C22 | semidirect |
| 18. #65036 | C5 | direct (N × H) |
| 30. C5×D20 | D4 | semidirect |
| 32. C5×Dic10 | D4 | semidirect |
| 35. #4144 | C2×C5 | semidirect |
| 38. #4086 | C2×C5 | semidirect |
| 39. #4054 | C2×C5 | semidirect |
| 42. C5×#100 | D5 | semidirect |
| 43. C5×#100 | C2×C5 | semidirect |
| 44. #3957 | C2×C5 | semidirect |
| 69. C2×D20 | C22×C5 | semidirect |
| 73. C5×M16 | C2×D5 | semidirect |
| 74. C5×M16 | C22×C5 | semidirect |
| 76. C4×Dic5 | C22×C5 | semidirect |
| 113. D20 | C5×D4 | semidirect |
| 115. Dic10 | C5×D4 | semidirect |
| 123. #100 | C5×D5 | semidirect |
| 124. C52 | #453 | semidirect |
| 158. M16 | C2×C5×D5 | semidirect |
| 189. C5 | #65036 | direct (N × H) |
| 190. C5 | C5×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4144 | 2 |
| C5×#4086 | 2 |
| C5×#4054 | 2 |
| C52×#100 | 2 |
| C5×#3957 | 2 |
| C5×#453 | 5 |
| #65036 | 5 |