Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C52×#124 | C2 | semidirect |
| 3. C5×#4088 | C2 | semidirect |
| 4. C5×#3965 | C2 | semidirect |
| 5. C5×#3937 | C2 | semidirect |
| 6. C2×C52×Q8 | C22 | semidirect |
| 13. C42×C52 | C22 | semidirect |
| 16. C5×#681 | C22 | semidirect |
| 18. #65350 | C5 | direct (N × H) |
| 37. C5×#124 | D5 | semidirect |
| 38. C5×#124 | C2×C5 | semidirect |
| 39. #4088 | C2×C5 | semidirect |
| 42. #3965 | C2×C5 | semidirect |
| 43. #3937 | C2×C5 | semidirect |
| 56. C2×C5×Q8 | C2×D5 | semidirect |
| 57. C2×C5×Q8 | C22×C5 | semidirect |
| 74. C42×C5 | C2×D5 | semidirect |
| 75. C42×C5 | C22×C5 | semidirect |
| 78. #681 | C22×C5 | semidirect |
| 120. #124 | C5×D5 | semidirect |
| 123. C52 | #455 | semidirect |
| 150. C2×Q8 | C2×C5×D5 | semidirect |
| 158. C42 | C2×C5×D5 | semidirect |
| 185. C5 | #65350 | direct (N × H) |
| 186. C5 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4144 | 2 |
| C52×#124 | 2 |
| C5×#4088 | 2 |
| C5×#3965 | 2 |
| C5×#3937 | 2 |
| C5×#455 | 5 |
| #65350 | 5 |