Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
342 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 4. C52×#103 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3948 | C2 | semidirect |
| 7. C5×#3942 | C2 | semidirect |
| 10. C5×Q8×D5 | C4 | semidirect |
| 23. #65091 | C5 | direct (N × H) |
| 51. C5×#103 | D5 | semidirect |
| 52. C5×#103 | C2×C5 | semidirect |
| 53. #3967 | C2×C5 | semidirect |
| 54. #3948 | C2×C5 | semidirect |
| 55. #3942 | C2×C5 | semidirect |
| 77. Q8×D5 | C4×C5 | semidirect |
| 149. #103 | C5×D5 | semidirect |
| 150. C52 | #419 | semidirect |
| 221. C5 | #65091 | direct (N × H) |
| 222. C5 | C5×#419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C5×#676 | 2 |
| C5×#4038 | 2 |
| C52×#103 | 2 |
| C5×#3967 | 2 |
| C5×#3948 | 2 |
| C5×#3942 | 2 |
| C5×#419 | 5 |
| #65091 | 5 |