Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 1. C52×#131 | C2 | semidirect |
| 3. C5×#4047 | C2 | semidirect |
| 4. C5×#3969 | C2 | semidirect |
| 5. C5×#3957 | C2 | semidirect |
| 6. C5×#3954 | C2 | semidirect |
| 7. C5×#3947 | C2 | semidirect |
| 14. C5×#689 | C4 | semidirect |
| 15. C5×#688 | C4 | semidirect |
| 16. C5×#687 | C4 | semidirect |
| 17. C5×#686 | C4 | semidirect |
| 24. #65434 | C5 | direct (N × H) |
| 44. C5×#131 | D5 | semidirect |
| 45. C5×#131 | C2×C5 | semidirect |
| 47. #4047 | C2×C5 | semidirect |
| 52. #3969 | C2×C5 | semidirect |
| 53. #3957 | C2×C5 | semidirect |
| 54. #3954 | C2×C5 | semidirect |
| 55. #3947 | C2×C5 | semidirect |
| 90. #689 | C4×C5 | semidirect |
| 91. #688 | C4×C5 | semidirect |
| 92. #687 | C4×C5 | semidirect |
| 93. #686 | C4×C5 | semidirect |
| 146. #131 | C5×D5 | semidirect |
| 151. C52 | #444 | semidirect |
| 216. C5 | #65434 | direct (N × H) |
| 217. C5 | C5×#444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#131 | 2 |
| C5×#4096 | 2 |
| C5×#4047 | 2 |
| C5×#3969 | 2 |
| C5×#3957 | 2 |
| C5×#3954 | 2 |
| C5×#3947 | 2 |
| C5×#444 | 5 |
| #65434 | 5 |