Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
364 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 364 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×#137 | C2 | semidirect |
| 3. C5×#4093 | C2 | semidirect |
| 4. C5×#4088 | C2 | semidirect |
| 5. C5×#3969 | C2 | semidirect |
| 6. C5×#3957 | C2 | semidirect |
| 7. C5×#3955 | C2 | semidirect |
| 9. C2×C52×Q8 | C22 | semidirect |
| 19. C52×M16 | C22 | semidirect |
| 23. C4×C5×Dic5 | C22 | semidirect |
| 24. C5×#681 | C22 | semidirect |
| 26. #65491 | C5 | direct (N × H) |
| 53. C5×#137 | D5 | semidirect |
| 54. C5×#137 | C2×C5 | semidirect |
| 56. #4093 | C2×C5 | semidirect |
| 57. #4088 | C2×C5 | semidirect |
| 61. #3969 | C2×C5 | semidirect |
| 62. #3957 | C2×C5 | semidirect |
| 63. #3955 | C2×C5 | semidirect |
| 83. C2×C5×Q8 | C2×D5 | semidirect |
| 84. C2×C5×Q8 | C22×C5 | semidirect |
| 106. C5×M16 | C2×D5 | semidirect |
| 107. C5×M16 | C22×C5 | semidirect |
| 113. C4×Dic5 | C22×C5 | semidirect |
| 114. #681 | C22×C5 | semidirect |
| 176. #137 | C5×D5 | semidirect |
| 181. C52 | #455 | semidirect |
| 216. C2×Q8 | C2×C5×D5 | semidirect |
| 226. M16 | C2×C5×D5 | semidirect |
| 265. C5 | #65491 | direct (N × H) |
| 266. C5 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4149 | 2 |
| C52×#137 | 2 |
| C5×#4093 | 2 |
| C5×#4088 | 2 |
| C5×#3969 | 2 |
| C5×#3957 | 2 |
| C5×#3955 | 2 |
| C5×#455 | 5 |
| #65491 | 5 |