Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
376 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C52×M16 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. C5×#3957 | C2 | semidirect |
| 9. C5×#709 | C4 | semidirect |
| 11. C2×C5×D20 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 15. C52×M16 | C22 | semidirect |
| 19. C4×C5×Dic5 | C22 | semidirect |
| 21. #65428 | C5 | direct (N × H) |
| 44. C2×C5×M16 | D5 | semidirect |
| 45. C2×C5×M16 | C2×C5 | semidirect |
| 47. #4072 | C2×C5 | semidirect |
| 49. #3957 | C2×C5 | semidirect |
| 76. #709 | C4×C5 | semidirect |
| 78. C2×D20 | C4×C5 | semidirect |
| 80. C2×Dic10 | C4×C5 | semidirect |
| 85. C5×M16 | C2×D5 | semidirect |
| 86. C5×M16 | C22×C5 | semidirect |
| 95. C4×Dic5 | C22×C5 | semidirect |
| 149. C2×M16 | C5×D5 | semidirect |
| 152. C52 | #421 | semidirect |
| 195. M16 | C2×C5×D5 | semidirect |
| 234. C5 | #65428 | direct (N × H) |
| 235. C5 | C5×#421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×C52×M16 | 2 |
| C5×#4072 | 2 |
| C5×#3957 | 2 |
| C5×#421 | 5 |
| #65428 | 5 |