Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
368 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 1. C2×C5×D40 | C2 | semidirect |
| 2. C5×#4020 | C2 | semidirect |
| 3. C4×C52×C8 | C2 | semidirect |
| 10. #64984 | C5 | direct (N × H) |
| 16. C52×C8 | D4 | semidirect |
| 19. C2×D40 | C2×C5 | semidirect |
| 20. #4020 | C2×C5 | semidirect |
| 22. C4×C5×C8 | D5 | semidirect |
| 23. C4×C5×C8 | C2×C5 | semidirect |
| 27. C4×C52 | D8 | semidirect |
| 58. C5×C8 | D20 | semidirect |
| 59. C5×C8 | C5×D4 | semidirect |
| 62. C4×C8 | C5×D5 | semidirect |
| 63. C52 | #493 | semidirect |
| 73. C4×C5 | D40 | semidirect |
| 74. C4×C5 | C5×D8 | semidirect |
| 95. C8 | C5×D20 | semidirect |
| 97. C5 | #64984 | direct (N × H) |
| 98. C5 | C5×#493 | semidirect |
| 102. C4 | C5×D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D40 | 2 |
| C5×#4020 | 2 |
| C4×C52×C8 | 2 |
| C5×#493 | 5 |
| #64984 | 5 |