Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 328 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. C2×C5×D40 | C2 | semidirect |
| 2. C2×C5×#677 | C2 | semidirect |
| 3. C5×#4021 | C2 | semidirect |
| 4. C5×#4020 | C2 | semidirect |
| 5. C52×#97 | C2 | semidirect |
| 16. #65001 | C5 | direct (N × H) |
| 27. C52×C8 | D4 | semidirect |
| 32. C2×D40 | C2×C5 | semidirect |
| 33. C2×#677 | C2×C5 | semidirect |
| 34. #4021 | C2×C5 | semidirect |
| 35. #4020 | C2×C5 | semidirect |
| 37. C5×#97 | D5 | semidirect |
| 38. C5×#97 | C2×C5 | semidirect |
| 95. C5×C8 | D20 | semidirect |
| 96. C5×C8 | C5×D4 | semidirect |
| 101. #97 | C5×D5 | semidirect |
| 102. C52 | #496 | semidirect |
| 151. C8 | C5×D20 | semidirect |
| 153. C5 | #65001 | direct (N × H) |
| 154. C5 | C5×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D40 | 2 |
| C2×C5×#677 | 2 |
| C5×#4021 | 2 |
| C5×#4020 | 2 |
| C52×#97 | 2 |
| C5×#496 | 5 |
| #65001 | 5 |