Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 102 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. C22×C52×D4 | C2 | semidirect |
| 2. C2×C5×#686 | C2 | semidirect |
| 3. C5×#4076 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 5. C5×C22⋊#168 | C2 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 15. C5×C4⋊Dic5 | C22 | semidirect |
| 16. C2×C5×#168 | C22 | semidirect |
| 18. #65506 | C5 | direct (N × H) |
| 27. C52×D4 | D4 | semidirect |
| 36. C22×C5×D4 | D5 | semidirect |
| 37. C22×C5×D4 | C2×C5 | semidirect |
| 40. C2×#686 | C2×C5 | semidirect |
| 41. #4076 | C2×C5 | semidirect |
| 44. #3964 | C2×C5 | semidirect |
| 45. C22⋊#168 | C2×C5 | semidirect |
| 52. C22×C52 | D8 | semidirect |
| 78. C2×D20 | C22×C5 | semidirect |
| 85. C4⋊Dic5 | C22×C5 | semidirect |
| 86. C2×#168 | C22×C5 | semidirect |
| 120. C5×D4 | C22⋊D5 | semidirect |
| 121. C5×D4 | C5×D4 | semidirect |
| 137. C22×D4 | C5×D5 | semidirect |
| 142. C52 | #447 | semidirect |
| 166. C22×C5 | #686 | semidirect |
| 167. C22×C5 | C5×D8 | semidirect |
| 219. D4 | C5×C22⋊D5 | semidirect |
| 226. C5 | #65506 | direct (N × H) |
| 227. C5 | C5×#447 | semidirect |
| 237. C22 | C5×#686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C5×#686 | 2 |
| C5×#4076 | 2 |
| C5×#3964 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#447 | 5 |
| #65506 | 5 |