Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
446 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 446 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. C22×C5×D20 | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C2×C5×D40 | C2 | semidirect |
| 4. C52×C22⋊C8 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 13. C2×C52×C8 | C22 | semidirect |
| 15. C5×C4⋊Dic5 | C22 | semidirect |
| 18. #65021 | C5 | direct (N × H) |
| 33. C5×D20 | D4 | semidirect |
| 36. C22×D20 | C2×C5 | semidirect |
| 39. #4076 | C2×C5 | semidirect |
| 40. C2×D40 | C2×C5 | semidirect |
| 43. C5×C22⋊C8 | D5 | semidirect |
| 44. C5×C22⋊C8 | C2×C5 | semidirect |
| 45. #3953 | C2×C5 | semidirect |
| 48. C22×C52 | D8 | semidirect |
| 74. C2×D20 | C22×C5 | semidirect |
| 77. C2×C5×C8 | C2×D5 | semidirect |
| 78. C2×C5×C8 | C22×C5 | semidirect |
| 82. C4⋊Dic5 | C22×C5 | semidirect |
| 124. D20 | C5×D4 | semidirect |
| 132. C22⋊C8 | C5×D5 | semidirect |
| 133. C52 | #447 | semidirect |
| 149. C22×C5 | D40 | semidirect |
| 150. C22×C5 | C5×D8 | semidirect |
| 176. C2×C8 | C2×C5×D5 | semidirect |
| 212. C5 | #65021 | direct (N × H) |
| 213. C5 | C5×#447 | semidirect |
| 223. C22 | C5×D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C5×#4076 | 2 |
| C2×C5×D40 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#447 | 5 |
| #65021 | 5 |