Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 158 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. C22×C52×C8 | C2 | semidirect |
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 4. C5×#3953 | C2 | direct (N × H) |
| 10. C2×C5×D20 | C4 | semidirect |
| 13. C2×C52×C8 | C22 | semidirect |
| 15. C5×C4⋊Dic5 | C22 | semidirect |
| 17. C2×#3953 | C5 | direct (N × H) |
| 31. C5×D20 | C2×C4 | semidirect |
| 36. C22×C5×C8 | D5 | semidirect |
| 37. C22×C5×C8 | C2×C5 | semidirect |
| 39. C2×C4⋊Dic5 | C2×C5 | semidirect |
| 41. #3953 | C2×C5 | direct (N × H) |
| 67. C2×D20 | C4×C5 | semidirect |
| 73. C2×C5×C8 | C2×D5 | semidirect |
| 74. C2×C5×C8 | C22×C5 | semidirect |
| 78. C4⋊Dic5 | C22×C5 | semidirect |
| 80. C2×C52 | #102 | semidirect |
| 117. D20 | C2×C4×C5 | semidirect |
| 122. C22×C8 | C5×D5 | semidirect |
| 125. C52 | C2×#102 | semidirect |
| 165. C2×C8 | C2×C5×D5 | semidirect |
| 173. C2×C5 | #3953 | direct (N × H) |
| 174. C2×C5 | C5×#102 | semidirect |
| 198. C5 | C2×#3953 | direct (N × H) |
| 199. C5 | C2×C5×#102 | semidirect |
| 213. C2 | C5×#3953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×C52×C8 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×#3953 | 2 |
| C2×C5×#102 | 5 |
| C2×#3953 | 5 |