Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
376 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C5×#214 | C2 | semidirect |
| 3. C2×C5×#204 | C2 | semidirect |
| 4. C5×#897 | C2 | semidirect |
| 5. C3×C5×#102 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C5×#809 | C2 | semidirect |
| 16. C2×C5×Dic6 | C22 | semidirect |
| 17. C2×C3×C5×C8 | C22 | semidirect |
| 18. C3×C5×C4⋊C4 | C22 | semidirect |
| 22. C2×C5×C3⋊C8 | C22 | semidirect |
| 24. #4776 | C5 | direct (N × H) |
| 30. C5×#102 | D3 | semidirect |
| 54. C2×#214 | C2×C5 | semidirect |
| 55. C2×#204 | C2×C5 | semidirect |
| 56. #897 | C2×C5 | semidirect |
| 57. C3×#102 | C2×C5 | semidirect |
| 58. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 59. #809 | C2×C5 | semidirect |
| 71. C2×C5×C8 | C2×D3 | semidirect |
| 73. C5×C4⋊C4 | C2×D3 | semidirect |
| 86. C2×C5×D3 | SD16 | semidirect |
| 99. C2×Dic6 | C22×C5 | semidirect |
| 100. C2×C3×C8 | C22×C5 | semidirect |
| 101. C3×C4⋊C4 | C22×C5 | semidirect |
| 105. C2×C3⋊C8 | C22×C5 | semidirect |
| 133. #102 | C5×D3 | semidirect |
| 189. C2×C8 | C2×C5×D3 | semidirect |
| 191. C4⋊C4 | C2×C5×D3 | semidirect |
| 193. C3×C5 | #450 | semidirect |
| 204. C2×D3 | C5×SD16 | semidirect |
| 243. C5 | #4776 | direct (N × H) |
| 260. C3 | C5×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×D4 | 2 |
| C2×C5×#214 | 2 |
| C2×C5×#204 | 2 |
| C5×#897 | 2 |
| C3×C5×#102 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#809 | 2 |
| C5×#450 | 3 |
| #4776 | 5 |