Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
592 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 206 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×#713 | C2 | semidirect |
| 2. C2×C52×Q16 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 4. C5×#4065 | C2 | direct (N × H) |
| 5. C2×C5×D40 | C2 | semidirect |
| 6. C2×C5×C8×D5 | C2 | semidirect |
| 9. C5×#713 | C22 | semidirect |
| 14. C52×Q16 | C22 | semidirect |
| 16. C5×#688 | C22 | semidirect |
| 18. C5×D40 | C22 | semidirect |
| 19. C5×C8×D5 | C22 | semidirect |
| 21. C2×#4065 | C5 | direct (N × H) |
| 38. C2×#713 | C2×C5 | semidirect |
| 41. C2×C5×Q16 | D5 | semidirect |
| 42. C2×C5×Q16 | C2×C5 | semidirect |
| 46. C2×#688 | C2×C5 | semidirect |
| 47. #4065 | C2×C5 | direct (N × H) |
| 48. C2×D40 | C2×C5 | semidirect |
| 49. C2×C8×D5 | C2×C5 | semidirect |
| 69. #713 | C22×C5 | semidirect |
| 75. C5×Q16 | C2×D5 | semidirect |
| 76. C5×Q16 | C22×C5 | semidirect |
| 84. #688 | C22×C5 | semidirect |
| 86. D40 | C22×C5 | semidirect |
| 87. C8×D5 | C22×C5 | semidirect |
| 89. C2×C52 | #135 | semidirect |
| 130. C2×Q16 | C5×D5 | semidirect |
| 134. C52 | C2×#135 | semidirect |
| 164. Q16 | C2×C5×D5 | semidirect |
| 174. C2×C5 | #4065 | direct (N × H) |
| 175. C2×C5 | C5×#135 | semidirect |
| 196. C5 | C2×#4065 | direct (N × H) |
| 197. C5 | C2×C5×#135 | semidirect |
| 209. C2 | C5×#4065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×C52×Q16 | 2 |
| C2×C5×#688 | 2 |
| C5×#4065 | 2 |
| C2×C5×D40 | 2 |
| C2×C5×C8×D5 | 2 |
| C2×C5×#135 | 5 |
| C2×#4065 | 5 |