Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
592 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 214 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×#709 | C2 | semidirect |
| 2. C2×C52×M16 | C2 | semidirect |
| 3. C5×#4055 | C2 | semidirect |
| 4. C5×#4054 | C2 | semidirect |
| 5. C5×#4050 | C2 | semidirect |
| 11. C5×#709 | C22 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 14. C2×C5×Dic10 | C22 | semidirect |
| 15. C52×M16 | C22 | semidirect |
| 16. C2×C52×C8 | C22 | semidirect |
| 17. C5×Dic20 | C22 | semidirect |
| 18. C5×D40 | C22 | semidirect |
| 19. C5×#677 | C22 | semidirect |
| 21. #66082 | C5 | direct (N × H) |
| 39. C2×#709 | C2×C5 | semidirect |
| 44. C2×C5×M16 | D5 | semidirect |
| 45. C2×C5×M16 | C2×C5 | semidirect |
| 46. #4055 | C2×C5 | semidirect |
| 47. #4054 | C2×C5 | semidirect |
| 48. #4050 | C2×C5 | semidirect |
| 73. #709 | C22×C5 | semidirect |
| 74. C2×D20 | C22×C5 | semidirect |
| 76. C2×Dic10 | C22×C5 | semidirect |
| 81. C5×M16 | C2×D5 | semidirect |
| 82. C5×M16 | C22×C5 | semidirect |
| 84. C2×C5×C8 | C2×D5 | semidirect |
| 85. C2×C5×C8 | C22×C5 | semidirect |
| 86. Dic20 | C22×C5 | semidirect |
| 87. D40 | C22×C5 | semidirect |
| 88. #677 | C22×C5 | semidirect |
| 136. C2×M16 | C5×D5 | semidirect |
| 137. C52 | #575 | semidirect |
| 174. M16 | C2×C5×D5 | semidirect |
| 175. C2×C8 | C2×C5×D5 | semidirect |
| 204. C5 | #66082 | direct (N × H) |
| 205. C5 | C5×#575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×C52×M16 | 2 |
| C5×#4055 | 2 |
| C5×#4054 | 2 |
| C5×#4050 | 2 |
| C5×#575 | 5 |
| #66082 | 5 |