Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 165 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×C4×#1044 | C2 | semidirect |
| 3. #11717438 | C2 | semidirect |
| 4. #11717377 | C2 | semidirect |
| 5. #11717365 | C2 | semidirect |
| 6. C4×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 7. #11717356 | C2 | semidirect |
| 8. #11717355 | C2 | semidirect |
| 12. C5×#709 | C4 | semidirect |
| 14. #87880 | C4 | semidirect |
| 17. #87873 | C4 | semidirect |
| 19. #87871 | C4 | semidirect |
| 37. C2×C4×C52 | C2×C4 | semidirect |
| 38. C2×#1039 | C2×C4 | semidirect |
| 39. C4×C5⋊D5 | C2×C4 | semidirect |
| 40. C4×C5⋊D5 | C2×C4 | semidirect |
| 43. C5×C22⋊D5 | C2×C4 | semidirect |
| 44. C5×D20 | C2×C4 | semidirect |
| 45. C4×C5×D5 | C2×C4 | semidirect |
| 46. C5×Dic10 | C2×C4 | semidirect |
| 47. #6039 | C2×C4 | semidirect |
| 48. #6038 | C2×C4 | semidirect |
| 49. #6037 | C2×C4 | semidirect |
| 51. D5×Dic5 | C2×C4 | semidirect |
| 68. #1044 | #41 | semidirect |
| 85. #709 | AGL(1,𝔽5) | semidirect |
| 121. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 124. C22⋊D5 | C2×AGL(1,𝔽5) | semidirect |
| 129. D20 | C2×AGL(1,𝔽5) | semidirect |
| 140. C4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 142. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 151. C52 | C4×#41 | semidirect |
| 228. C2×C4 | D5⋊AGL(1,𝔽5) | semidirect |
| 230. C5 | #41×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| C2×C4×#1044 | 2 |
| #11717438 | 2 |
| #11717377 | 2 |
| #11717365 | 2 |
| C4×D5⋊AGL(1,𝔽5) | 2 |
| #11717356 | 2 |
| #11717355 | 2 |
| #41×AGL(1,𝔽5) | 5 |