Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
690 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 690 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. Q8×#1044 | C2 | semidirect |
| 3. Q8×#1043 | C2 | semidirect |
| 4. #11717365 | C2 | semidirect |
| 5. #11717363 | C2 | semidirect |
| 6. C4×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 7. #11717354 | C2 | semidirect |
| 11. C5×#713 | C4 | semidirect |
| 14. #87870 | C4 | semidirect |
| 30. C52×Q8 | C2×C4 | semidirect |
| 32. #6045 | C2×C4 | semidirect |
| 33. C5×D20 | C2×C4 | semidirect |
| 34. C4×C5×D5 | C2×C4 | semidirect |
| 35. #6037 | C2×C4 | semidirect |
| 37. D5×Dic5 | C2×C4 | semidirect |
| 51. #1044 | #41 | semidirect |
| 53. #1043 | #41 | semidirect |
| 60. #713 | AGL(1,𝔽5) | semidirect |
| 91. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 96. D20 | C2×AGL(1,𝔽5) | semidirect |
| 101. C4×D5 | C2×AGL(1,𝔽5) | semidirect |
| 111. C52 | C4×#41 | semidirect |
| 154. Q8 | D5⋊AGL(1,𝔽5) | semidirect |
| 168. 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 |
|---|---|
| #11717484 | 2 |
| Q8×#1044 | 2 |
| Q8×#1043 | 2 |
| #11717365 | 2 |
| #11717363 | 2 |
| C4×D5⋊AGL(1,𝔽5) | 2 |
| #11717354 | 2 |
| #41×AGL(1,𝔽5) | 5 |