Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 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×AGL(1,𝔽5) | C2 | semidirect |
| 3. D5⋊M16 | C2 | semidirect |
| 4. #4010 | C2 | semidirect |
| 5. #4008 | C2 | semidirect |
| 7. C5×#41 | C4 | semidirect |
| 9. Q8×D5 | C4 | semidirect |
| 13. D4×D5 | C4 | semidirect |
| 15. #709 | C4 | semidirect |
| 20. C4×AGL(1,𝔽5) | C22 | semidirect |
| 21. #700 | C22 | semidirect |
| 28. C5×Q8 | C2×C4 | semidirect |
| 30. C5×D4 | C2×C4 | semidirect |
| 39. D20 | C2×C4 | semidirect |
| 48. Dic10 | C2×C4 | semidirect |
| 74. #41 | AGL(1,𝔽5) | semidirect |
| 91. D5 | #104 | semidirect |
| 96. Q8 | C2×AGL(1,𝔽5) | semidirect |
| 103. D4 | C2×AGL(1,𝔽5) | semidirect |
| 118. C5 | C2×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#41 | 2 |
| C2×C4×AGL(1,𝔽5) | 2 |
| D5⋊M16 | 2 |
| #4010 | 2 |
| #4008 | 2 |
| C2×#104 | 5 |