Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 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. C23×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 12. C2×C5×D4 | C4 | semidirect |
| 13. C2×C22⋊D5 | C4 | semidirect |
| 14. C2×C22⋊D5 | C4 | semidirect |
| 17. C2×D20 | C4 | semidirect |
| 23. C23×C5 | C2×C4 | semidirect |
| 31. C22×D5 | C2×C4 | semidirect |
| 41. C2×AGL(1,𝔽5) | D4 | semidirect |
| 43. C2×C4×C5 | C2×C4 | semidirect |
| 46. C2×Dic5 | C2×C4 | semidirect |
| 58. C22×C5 | C22⋊C4 | semidirect |
| 69. C2×D5 | C22⋊C4 | semidirect |
| 85. C2×D4 | AGL(1,𝔽5) | semidirect |
| 114. C23 | C2×AGL(1,𝔽5) | semidirect |
| 129. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 130. C5 | #386 | semidirect |
| 148. C22 | C22⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽5) | 2 |
| C2×D4×D5 | 2 |
| C2×C22⋊AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊C4 | 2 |
| #386 | 5 |