Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. (C2×AGL(1,𝔽5))⋊C4 | C2 | direct (N × H) |
| 7. C22×AGL(1,𝔽5) | C4 | semidirect |
| 9. C22×C4×C5 | C4 | semidirect |
| 10. C22×Dic5 | C4 | semidirect |
| 12. C2×C4×D5 | C4 | semidirect |
| 25. C2×AGL(1,𝔽5) | C2×C4 | semidirect |
| 27. C2×C4×C5 | C2×C4 | semidirect |
| 29. C2×Dic5 | C2×C4 | semidirect |
| 60. C22×C4 | AGL(1,𝔽5) | semidirect |
| 61. C2×C5 | #95 | semidirect |
| 65. D5 | #95 | semidirect |
| 84. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 85. C5 | C2×#95 | semidirect |
| 105. C2 | (C2×AGL(1,𝔽5))⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽5) | 2 |
| C22×C4×D5 | 2 |
| (C2×AGL(1,𝔽5))⋊C4 | 2 |
| C2×#95 | 5 |