Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
396 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C5 | D4 |
| commutator | C4 | C2×C42×C5 |
| Frattini, cosocle | C22×C4 | C23×C5 |
| socle | C23×C5 | C2×D4 |
| prime radical | C22×C5×D4 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×C5×C8 | C2 | semidirect |
| 4. C4×C5×C4⋊C4 | C2 | semidirect |
| 5. C5×#340 | C2 | semidirect |
| 10. C4×C5×D4 | C4 | semidirect |
| 16. C5×#102 | C4 | direct (N × H) |
| 19. C4×#102 | C5 | direct (N × H) |
| 35. C2×C5×C8 | C2×C4 | semidirect |
| 39. C5×C4⋊C4 | C2×C4 | semidirect |
| 46. C2×C4×C8 | C2×C5 | semidirect |
| 47. C4×C4⋊C4 | C2×C5 | semidirect |
| 48. #340 | C2×C5 | semidirect |
| 57. C5×D4 | C42 | semidirect |
| 79. C4×D4 | C4×C5 | semidirect |
| 85. #102 | C4×C5 | direct (N × H) |
| 101. C4×C5 | #102 | direct (N × H) |
| 120. C2×C8 | C2×C4×C5 | semidirect |
| 124. C4⋊C4 | C2×C4×C5 | semidirect |
| 143. D4 | C42×C5 | semidirect |
| 161. C5 | C4×#102 | direct (N × H) |
| 175. C4 | C5×#102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D4 | 2 |
| C2×C5×#102 | 2 |
| C2×C4×C5×C8 | 2 |
| C4×C5×C4⋊C4 | 2 |
| C5×#340 | 2 |
| C4×#102 | 5 |