Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#41 | C2 | semidirect |
| 2. C22×C5×D4 | C2 | semidirect |
| 3. C5×#127 | C2 | semidirect |
| 4. C5×#124 | C2 | semidirect |
| 5. C5×#121 | C2 | semidirect |
| 6. C5×#120 | C2 | semidirect |
| 7. C5×#117 | C2 | semidirect |
| 10. C2×C5×Q8 | C22 | semidirect |
| 15. C2×C5×D4 | C22 | semidirect |
| 16. C2×C5×D4 | C22 | semidirect |
| 18. C22×C4×C5 | C22 | semidirect |
| 19. C5×C4⋊C4 | C22 | semidirect |
| 21. C5×C22⋊C4 | C22 | semidirect |
| 22. C42×C5 | C22 | semidirect |
| 23. #535 | C5 | direct (N × H) |
| 36. C2×C4×C5 | D4 | semidirect |
| 41. C2×#41 | C2×C5 | semidirect |
| 42. C22×D4 | C2×C5 | semidirect |
| 43. #127 | C2×C5 | semidirect |
| 44. #124 | C2×C5 | semidirect |
| 45. #121 | C2×C5 | semidirect |
| 46. #120 | C2×C5 | semidirect |
| 47. #117 | C2×C5 | semidirect |
| 62. C2×Q8 | C22×C5 | semidirect |
| 67. C2×D4 | C22×C5 | semidirect |
| 68. C2×D4 | C22×C5 | semidirect |
| 70. C22×C4 | C22×C5 | semidirect |
| 71. C4⋊C4 | C22×C5 | semidirect |
| 73. C22⋊C4 | C22×C5 | semidirect |
| 74. C42 | C22×C5 | semidirect |
| 92. C2×C4 | C5×D4 | semidirect |
| 97. C5 | #535 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C22×C5×D4 | 2 |
| C5×#127 | 2 |
| C5×#124 | 2 |
| C5×#121 | 2 |
| C5×#120 | 2 |
| C5×#117 | 2 |
| #535 | 5 |