Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1116 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3548 | C2 | semidirect |
| 2. C5×#3151 | C2 | semidirect |
| 3. C5×#3138 | C2 | semidirect |
| 4. C5×#1656 | C2 | semidirect |
| 5. C5×#1526 | C2 | semidirect |
| 6. C5×#1525 | C2 | semidirect |
| 8. C5×#562 | C22 | semidirect |
| 25. C5×#330 | C22 | semidirect |
| 26. C5×#329 | C22 | semidirect |
| 27. #19075 | C5 | direct (N × H) |
| 68. #3548 | C2×C5 | semidirect |
| 69. #3151 | C2×C5 | semidirect |
| 70. #3138 | C2×C5 | semidirect |
| 71. #1656 | C2×C5 | semidirect |
| 72. #1526 | C2×C5 | semidirect |
| 73. #1525 | C2×C5 | semidirect |
| 115. #562 | C22×C5 | semidirect |
| 132. #330 | C22×C5 | semidirect |
| 133. #329 | C22×C5 | semidirect |
| 290. C5 | #19075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3548 | 2 |
| C5×#3151 | 2 |
| C5×#3138 | 2 |
| C5×#1656 | 2 |
| C5×#1526 | 2 |
| C5×#1525 | 2 |
| #19075 | 5 |