Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 102 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×#99 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C5 |
| prime radical | C5×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#117 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1740 | C2 | semidirect |
| 3. C5×#1464 | C2 | semidirect |
| 4. C5×#1352 | C2 | semidirect |
| 6. C2×C4×C5×D4 | C4 | semidirect |
| 10. C5×#400 | C4 | semidirect |
| 12. C5×#394 | C4 | semidirect |
| 18. C5×#383 | C4 | semidirect |
| 23. #11754 | C5 | direct (N × H) |
| 60. #1740 | C2×C5 | semidirect |
| 61. #1464 | C2×C5 | semidirect |
| 62. #1352 | C2×C5 | semidirect |
| 111. C2×C4×D4 | C4×C5 | semidirect |
| 115. #400 | C4×C5 | semidirect |
| 117. #394 | C4×C5 | semidirect |
| 123. #383 | C4×C5 | semidirect |
| 350. C5 | #11754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2598 | 2 |
| C5×#1740 | 2 |
| C5×#1464 | 2 |
| C5×#1352 | 2 |
| C5×#1343 | 2 |
| #11754 | 5 |