Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
720 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C5 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3199 | C2 | semidirect |
| 2. C5×#3027 | C2 | semidirect |
| 3. C5×#3021 | C2 | semidirect |
| 4. C5×#2134 | C2 | semidirect |
| 5. C5×#2122 | C2 | semidirect |
| 6. C5×#1791 | C2 | semidirect |
| 7. C5×#1395 | C2 | semidirect |
| 33. #13353 | C5 | direct (N × H) |
| 46. C22×C5×D4 | D4 | semidirect |
| 55. C2×C5×M16 | D4 | semidirect |
| 56. C22×C5×C8 | D4 | semidirect |
| 75. C5×#117 | D4 | semidirect |
| 85. C5×#101 | D4 | semidirect |
| 95. #3199 | C2×C5 | semidirect |
| 96. #3027 | C2×C5 | semidirect |
| 97. #3021 | C2×C5 | semidirect |
| 98. #2134 | C2×C5 | semidirect |
| 99. #2122 | C2×C5 | semidirect |
| 100. #1791 | C2×C5 | semidirect |
| 101. #1395 | C2×C5 | semidirect |
| 284. C22×D4 | C5×D4 | semidirect |
| 293. C2×M16 | C5×D4 | semidirect |
| 294. C22×C8 | C5×D4 | semidirect |
| 313. #117 | C5×D4 | semidirect |
| 323. #101 | C5×D4 | semidirect |
| 514. C5 | #13353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3199 | 2 |
| C5×#3027 | 2 |
| C5×#3021 | 2 |
| C5×#2134 | 2 |
| C5×#2122 | 2 |
| C5×#1791 | 2 |
| C5×#1395 | 2 |
| #13353 | 5 |