Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1104 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | C2×#127 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87877 | C2 | semidirect |
| 2. C42×C5⋊D5 | C2 | semidirect |
| 3. C5×#4020 | C2 | semidirect |
| 4. #11717032 | C2 | semidirect |
| 7. C2×C5×D20 | C22 | semidirect |
| 8. C2×#6037 | C22 | semidirect |
| 10. C42×C52 | C22 | semidirect |
| 11. C4×#1039 | C22 | semidirect |
| 18. C4×C5⋊D5 | D4 | semidirect |
| 24. #4020 | D5 | semidirect |
| 31. C4×C52 | C2×D4 | semidirect |
| 32. #1039 | C2×D4 | semidirect |
| 37. C2×D20 | C2×D5 | semidirect |
| 41. C42×C5 | C2×D5 | semidirect |
| 46. C5⋊D5 | #127 | semidirect |
| 66. C52 | C2×#127 | semidirect |
| 75. C4×C5 | D4×D5 | semidirect |
| 84. C42 | D52 | semidirect |
| 100. C5 | D5×#127 | semidirect |
| 106. C4 | #87877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87877 | 2 |
| C42×C5⋊D5 | 2 |
| C5×#4020 | 2 |
| #11717032 | 2 |
| D5×#127 | 5 |