Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
387 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 149 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×#1042 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting | C42×C52 | C4 |
| prime radical, cosocle | C22×C5×D5 | C23 |
| hypercenter | C42 | #1042 |
| hypocenter | C52 | #384 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C42×C52 | C4 | semidirect |
| 7. C4×C5×Dic5 | C4 | semidirect |
| 24. C4×C52 | C4⋊C4 | semidirect |
| 25. C5×Dic5 | C4⋊C4 | semidirect |
| 33. C42×C5 | Dic5 | semidirect |
| 34. C42×C5 | AGL(1,𝔽5) | semidirect |
| 36. C4×Dic5 | Dic5 | semidirect |
| 56. C52 | #384 | semidirect |
| 67. C4×C5 | C4⋊Dic5 | semidirect |
| 68. C4×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 70. Dic5 | C4⋊Dic5 | semidirect |
| 75. C42 | #1042 | semidirect |
| 90. C5 | #65224 | semidirect |
| 91. C5 | #65688 | semidirect |
| 97. C4 | C4⋊#1042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1042 | 2 |
| C42×C5×D5 | 2 |
| #65688 | 5 |
| #65224 | 5 |