Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
650 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C4×C52×Q8 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C4×C5×Q8 | D5 |
| hypocenter | C5 | C5×#548 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C4×C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#713 | C2 | semidirect |
| 2. C2×C5×Q8×D5 | C2 | semidirect |
| 3. C4×C52×Q8 | C2 | semidirect |
| 4. C5×#4043 | C2 | semidirect |
| 5. C5×#4041 | C2 | semidirect |
| 6. C5×#4021 | C2 | semidirect |
| 7. C4×C5×D20 | C2 | semidirect |
| 23. #65910 | C5 | direct (N × H) |
| 26. C52×Q8 | D4 | semidirect |
| 39. C2×#713 | C2×C5 | semidirect |
| 40. C2×Q8×D5 | C2×C5 | semidirect |
| 45. C4×C5×Q8 | D5 | semidirect |
| 46. C4×C5×Q8 | C2×C5 | semidirect |
| 48. #4043 | C2×C5 | semidirect |
| 49. #4041 | C2×C5 | semidirect |
| 50. #4021 | C2×C5 | semidirect |
| 51. C4×D20 | C2×C5 | semidirect |
| 58. C2×C5×D5 | #41 | semidirect |
| 107. C5×Q8 | D20 | semidirect |
| 108. C5×Q8 | C5×D4 | semidirect |
| 136. C4×Q8 | C5×D5 | semidirect |
| 138. C52 | #548 | semidirect |
| 153. C2×D5 | C5×#41 | semidirect |
| 197. Q8 | C5×D20 | semidirect |
| 208. C5 | #65910 | direct (N × H) |
| 209. C5 | C5×#548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×C5×Q8×D5 | 2 |
| C4×C52×Q8 | 2 |
| C5×#4043 | 2 |
| C5×#4041 | 2 |
| C5×#4021 | 2 |
| C4×C5×D20 | 2 |
| C5×#548 | 5 |
| #65910 | 5 |