Finite Group Databasebeta

← C5×C11×AGL(1,𝔽5)×C29 #44542071

Subgroups — C5×C11×AGL(1,𝔽5)×C29 #44542071

Order 31900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D5×C11×C29C211yesmaximal, characteristic
2C52×C11×C29C411yescharacteristic, complemented, Hall
3C11×AGL(1,𝔽5)×C29C511yesmaximal, characteristic, direct product factor
4C4×C5×C11×C29—51nomaximal
5D5×C11×C29C2×C511yescharacteristic
6C2×C5×C11×C29—51no—
7C5×AGL(1,𝔽5)×C29C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C29—41no—
9C5×C11×C29C4×C511yescharacteristic, complemented
10C5×C11×C29AGL(1,𝔽5)11yescharacteristic, direct product factor
11C5×D5×C29C2×C1111yescharacteristic
12C4×C11×C29—51noHall
13C5×C11×AGL(1,𝔽5)C2911yesmaximal, characteristic, direct product factor, Hall
14C52×C29C4×C1111yescharacteristic, complemented, Hall
15C2×C11×C29—51no—
16AGL(1,𝔽5)×C29C5×C1111yescharacteristic, direct product factor
17C4×C5×C29—51no—
18C5×D5×C11C2×C2911yescharacteristic
19C11×C29C5×AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
20C2×C5×C29—51no—
21D5×C29C2×C5×C1111yescharacteristic
22C52×C11C4×C2911yescharacteristic, complemented, Hall
23C11×AGL(1,𝔽5)C5×C2911yescharacteristic, direct product factor
24C4×C5×C11—51no—
25C5×C29—41no—
26C5×C29C4×C5×C1111yescharacteristic, complemented
27C5×C29C11×AGL(1,𝔽5)11yescharacteristic, direct product factor
28C4×C29—51noHall
29C2×C5×C11—51no—
30D5×C11C2×C5×C2911yescharacteristic
31C5×AGL(1,𝔽5)C11×C2911yescharacteristic, direct product factor, Hall
32C2×C29—51no—
33C5×C11—41no—
34C5×C11C4×C5×C2911yescharacteristic, complemented
35C5×C11AGL(1,𝔽5)×C2911yescharacteristic, direct product factor
36C5×D5C2×C11×C2911yescharacteristic
37C4×C11—51noHall
38C29C5×C11×AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
39C52C4×C11×C2911yescharacteristic, complemented, Sylow
40C2×C11—51no—
41AGL(1,𝔽5)C5×C11×C2911yescharacteristic, direct product factor
42C4×C5—51no—
43C11C5×AGL(1,𝔽5)×C2911yescharacteristic, direct product factor, Sylow
44C2×C5—51no—
45D5C2×C5×C11×C2911yescharacteristic
46C5—41no—
47C5C4×C5×C11×C2911yescharacteristic, complemented
48C5C11×AGL(1,𝔽5)×C2911yescharacteristic, direct product factor
49C4—51noSylow
50C2—51no—
subgroupG/H
center, hypercenterC5×C11×C29AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C11×C29
FrattiniC1G
Fitting, socleC52×C11×C29C4
prime radicalC5×D5×C11×C29C2
cosocleD5C2×C5×C11×C29
LCSG ▷ C5
UCSC1 ◁ C5×C11×C29

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C52×C11×C29C4semidirect
3. C11×AGL(1,𝔽5)×C29C5direct (N × H)
7. C5×AGL(1,𝔽5)×C29C11direct (N × H)
9. C5×C11×C29C4×C5semidirect
10. C5×C11×C29AGL(1,𝔽5)direct (N × H)
13. C5×C11×AGL(1,𝔽5)C29direct (N × H)
14. C52×C29C4×C11semidirect
16. AGL(1,𝔽5)×C29C5×C11direct (N × H)
19. C11×C29C5×AGL(1,𝔽5)direct (N × H)
22. C52×C11C4×C29semidirect
23. C11×AGL(1,𝔽5)C5×C29direct (N × H)
26. C5×C29C4×C5×C11semidirect
27. C5×C29C11×AGL(1,𝔽5)direct (N × H)
31. C5×AGL(1,𝔽5)C11×C29direct (N × H)
34. C5×C11C4×C5×C29semidirect
35. C5×C11AGL(1,𝔽5)×C29direct (N × H)
38. C29C5×C11×AGL(1,𝔽5)direct (N × H)
39. C52C4×C11×C29semidirect
41. AGL(1,𝔽5)C5×C11×C29direct (N × H)
43. C11C5×AGL(1,𝔽5)×C29direct (N × H)
47. C5C4×C5×C11×C29semidirect
48. C5C11×AGL(1,𝔽5)×C29direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×D5×C11×C292
C11×AGL(1,𝔽5)×C295
C4×C5×C11×C295
C5×AGL(1,𝔽5)×C2911
C5×C11×AGL(1,𝔽5)29