Finite Group Databasebeta

← C5×(C23⋊C11)⋊AGL(1,𝔽5) #38760739

Subgroups — C5×(C23⋊C11)⋊AGL(1,𝔽5) #38760739

Order 25300.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D5×C23⋊C11C211yesmaximal, characteristic
2C52×C23⋊C11C411yescharacteristic, complemented, Hall
3(C23⋊C11)⋊AGL(1,𝔽5)C511yesmaximal, characteristic, direct product factor
4C5×Dic23⋊C11—51nomaximal
5D5×C23⋊C11C2×C511yescharacteristic
6C2×C5×C23⋊C11—51no—
7C5×C23⋊AGL(1,𝔽5)C1111yesmaximal, characteristic, complemented, Hall
8C5×C23⋊C11—41no—
9C5×C23⋊C11C4×C511yescharacteristic, complemented
10C5×C23⋊C11AGL(1,𝔽5)11yescharacteristic, complemented
11C5×D5×C23C2×C1111yescharacteristic
12C5×C11×AGL(1,𝔽5)—231nomaximal, Hall
13Dic23⋊C11—51noHall
14C52×C23C4×C1111yescharacteristic, complemented, Hall
15C5×D5×C11—231no—
16C2×C23⋊C11—51no—
17C23⋊AGL(1,𝔽5)C5×C1111yescharacteristic, complemented
18C5×Dic23—51no—
19C52×C11—231noHall
20C23⋊C11C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
21C2×C5×C23—51no—
22D5×C23C2×C5×C1111yescharacteristic
23C11×AGL(1,𝔽5)—231no—
24C4×C5×C11—1151no—
25C5×C23—41no—
26C5×C23C4×C5×C1111yescharacteristic, complemented
27C5×C23C11×AGL(1,𝔽5)11yescharacteristic, complemented
28C2×C5×C11—1151no—
29D5×C11—231no—
30C5×AGL(1,𝔽5)—2531noHall
31Dic23—51noHall
32C5×C11—231no—
33C5×C11—231no—
34C5×C11—921no—
35C5×D5AGL(1,𝔽23)11yescharacteristic
36C2×C23—51no—
37C4×C11—1151noHall
38C52Dic23⋊C1111yescharacteristic, complemented, Sylow
39C23C5×C11×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
40C2×C11—1151no—
41AGL(1,𝔽5)—2531no—
42C4×C5—12651no—
43C11—231noSylow
44C2×C5—51no—
45D5C5×AGL(1,𝔽23)11yescharacteristic
46C5—41no—
47C5C5×Dic23⋊C1111yescharacteristic, complemented
48C5(C23⋊C11)⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
49C4—12651noSylow
50C2—51no—
subgroupG/H
center, hypercenterC5(C23⋊C11)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C23C4×C5×C11
FrattiniC1G
Fitting, socleC52×C23C4×C11
prime radicalC5×D5×C23⋊C11C2
cosocleD5×C23C2×C5×C11
LCSG ▷ C5×C23
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
2. C52×C23⋊C11C4semidirect
3. (C23⋊C11)⋊AGL(1,𝔽5)C5direct (N × H)
7. C5×C23⋊AGL(1,𝔽5)C11semidirect
9. C5×C23⋊C11C4×C5semidirect
10. C5×C23⋊C11AGL(1,𝔽5)semidirect
14. C52×C23C4×C11semidirect
17. C23⋊AGL(1,𝔽5)C5×C11semidirect
20. C23⋊C11C5×AGL(1,𝔽5)semidirect
26. C5×C23C4×C5×C11semidirect
27. C5×C23C11×AGL(1,𝔽5)semidirect
38. C52Dic23⋊C11semidirect
39. C23C5×C11×AGL(1,𝔽5)semidirect
47. C5C5×Dic23⋊C11semidirect
48. C5(C23⋊C11)⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D5×C23⋊C112
(C23⋊C11)⋊AGL(1,𝔽5)5
C5×Dic23⋊C115
C5×C23⋊AGL(1,𝔽5)11
C5×C11×AGL(1,𝔽5)23