Finite Group Databasebeta

← C2×AGL(1,𝔽5)×C11⋊C5 #72228513

Subgroups — C2×AGL(1,𝔽5)×C11⋊C5 #72228513

Order 2200.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C11⋊C5C211yesmaximal, characteristic
2AGL(1,𝔽5)×C11⋊C5C212yesmaximal, direct product factor
3C2×C5×C11⋊C5C411yescharacteristic, complemented
4D5×C11⋊C5C411yescharacteristic, complemented
5D5×C11⋊C5C2211yescharacteristic
6C2×C11×AGL(1,𝔽5)C511yesmaximal, characteristic, complemented
7C2×C4×C11⋊C5—51nomaximal
8C5×C11⋊C5C2×C411yescharacteristic, complemented, Hall
9C2×D5×C11C2×C511yescharacteristic
10C11×AGL(1,𝔽5)C2×C512yescomplemented
11C22×C11⋊C5—51no—
12C4×C11⋊C5—52no—
13C2×C5×AGL(1,𝔽5)—111nomaximal, Hall
14C2×C5×C11C4×C511yescharacteristic, complemented
15D5×C11C4×C511yescharacteristic, complemented
16D5×C11C22×C511yescharacteristic
17C2×C11⋊C5—41no—
18C2×C11⋊C5—51no—
19C2×C11⋊C5—51no—
20C2×C11⋊C5AGL(1,𝔽5)11yescharacteristic, direct product factor
21C2×C5×D5—111no—
22C5×AGL(1,𝔽5)—112no—
23C2×C4×C11—51noHall
24C5×C11C2×C4×C511yescharacteristic, complemented
25C11⋊C5—41no—
26C11⋊C5C2×AGL(1,𝔽5)11yescharacteristic, direct product factor
27C2×C52—111no—
28C5×D5—111no—
29C5×D5—111no—
30C22×C11—51no—
31C4×C11—52no—
32C2×AGL(1,𝔽5)C11⋊C511yescharacteristic, direct product factor
33C2×C4×C5—551no—
34C52—111noSylow
35C2×C11—51no—
36C2×C11—51no—
37C2×C11C5×AGL(1,𝔽5)11yescharacteristic, complemented
38C22×C5—551no—
39C2×D5C2×C11⋊C511yescharacteristic
40AGL(1,𝔽5)C2×C11⋊C512yesdirect product factor
41C4×C5—552no—
42C11C2×C5×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
43C2×C5—111no—
44C2×C5—441no—
45C2×C5—551no—
46C2×C5—551no—
47C2×C5C4×C11⋊C511yescharacteristic, complemented
48D5C4×C11⋊C511yescharacteristic, complemented
49D5C22×C11⋊C511yescharacteristic
50C2×C4—51noSylow
51C5—111no—
52C5—441no—
53C5C2×C4×C11⋊C511yescharacteristic, complemented
54C22—51no—
55C4—52no—
56C2—51no—
57C2—51no—
58C2AGL(1,𝔽5)×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×C11⋊C5
commutator, hypocenterC5×C11C2×C4×C5
FrattiniC1G
Fitting, socleC2×C5×C11C4×C5
prime radicalC2×D5×C11⋊C5C2
cosocleD5×C11C22×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. AGL(1,𝔽5)×C11⋊C5C2direct (N × H)
3. C2×C5×C11⋊C5C4semidirect
4. D5×C11⋊C5C4semidirect
6. C2×C11×AGL(1,𝔽5)C5semidirect
8. C5×C11⋊C5C2×C4semidirect
10. C11×AGL(1,𝔽5)C2×C5semidirect
14. C2×C5×C11C4×C5semidirect
15. D5×C11C4×C5semidirect
20. C2×C11⋊C5AGL(1,𝔽5)direct (N × H)
24. C5×C11C2×C4×C5semidirect
26. C11⋊C5C2×AGL(1,𝔽5)direct (N × H)
32. C2×AGL(1,𝔽5)C11⋊C5direct (N × H)
37. C2×C11C5×AGL(1,𝔽5)semidirect
40. AGL(1,𝔽5)C2×C11⋊C5direct (N × H)
42. C11C2×C5×AGL(1,𝔽5)semidirect
47. C2×C5C4×C11⋊C5semidirect
48. D5C4×C11⋊C5semidirect
53. C5C2×C4×C11⋊C5semidirect
58. C2AGL(1,𝔽5)×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C11⋊C52
AGL(1,𝔽5)×C11⋊C52
C2×C11×AGL(1,𝔽5)5
C2×C4×C11⋊C55
C2×C5×AGL(1,𝔽5)11