Finite Group Databasebeta

← C11×#4010 #13182630

Subgroups — C11×#4010 #13182630

Order 1760.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#713C211yesmaximal, characteristic
2C4×C11×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C11×#700C211yesmaximal, characteristic, complemented
4C2×C11×AGL(1,𝔽5)—21no—
5C5×Q8×C11C411yescharacteristic, complemented
6C11×D20—21no—
7C11×D20C411yescharacteristic, complemented
8C4×D5×C11—21no—
9C4×D5×C11C2211yescharacteristic
10C11×#170—21no—
11C11×#104—51nomaximal, Hall
12C2×D5×C11—21no—
13C2×D5×C11D411yescharacteristic
14C11×AGL(1,𝔽5)—22no—
15C4×C5×C11—21no—
16C4×C5×C11C2×C411yescharacteristic
17C11×Dic5D411yescharacteristic
18C11×#41—51no—
19C11×M16—51no—
20C42×C11—51no—
21#4010C1111yesmaximal, characteristic, direct product factor, Hall
22C2×C5×C11C22⋊C411yescharacteristic
23D5×C11—21no—
24D5×C11—41no—
25Q8×C11AGL(1,𝔽5)11yescharacteristic, complemented
26D4×C11—51no—
27D4×C11—101no—
28C2×C4×C11—51no—
29C2×C4×C11—101no—
30C2×C4×C11—101no—
31C8×C11—101no—
32#713C2×C1111yescharacteristic
33C4×AGL(1,𝔽5)C2×C1111yescharacteristic, complemented
34#700C2×C1111yescharacteristic, complemented
35C5×C11#10411yescharacteristic, complemented, Hall
36C22×C11—51no—
37C22×C11—101no—
38C4×C11—21no—
39C4×C11—51no—
40C4×C11—102no—
41C4×C11C2×AGL(1,𝔽5)11yescharacteristic
42C2×AGL(1,𝔽5)—21no—
43C5×Q8C4×C1111yescharacteristic, complemented
44D20—21no—
45D20C4×C1111yescharacteristic, complemented
46C4×D5—21no—
47C4×D5C22×C1111yescharacteristic
48#170—21no—
49#104—51noSylow
50C2×C11—101no—
51C2×C11—201no—
52C2×C11C22⋊AGL(1,𝔽5)11yescharacteristic
53C2×D5—21no—
54C2×D5D4×C1111yescharacteristic
55AGL(1,𝔽5)—22no—
56C4×C5—21no—
57C4×C5C2×C4×C1111yescharacteristic
58Dic5D4×C1111yescharacteristic
59#41—51no—
60M16—51no—
61C42—51no—
62C11#401011yescharacteristic, direct product factor, Sylow
63C2×C5C11×C22⋊C411yescharacteristic
64D5—21no—
65D5—41no—
66Q8C11×AGL(1,𝔽5)11yescharacteristic, complemented
67D4—51no—
68D4—101no—
69C2×C4—51no—
70C2×C4—101no—
71C2×C4—101no—
72C8—101no—
73C5C11×#10411yescharacteristic, complemented, Sylow
74C22—51no—
75C22—101no—
76C4—21no—
77C4—51no—
78C4—102no—
79C4C2×C11×AGL(1,𝔽5)11yescharacteristic
80C2—101no—
81C2—201no—
82C2C11×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C11C22⋊AGL(1,𝔽5)
commutatorC4×C5C2×C4×C11
FrattiniC4C2×C11×AGL(1,𝔽5)
FittingC5×Q8×C11C4
socleC2×C5×C11C22⋊C4
prime radicalC11×#713C2
cosocleC4×D5C22×C11
hypercenterQ8×C11AGL(1,𝔽5)
hypocenterC5C11×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ Q8×C11

Complements

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

NH ≅ G/Ntype
2. C4×C11×AGL(1,𝔽5)C2semidirect
3. C11×#700C2semidirect
5. C5×Q8×C11C4semidirect
7. C11×D20C4semidirect
21. #4010C11direct (N × H)
25. Q8×C11AGL(1,𝔽5)semidirect
33. C4×AGL(1,𝔽5)C2×C11semidirect
34. #700C2×C11semidirect
35. C5×C11#104semidirect
43. C5×Q8C4×C11semidirect
45. D20C4×C11semidirect
62. C11#4010direct (N × H)
66. Q8C11×AGL(1,𝔽5)semidirect
73. C5C11×#104semidirect

Maximal subgroups

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

subgroupindex
C11×#7132
C4×C11×AGL(1,𝔽5)2
C11×#7002
C11×#1045
#401011