Finite Group Databasebeta

← #13182654

Subgroups — #13182654

Order 1760.

100 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D5×C11C211yesmaximal, characteristic
2C4⋊(C11⋊AGL(1,𝔽5))C211yesmaximal, characteristic, complemented
3D5⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
4C22×D5×C11—21no—
5C2×C11⋊AGL(1,𝔽5)—21no—
6C5×D4×C11C411yescharacteristic, complemented
7C11×C22⋊D5—21no—
8C11×D20C411yescharacteristic, complemented
9C4×D5×C11C2211yescharacteristic
10C11⋊#170—21no—
11#66896—51nomaximal, Hall
12C22×C5×C11—21no—
13C2×D5×C11—21no—
14C2×D5×C11—41no—
15C2×D5×C11—41no—
16C2×D5×C11D411yescharacteristic
17C11⋊AGL(1,𝔽5)—41no—
18C4×C5×C11C2×C411yescharacteristic
19C11×Dic5D411yescharacteristic
20C2×D4×C11—51no—
21C4⋊Dic11—51no—
22C2×C11⋊C8—51no—
23#4007—111nomaximal, Hall
24C2×C5×C11—41no—
25C2×C5×C11C22⋊C411yescharacteristic
26D5×C11—41no—
27D5×C11D811yescharacteristic
28D5×C11SD1611yescharacteristic
29C23×C11—101no—
30D4×C11—51no—
31D4×C11—101no—
32D4×C11AGL(1,𝔽5)11yescharacteristic, complemented
33C2×C4×C11—51no—
34C2×Dic11—101no—
35C11⋊C8—101no—
36D4×D5D1111yescharacteristic
37C4⋊AGL(1,𝔽5)—111no—
38D5⋊C8—111no—
39C5×C11#10211yescharacteristic, complemented, Hall
40C22×C11—21no—
41C22×C11—51no—
42C22×C11—101no—
43C22×C11—201no—
44C22×C11—201no—
45C4×C11—51no—
46C4×C11C2×AGL(1,𝔽5)11yescharacteristic
47Dic11—201no—
48C22×D5—21no—
49C2×AGL(1,𝔽5)—221no—
50C5×D4Dic1111yescharacteristic, complemented
51C22⋊D5—21no—
52D20Dic1111yescharacteristic, complemented
53C4×D5C2×D1111yescharacteristic
54#170—221no—
55#102—551noSylow
56C2×C11—41no—
57C2×C11—51no—
58C2×C11—51no—
59C2×C11—201no—
60C2×C11C22⋊AGL(1,𝔽5)11yescharacteristic
61C22×C5—21no—
62C2×D5—21no—
63C2×D5—41no—
64C2×D5—41no—
65C2×D5C22⋊D1111yescharacteristic
66AGL(1,𝔽5)—441no—
67C4×C5C2×Dic1111yescharacteristic
68Dic5C22⋊D1111yescharacteristic
69C2×D4—51no—
70C2×C8—551no—
71C4⋊C4—551no—
72C11#400711yescharacteristic, complemented, Sylow
73C2×C5—41no—
74C2×C5C22⋊Dic1111yescharacteristic
75D5—41no—
76D5#432311yescharacteristic
77D5#432411yescharacteristic
78C23—101no—
79D4—51no—
80D4—101no—
81D4C11⋊AGL(1,𝔽5)11yescharacteristic, complemented
82C2×C4—51no—
83C2×C4—1101no—
84C8—1101no—
85C5#6689611yescharacteristic, complemented, Sylow
86C22—21no—
87C22—51no—
88C22—101no—
89C22—201no—
90C22—201no—
91C4—51no—
92C4—2201no—
93C4C2×C11⋊AGL(1,𝔽5)11yescharacteristic
94C2—41no—
95C2—51no—
96C2—51no—
97C2—201no—
98C2C22⋊(C11⋊AGL(1,𝔽5))11yescharacteristic
subgroupG/H
centerC2C22⋊(C11⋊AGL(1,𝔽5))
commutatorC4×C5×C11C2×C4
FrattiniC4C2×C11⋊AGL(1,𝔽5)
FittingC5×D4×C11C4
socleC2×C5×C11C22⋊C4
prime radicalD4×D5×C11C2
cosocleC4×D5×C11C22
hypercenterD4C11⋊AGL(1,𝔽5)
hypocenterC5×C11#102
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
2. C4⋊(C11⋊AGL(1,𝔽5))C2semidirect
3. D5⋊(C11⋊C8)C2semidirect
6. C5×D4×C11C4semidirect
8. C11×D20C4semidirect
32. D4×C11AGL(1,𝔽5)semidirect
39. C5×C11#102semidirect
50. C5×D4Dic11semidirect
52. D20Dic11semidirect
72. C11#4007semidirect
81. D4C11⋊AGL(1,𝔽5)semidirect
85. C5#66896semidirect

Maximal subgroups

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

subgroupindex
D4×D5×C112
C4⋊(C11⋊AGL(1,𝔽5))2
D5⋊(C11⋊C8)2
#668965
#400711