Finite Group Databasebeta

← #13182906

Subgroups — #13182906

Order 1760.

136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C5×D4×D11C211yesmaximal, characteristic, complemented
2#11724989C211yesmaximal, characteristic, complemented
3#11724934C211yesmaximal, characteristic, complemented
4C11×#686C211yesmaximal, characteristic, complemented
5#11724876C211yesmaximal, characteristic, complemented
6#11724871C211yesmaximal, characteristic, complemented
7#11724868C211yesmaximal, characteristic, complemented
8C22×C5×D11—21no—
9C5×D4×C11C2211yescharacteristic
10Dic110C2211yescharacteristic, complemented
11C11×D20C2211yescharacteristic, complemented
12C5×C22⋊D11—21no—
13C5×D44C2211yescharacteristic
14C4×C5×D11C2211yescharacteristic
15#89167—21no—
16D5×Dic11—21no—
17C11⋊#168C2211yescharacteristic, complemented
18C11×#168C2211yescharacteristic, complemented
19#66964—51nomaximal, Hall
20C22×C5×C11—21no—
21C2×D5×C11—21no—
22C2×C5×D11—21no—
23C2×C5×D11—42no—
24C2×C5×D11D411yescharacteristic
25C4×C5×C11C2311yescharacteristic
26Dic55—21no—
27C5×Dic11D411yescharacteristic
28#4341—51no—
29D4×D11D511yescharacteristic, complemented
30C11×D8—51no—
31#4324—51no—
32#4323—51no—
33#4314—51no—
34#4313—51no—
35#4078—111nomaximal, Hall
36C2×C5×C11—41no—
37C2×C5×C11C2×D411yescharacteristic
38C5×D11—21no—
39C5×D11—41no—
40D5×C11—41no—
41C22×D11—21no—
42D4×C11—51no—
43D4×C11C2×D511yescharacteristic
44C22⋊D11—21no—
45C22⋊D11—101no—
46C2×Dic11—101no—
47D44C2×D511yescharacteristic
48C4×D11C2×D511yescharacteristic
49Dic22—51no—
50C8×C11—51no—
51C11⋊C8—51no—
52C2×C5×D4—111no—
53#709—111no—
54#687—111no—
55#687—111no—
56#686—111no—
57#686D1111yescharacteristic, complemented
58#681—111no—
59C5×C11AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
60C22×C11—21no—
61C22×C11—101no—
62C2×D11—21no—
63C2×D11—42no—
64C2×D11C22⋊D511yescharacteristic
65C4×C11C22×D511yescharacteristic
66Dic11—101no—
67Dic11C22⋊D511yescharacteristic
68C23×C5—221no—
69C5×D4—111no—
70C5×D4—221no—
71C5×D4C2×D1111yescharacteristic
72C2×C4×C5—111no—
73C22⋊D5—221no—
74D20C2×D1111yescharacteristic, complemented
75C4×D5—221no—
76Dic10—111no—
77#168—111no—
78#168C2×D1111yescharacteristic, complemented
79AGL(1,ℤ/8)—551noSylow
80C2×C11—41no—
81C2×C11—201no—
82C2×C11C2×C22⋊D511yescharacteristic
83D11—21no—
84D11—41no—
85C22×C5—21no—
86C22×C5—111no—
87C22×C5—221no—
88C22×C5—442no—
89C2×D5—21no—
90C4×C5—111no—
91C4×C5C22×D1111yescharacteristic
92Dic5—221no—
93#41—551no—
94C2×D4—111no—
95SD16—551no—
96SD16—551no—
97D8—51no—
98D8—551no—
99M16—551no—
100C11#407811yescharacteristic, complemented, Sylow
101C2×C5—41no—
102C2×C5—221no—
103C2×C5—441no—
104C2×C5D4×D1111yescharacteristic
105D5—41no—
106C23—221no—
107Q8—551no—
108D4—51no—
109D4—111no—
110D4—221no—
111D4—1101no—
112D4D5×D1111yescharacteristic
113C2×C4—111no—
114C2×C4—1101no—
115C8—51no—
116C8—551no—
117C5#6696411yescharacteristic, complemented, Sylow
118C22—21no—
119C22—101no—
120C22—111no—
121C22—221no—
122C22—442no—
123C4—111no—
124C4—1101no—
125C4C2×D5×D1111yescharacteristic
126C2—41no—
127C2—201no—
128C2—221no—
129C2—441no—
130C2D11×C22⋊D511yescharacteristic
subgroupG/H
centerC2D11×C22⋊D5
commutator, cosocleC4×C5×C11C23
FrattiniC4C2×D5×D11
FittingC5×D4×C11C22
socleC2×C5×C11C2×D4
hypercenterD4D5×D11
hypocenterC5×C11AGL(1,ℤ/8)
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
1. C5×D4×D11C2semidirect
2. #11724989C2semidirect
3. #11724934C2semidirect
4. C11×#686C2semidirect
5. #11724876C2semidirect
6. #11724871C2semidirect
7. #11724868C2semidirect
10. Dic110C22semidirect
11. C11×D20C22semidirect
17. C11⋊#168C22semidirect
18. C11×#168C22semidirect
29. D4×D11D5semidirect
57. #686D11semidirect
59. C5×C11AGL(1,ℤ/8)semidirect
74. D20C2×D11semidirect
78. #168C2×D11semidirect
100. C11#4078semidirect
117. C5#66964semidirect

Maximal subgroups

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

subgroupindex
C5×D4×D112
#117249892
#117249342
C11×#6862
#117248762
#117248712
#117248682
#669645
#407811