Finite Group Databasebeta

← #13183236

Subgroups — #13183236

Order 1760.

136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C2×C5×D4×C11C211yesmaximal, characteristic, complemented
2#11725031C211yesmaximal, characteristic, complemented
3#11724934C212yesmaximal, complemented
4#11724933C212yesmaximal, complemented
5#11724928C211yesmaximal, characteristic, complemented
6C23×C5×C11—21no—
7C5×D4×C11—21no—
8C5×D4×C11C2212yes—
9C2×C4×C5×C11C2211yescharacteristic
10C22⋊D55—21no—
11D220C2211yescharacteristic, complemented
12C4×D55—21no—
13Dic110C2211yescharacteristic, complemented
14C11⋊#168C2212yescomplemented
15#66985—51nomaximal, Hall
16C22×C5×C11—22no—
17C22×C5×C11—42no—
18C22×C5×C11D411yescharacteristic
19C2×D55—21no—
20C4×C5×C11D411yescharacteristic
21C4×C5×C11C2311yescharacteristic
22Dic55—21no—
23C2×D4×C11D511yescharacteristic, complemented
24#4339—51no—
25#4324—52no—
26#4323—52no—
27#4318—51no—
28#4078—111nomaximal, Hall
29C2×C5×C11—21no—
30C2×C5×C11—42no—
31C2×C5×C11C2×D411yescharacteristic
32D55—41no—
33C23×C11—21no—
34D4×C11—21no—
35D4×C11C2×D512yes—
36C2×C4×C11C2×D511yescharacteristic
37C22⋊D11—101no—
38D44—51no—
39C4×D11—101no—
40Dic22—51no—
41C11⋊C8—52no—
42C2×C5×D4D1111yescharacteristic, complemented
43#709—111no—
44#687—112no—
45#686—112no—
46#681—111no—
47C5×C11AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
48C22×C11—22no—
49C22×C11—42no—
50C22×C11C22⋊D511yescharacteristic
51C2×D11—101no—
52C4×C11C22⋊D511yescharacteristic
53C4×C11C22×D511yescharacteristic
54Dic11—101no—
55C23×C5—21no—
56C5×D4—21no—
57C5×D4C2×D1112yes—
58C2×C4×C5C2×D1111yescharacteristic
59C22⋊D5—221no—
60D20—111no—
61C4×D5—221no—
62Dic10—111no—
63#168—112no—
64AGL(1,ℤ/8)—551noSylow
65C2×C11—21no—
66C2×C11—42no—
67C2×C11C2×C22⋊D511yescharacteristic
68D11—201no—
69C22×C5—22no—
70C22×C5—42no—
71C22×C5C22⋊D1111yescharacteristic
72C2×D5—221no—
73C4×C5C22⋊D1111yescharacteristic
74C4×C5C22×D1111yescharacteristic
75Dic5—221no—
76#41—551no—
77C2×D4D5511yescharacteristic, complemented
78SD16—552no—
79D8—552no—
80M16—551no—
81C11#407811yescharacteristic, complemented, Sylow
82C2×C5—21no—
83C2×C5—42no—
84C2×C5C2×C22⋊D1111yescharacteristic
85D5—441no—
86C23—21no—
87Q8—551no—
88D4—21no—
89D4—551no—
90D4—1101no—
91D4C2×D5512yes—
92C2×C4—1101no—
93C2×C4C2×D5511yescharacteristic
94C8—552no—
95C5#6698511yescharacteristic, complemented, Sylow
96C22—22no—
97C22—42no—
98C22—1101no—
99C22C22⋊D5511yescharacteristic
100C4—1101no—
101C4C22⋊D5511yescharacteristic
102C4C22×D5511yescharacteristic
103C2—21no—
104C2—42no—
105C2—2201no—
106C2C2×C22⋊D5511yescharacteristic
subgroupG/H
centerC2C2×C22⋊D55
commutator, cosocleC4×C5×C11C23
FrattiniC4C22×D55
FittingC2×C5×D4×C11C2
socleC2×C5×C11C2×D4
hypercenterC2×D4D55
hypocenterC5×C11AGL(1,ℤ/8)
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×C11C2semidirect
2. #11725031C2semidirect
3. #11724934C2semidirect
4. #11724933C2semidirect
5. #11724928C2semidirect
11. D220C22semidirect
13. Dic110C22semidirect
14. C11⋊#168C22semidirect
23. C2×D4×C11D5semidirect
42. C2×C5×D4D11semidirect
47. C5×C11AGL(1,ℤ/8)semidirect
77. C2×D4D55semidirect
81. C11#4078semidirect
95. C5#66985semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×C112
#117250312
#117249342
#117249332
#117249282
#669855
#407811