Finite Group Databasebeta

← #13182734

Subgroups — #13182734

Order 1760.

112 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 48 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
1#11724930C211yesmaximal, characteristic
2C11×#683C211yesmaximal, characteristic
3C4×C5×Dic11C211yesmaximal, characteristic
4#11724889C211yesmaximal, characteristic
5#11724888C211yesmaximal, characteristic
6Dic11⋊Dic5C211yesmaximal, characteristic
7Dic11⋊Dic5C211yesmaximal, characteristic
8C2×C4×C5×C11C2211yescharacteristic
9C2×Dic55C2211yescharacteristic
10C2×Dic55C2211yescharacteristic
11C2×C11×Dic5C2211yescharacteristic
12C2×C11×Dic5C2211yescharacteristic
13C2×C5×Dic11C2211yescharacteristic
14C2×C5×Dic11C2211yescharacteristic
15#66942—51nomaximal, Hall
16C22×C5×C11C2311yescharacteristic
17C4×C5×C11—21no—
18Dic55—21no—
19Dic55—21no—
20C5×Dic11—21no—
21C5×Dic11Q812yes—
22C11×Dic5—21no—
23C11×Dic5—21no—
24C11×C4⋊C4—51no—
25C4⋊Dic11—51no—
26Dic11⋊C4—51no—
27Dic11⋊C4—51no—
28Dic11⋊C4—51no—
29Dic11⋊C4—51no—
30C4×Dic11D511yescharacteristic
31#4016—111nomaximal, Hall
32C2×C5×C11C2×Q811yescharacteristic
33C2×C5×C11#4111yescharacteristic
34C2×C5×C11#4111yescharacteristic
35C2×C4×C11—51no—
36C2×C4×C11—51no—
37C2×C4×C11C2×D511yescharacteristic
38C2×Dic11—51no—
39C2×Dic11—51no—
40C2×Dic11C2×D511yescharacteristic
41C2×Dic11C2×D511yescharacteristic
42C42×C5—111no—
43C4⋊Dic5—111no—
44C4⋊Dic5—111no—
45#683—111no—
46#683—111no—
47#683—111no—
48#683D1111yescharacteristic
49C5×C11#12511yescharacteristic, complemented, Hall
50C22×C11C22×D511yescharacteristic
51C4×C11—21no—
52C4×C11—101no—
53C4×C11—101no—
54Dic11—21no—
55Dic11—101no—
56Dic11—101no—
57Dic11Dic1012yes—
58C2×C4×C5—111no—
59C2×C4×C5—111no—
60C2×C4×C5C2×D1111yescharacteristic
61C2×Dic5—111no—
62C2×Dic5—111no—
63C2×Dic5C2×D1111yescharacteristic
64C2×Dic5C2×D1111yescharacteristic
65#125—551noSylow
66C2×C11C2×Dic1011yescharacteristic
67C2×C11#70911yescharacteristic
68C2×C11#70911yescharacteristic
69C22×C5C22×D1111yescharacteristic
70C4×C5—21no—
71C4×C5—112no—
72C4×C5—221no—
73Dic5—21no—
74Dic5—21no—
75Dic5—221no—
76Dic5—221no—
77C4⋊C4—51no—
78C4⋊C4—551no—
79C4⋊C4—551no—
80C4⋊C4—551no—
81C4⋊C4—551no—
82C4⋊C4—551no—
83C42—111no—
84C11#401611yescharacteristic, complemented, Sylow
85C2×C5#433911yescharacteristic
86C2×C5#434111yescharacteristic
87C2×C5Q8×D1111yescharacteristic
88C2×C4—51no—
89C2×C4—51no—
90C2×C4—111no—
91C2×C4—111no—
92C2×C4—551no—
93C2×C4—551no—
94C2×C4D5×D1111yescharacteristic
95C5#6694211yescharacteristic, complemented, Sylow
96C22C2×D5×D1111yescharacteristic
97C4—21no—
98C4—101no—
99C4—101no—
100C4—112no—
101C4—221no—
102C4—1101no—
103C4—1101no—
104C2D11×Dic1011yescharacteristic
105C2#1172498811yescharacteristic
106C2#1172499911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, prime radical, cosocleC22×C5×C11C23
FittingC2×C4×C5×C11C22
hypercenterC2×C4D5×D11
hypocenterC5×C11#125
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
49. C5×C11#125semidirect
84. C11#4016semidirect
95. C5#66942semidirect

Maximal subgroups

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

subgroupindex
#117249302
C11×#6832
C4×C5×Dic112
#117248892
#117248882
Dic11⋊Dic52
#669425
#401611