Finite Group Databasebeta

← #13182910

Subgroups — #13182910

Order 1760.

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

normal subgroups only

This group has 124 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
1C11×#711C211yesmaximal, characteristic, complemented
2#11724982C211yesmaximal, characteristic, complemented
3#11724934C211yesmaximal, characteristic, complemented
4C5×#4323C211yesmaximal, characteristic, complemented
5#11724882C211yesmaximal, characteristic, complemented
6#11724874C211yesmaximal, characteristic, complemented
7D5×C11⋊C8C211yesmaximal, characteristic, complemented
8C5×D4×C11C2211yescharacteristic
9Dic110C2211yescharacteristic
10C11×C22⋊D5—21no—
11C2×C11×Dic5—21no—
12C4×D5×C11C2211yescharacteristic
13C11×Dic10C2211yescharacteristic
14C5×D44C2211yescharacteristic
15#89167—21no—
16Dic5×D11—21no—
17C11⋊#168C2211yescharacteristic
18C5×C11⋊C8C2211yescharacteristic
19#67003—51nomaximal, Hall
20C22×C5×C11—21no—
21C2×D5×C11D411yescharacteristic
22C2×C5×D11—21no—
23C4×C5×C11C2311yescharacteristic
24Dic55—21no—
25C11×Dic5—21no—
26C11×Dic5D411yescharacteristic
27C11×#41—51no—
28#4339—51no—
29#4326—51no—
30#4325—51no—
31#4324—51no—
32#4323D511yescharacteristic, complemented
33C2×C11⋊C8—51no—
34#4058—111nomaximal, Hall
35C2×C5×C11—41no—
36C2×C5×C11C2×D411yescharacteristic
37C5×D11—41no—
38D5×C11—21no—
39Q8×C11—51no—
40D4×C11—101no—
41D4×C11C2×D511yescharacteristic
42C2×C4×C11—51no—
43C2×C4×C11—101no—
44C22⋊D11—101no—
45D44C2×D511yescharacteristic
46C4×D11—101no—
47Dic22—51no—
48C11⋊C8—51no—
49C11⋊C8C2×D511yescharacteristic
50#711—111no—
51#711D1111yescharacteristic, complemented
52C5×D8—111no—
53#687—111no—
54#687—111no—
55Dic20—111no—
56C8×D5—111no—
57C5×C11#13511yescharacteristic, complemented, Hall
58C22×C11—21no—
59C22×C11—51no—
60C2×D11—21no—
61C4×C11—51no—
62C4×C11—101no—
63C4×C11C22×D511yescharacteristic
64Dic11—101no—
65C5×D4—111no—
66C5×D4C2×D1111yescharacteristic
67C22⋊D5—21no—
68C22⋊D5—221no—
69C2×Dic5—21no—
70C2×Dic5—221no—
71C4×D5C2×D1111yescharacteristic
72Dic10—111no—
73Dic10C2×D1111yescharacteristic
74C5×C8—111no—
75#168—111no—
76#135—551noSylow
77C2×C11—41no—
78C2×C11—101no—
79C2×C11D4×D511yescharacteristic
80D11—41no—
81C22×C5—21no—
82C22×C5—221no—
83C2×D5C22⋊D1111yescharacteristic
84C4×C5C22×D1111yescharacteristic
85Dic5—21no—
86Dic5—221no—
87Dic5C22⋊D1111yescharacteristic
88#41—51no—
89#41—551no—
90Q16—551no—
91SD16—551no—
92SD16—551no—
93D8—111no—
94C2×C8—551no—
95C11#405811yescharacteristic, complemented, Sylow
96C2×C5—41no—
97C2×C5—441no—
98C2×C5C2×C22⋊D1111yescharacteristic
99D5—21no—
100Q8—51no—
101Q8—551no—
102D4—101no—
103D4—111no—
104D4—1101no—
105D4D5×D1111yescharacteristic
106C2×C4—51no—
107C2×C4—101no—
108C2×C4—1101no—
109C8—111no—
110C8—551no—
111C5#6700311yescharacteristic, complemented, Sylow
112C22—21no—
113C22—51no—
114C22—221no—
115C4—51no—
116C4—101no—
117C4—1101no—
118C4C2×D5×D1111yescharacteristic
119C2—41no—
120C2—101no—
121C2—441no—
122C2D5×C22⋊D1111yescharacteristic
subgroupG/H
centerC2D5×C22⋊D11
commutator, cosocleC4×C5×C11C23
FrattiniC4C2×D5×D11
FittingC5×D4×C11C22
socleC2×C5×C11C2×D4
hypercenterD4D5×D11
hypocenterC5×C11#135
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. C11×#711C2semidirect
2. #11724982C2semidirect
3. #11724934C2semidirect
4. C5×#4323C2semidirect
5. #11724882C2semidirect
6. #11724874C2semidirect
7. D5×C11⋊C8C2semidirect
32. #4323D5semidirect
51. #711D11semidirect
57. C5×C11#135semidirect
95. C11#4058semidirect
111. C5#67003semidirect

Maximal subgroups

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

subgroupindex
C11×#7112
#117249822
#117249342
C5×#43232
#117248822
#117248742
D5×C11⋊C82
#670035
#405811