Finite Group Databasebeta

← #13183215

Subgroups — #13183215

Order 1760.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#11725035C211yesmaximal, characteristic, complemented
2#11725033C211yesmaximal, characteristic, complemented
3C5×C11×SD16C211yesmaximal, characteristic, complemented
4#11724936C211yesmaximal, characteristic, complemented
5#11724933C211yesmaximal, characteristic, complemented
6#11724924C211yesmaximal, characteristic, complemented
7C8×D55C211yesmaximal, characteristic, complemented
8C5×Q8×C11C2211yescharacteristic
9C5×D4×C11C2211yescharacteristic
10C22⋊D55—21no—
11C2×Dic55—21no—
12D220—21no—
13D220C2211yescharacteristic
14C4×D55—21no—
15C4×D55C2211yescharacteristic
16Dic110C2211yescharacteristic
17C5×C8×C11C2211yescharacteristic
18C11⋊#168C2211yescharacteristic
19#66969—51nomaximal, Hall
20C22×C5×C11—21no—
21C2×D55—21no—
22C2×D55D411yescharacteristic
23C4×C5×C11—21no—
24C4×C5×C11C2311yescharacteristic
25Dic55—21no—
26Dic55D411yescharacteristic
27#4343—51no—
28#4341—51no—
29C11×SD16D511yescharacteristic, complemented
30#4326—51no—
31#4323—51no—
32#4314—51no—
33C8×D11—51no—
34#4062—111nomaximal, Hall
35C2×C5×C11—41no—
36C2×C5×C11C2×D411yescharacteristic
37D55—21no—
38D55—41no—
39Q8×C11C2×D511yescharacteristic
40D4×C11C2×D511yescharacteristic
41C22⋊D11—101no—
42C2×Dic11—101no—
43D44—51no—
44D44—101no—
45C4×D11—51no—
46C4×D11—101no—
47Dic22—51no—
48C8×C11C2×D511yescharacteristic
49C11⋊C8—51no—
50#713—111no—
51#711—111no—
52C5×SD16D1111yescharacteristic, complemented
53#689—111no—
54#686—111no—
55#677—111no—
56C8×D5—111no—
57C5×C11#13511yescharacteristic, complemented, Hall
58C22×C11—21no—
59C2×D11—51no—
60C2×D11—101no—
61C4×C11—21no—
62C4×C11C22×D511yescharacteristic
63Dic11—51no—
64Dic11—101no—
65C5×Q8C2×D1111yescharacteristic
66C5×D4C2×D1111yescharacteristic
67C22⋊D5—221no—
68C2×Dic5—221no—
69D20—111no—
70D20—221no—
71C4×D5—111no—
72C4×D5—221no—
73Dic10—111no—
74C5×C8C2×D1111yescharacteristic
75#168—111no—
76#135—551noSylow
77C2×C11—41no—
78C2×C11D4×D511yescharacteristic
79D11—101no—
80D11—201no—
81C22×C5—21no—
82C2×D5—111no—
83C2×D5—221no—
84C4×C5—21no—
85C4×C5C22×D1111yescharacteristic
86Dic5—111no—
87Dic5—221no—
88#41—551no—
89#41—551no—
90Q16—551no—
91SD16—551no—
92SD16D5511yescharacteristic, complemented
93D8—551no—
94C2×C8—551no—
95C11#406211yescharacteristic, complemented, Sylow
96C2×C5—41no—
97C2×C5D4×D1111yescharacteristic
98D5—221no—
99D5—441no—
100Q8—551no—
101Q8C2×D5511yescharacteristic
102D4—551no—
103D4—1101no—
104D4—1101no—
105D4C2×D5511yescharacteristic
106C2×C4—551no—
107C2×C4—1101no—
108C2×C4—1101no—
109C8—551no—
110C8C2×D5511yescharacteristic
111C5#6696911yescharacteristic, complemented, Sylow
112C22—21no—
113C22—551no—
114C22—1101no—
115C4—21no—
116C4—551no—
117C4—1101no—
118C4C22×D5511yescharacteristic
119C2—41no—
120C2—1101no—
121C2—2201no—
122C2D4×D5511yescharacteristic
subgroupG/H
centerC2D4×D55
commutator, cosocleC4×C5×C11C23
FrattiniC4C22×D55
FittingC5×C11×SD16C2
socleC2×C5×C11C2×D4
hypercenterSD16D55
hypocenterC5×C11#135
LCSG ▷ C4×C5×C11 ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #11725035C2semidirect
2. #11725033C2semidirect
3. C5×C11×SD16C2semidirect
4. #11724936C2semidirect
5. #11724933C2semidirect
6. #11724924C2semidirect
7. C8×D55C2semidirect
29. C11×SD16D5semidirect
52. C5×SD16D11semidirect
57. C5×C11#135semidirect
92. SD16D55semidirect
95. C11#4062semidirect
111. C5#66969semidirect

Maximal subgroups

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

subgroupindex
#117250352
#117250332
C5×C11×SD162
#117249362
#117249332
#117249242
C8×D552
#669695
#406211