Finite Group Databasebeta

← #13182816

Subgroups — #13182816

Order 1760.

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

normal subgroups only

This group has 156 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
1C2×C11×D20C211yesmaximal, characteristic
2C2×D5×Dic11C211yesmaximal, characteristic, complemented
3#11724930C211yesmaximal, characteristic, complemented
4C5×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#11724885C211yesmaximal, characteristic, complemented
6#11724885C211yesmaximal, characteristic, complemented
7#11724885C211yesmaximal, characteristic, complemented
8C22×D5×C11C2211yescharacteristic
9C22×D5×C11C2211yescharacteristic
10C2×C4×C5×C11C2211yescharacteristic
11C2×Dic55C2211yescharacteristic
12C2×Dic55C2211yescharacteristic
13C11×D20—22no—
14C2×C5×Dic11C2211yescharacteristic
15C2×C5×Dic11C2211yescharacteristic
16D5×Dic11—22no—
17#66988—51nomaximal, Hall
18C22×C5×C11C2311yescharacteristic
19C2×D5×C11—21no—
20C2×D5×C11—21no—
21C2×D5×C11—21no—
22C2×D5×C11—21no—
23C2×D5×C11—21no—
24C2×D5×C11D412yes—
25C4×C5×C11—21no—
26Dic55—21no—
27Dic55—21no—
28C5×Dic11—21no—
29C5×Dic11—21no—
30C2×D4×C11—51no—
31C22×Dic11—51no—
32C22⋊Dic11—51no—
33C22⋊Dic11—51no—
34C22⋊Dic11—51no—
35Dic11⋊C4—51no—
36Dic11⋊C4D511yescharacteristic, complemented
37#4040—111nomaximal, Hall
38C2×C5×C11C2×D411yescharacteristic
39C2×C5×C11#4111yescharacteristic
40C2×C5×C11#4111yescharacteristic
41D5×C11—22no—
42D5×C11—41no—
43C23×C11—51no—
44C23×C11—51no—
45D4×C11—102no—
46C2×C4×C11C2×D511yescharacteristic
47C2×Dic11—51no—
48C2×Dic11—51no—
49C2×Dic11—102no—
50C2×Dic11C2×D511yescharacteristic
51C2×Dic11C2×D511yescharacteristic
52C2×D20D1111yescharacteristic
53C2×C4×D5—111no—
54C5×C4⋊C4—111no—
55#685—111no—
56#685—111no—
57#685—111no—
58#683—111no—
59C5×C11#12311yescharacteristic, complemented, Hall
60C22×C11—52no—
61C22×C11—101no—
62C22×C11—101no—
63C22×C11—101no—
64C22×C11—101no—
65C22×C11—101no—
66C22×C11C22×D511yescharacteristic
67C4×C11—21no—
68Dic11—21no—
69Dic11—21no—
70Dic11—101no—
71Dic11—101no—
72C22×D5C2×D1111yescharacteristic
73C22×D5C2×D1111yescharacteristic
74C2×C4×C5—111no—
75C2×C4×C5—111no—
76C2×C4×C5C2×D1111yescharacteristic
77C2×Dic5—111no—
78C2×Dic5—111no—
79D20—22no—
80C4×D5—222no—
81#123—551noSylow
82C2×C11—102no—
83C2×C11—201no—
84C2×C11#70911yescharacteristic
85C2×C11D4×D511yescharacteristic
86C2×C11#71311yescharacteristic
87C22×C5C22×D1111yescharacteristic
88C2×D5—21no—
89C2×D5—21no—
90C2×D5—21no—
91C2×D5—21no—
92C2×D5—21no—
93C2×D5C22⋊D1112yes—
94C4×C5—21no—
95C4×C5—221no—
96C4×C5—221no—
97Dic5—221no—
98Dic5—221no—
99C2×D4—51no—
100C22×C4—551no—
101C4⋊C4—111no—
102C4⋊C4—551no—
103C22⋊C4—551no—
104C22⋊C4—551no—
105C22⋊C4—551no—
106C11#404011yescharacteristic, complemented, Sylow
107C2×C5#434111yescharacteristic
108C2×C5#434111yescharacteristic
109C2×C5C2×C22⋊D1111yescharacteristic
110D5—22no—
111D5—41no—
112C23—51no—
113C23—51no—
114D4—102no—
115C2×C4—111no—
116C2×C4—111no—
117C2×C4—551no—
118C2×C4—551no—
119C2×C4—1102no—
120C2×C4D5×D1111yescharacteristic
121C5#6698811yescharacteristic, complemented, Sylow
122C22—52no—
123C22—101no—
124C22—101no—
125C22—101no—
126C22—101no—
127C22—101no—
128C22C2×D5×D1111yescharacteristic
129C4—21no—
130C4—221no—
131C4—221no—
132C4—1101no—
133C4—1101no—
134C2—102no—
135C2—201no—
136C2#1172498511yescharacteristic
137C2#1172498911yescharacteristic
138C2D5×C22⋊D1111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, cosocleC22×C5×C11C23
FittingC2×C4×C5×C11C22
prime radicalC2×C11×D20C2
hypercenterC2×C4D5×D11
hypocenterC5×C11#123
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5×Dic11C2semidirect
3. #11724930C2semidirect
4. C5×Dic11⋊C4C2semidirect
5. #11724885C2semidirect
6. #11724885C2semidirect
7. #11724885C2semidirect
36. Dic11⋊C4D5semidirect
59. C5×C11#123semidirect
106. C11#4040semidirect
121. C5#66988semidirect

Maximal subgroups

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

subgroupindex
C2×C11×D202
C2×D5×Dic112
#117249302
C5×Dic11⋊C42
#117248852
#669885
#404011