Finite Group Databasebeta

← #13183194

Subgroups — #13183194

Order 1760.

156 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 49 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×D220C211yesmaximal, characteristic
2C2×C4×D55C211yesmaximal, characteristic, complemented
3C5×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4#11724932C211yesmaximal, characteristic, complemented
5#11724932C211yesmaximal, characteristic, complemented
6#11724932C211yesmaximal, characteristic, complemented
7#11724930C211yesmaximal, characteristic, complemented
8C22×D55C2211yescharacteristic
9C22×D55C2211yescharacteristic
10C2×C4×C5×C11C2211yescharacteristic
11C2×C4×C5×C11C2211yescharacteristic
12C2×C4×C5×C11C2211yescharacteristic
13C2×Dic55C2211yescharacteristic
14C2×Dic55C2211yescharacteristic
15D220—22no—
16C4×D55—22no—
17#66947—51nomaximal, Hall
18C22×C5×C11C2311yescharacteristic
19C2×D55—21no—
20C2×D55—21no—
21C2×D55—21no—
22C2×D55—21no—
23C2×D55—21no—
24C2×D55D412yes—
25C4×C5×C11—21no—
26C4×C5×C11—21no—
27C4×C5×C11—21no—
28Dic55—21no—
29Dic55—21no—
30C2×D44—51no—
31C2×C4×D11—51no—
32C11×C4⋊C4D511yescharacteristic, complemented
33(C2×D11)⋊C4—51no—
34(C2×D11)⋊C4—51no—
35(C2×D11)⋊C4—51no—
36Dic11⋊C4—51no—
37#4040—111nomaximal, Hall
38C2×C5×C11C2×D411yescharacteristic
39C2×C5×C11#4111yescharacteristic
40C2×C5×C11#4111yescharacteristic
41D55—22no—
42D55—41no—
43C22×D11—51no—
44C22×D11—51no—
45C2×C4×C11C2×D511yescharacteristic
46C2×C4×C11C2×D511yescharacteristic
47C2×C4×C11C2×D511yescharacteristic
48C2×Dic11—51no—
49C2×Dic11—51no—
50D44—102no—
51C4×D11—102no—
52C2×D20—111no—
53C2×C4×D5—111no—
54C5×C4⋊C4D1111yescharacteristic, complemented
55#685—111no—
56#685—111no—
57#685—111no—
58#683—111no—
59C5×C11#12311yescharacteristic, complemented, Hall
60C22×C11C22×D511yescharacteristic
61C2×D11—52no—
62C2×D11—101no—
63C2×D11—101no—
64C2×D11—101no—
65C2×D11—101no—
66C2×D11—101no—
67C4×C11—21no—
68C4×C11—21no—
69C4×C11—21no—
70Dic11—101no—
71Dic11—101no—
72C22×D5—111no—
73C22×D5—111no—
74C2×C4×C5C2×D1111yescharacteristic
75C2×C4×C5C2×D1111yescharacteristic
76C2×C4×C5C2×D1111yescharacteristic
77C2×Dic5—111no—
78C2×Dic5—111no—
79D20—222no—
80C4×D5—222no—
81#123—551noSylow
82C2×C11#70911yescharacteristic
83C2×C11D4×D511yescharacteristic
84C2×C11#71311yescharacteristic
85D11—102no—
86D11—201no—
87C22×C5C22×D1111yescharacteristic
88C2×D5—112no—
89C2×D5—221no—
90C2×D5—221no—
91C2×D5—221no—
92C2×D5—221no—
93C2×D5—221no—
94C4×C5—21no—
95C4×C5—21no—
96C4×C5—21no—
97Dic5—221no—
98Dic5—221no—
99C2×D4—551no—
100C22×C4—551no—
101C4⋊C4—551no—
102C4⋊C4D5511yescharacteristic, complemented
103C22⋊C4—551no—
104C22⋊C4—551no—
105C22⋊C4—551no—
106C11#404011yescharacteristic, complemented, Sylow
107C2×C5#433911yescharacteristic
108C2×C5D4×D1111yescharacteristic
109C2×C5#434311yescharacteristic
110D5—222no—
111D5—441no—
112C23—551no—
113C23—551no—
114D4—1102no—
115C2×C4—551no—
116C2×C4—551no—
117C2×C4—1102no—
118C2×C4C2×D5511yescharacteristic
119C2×C4C2×D5511yescharacteristic
120C2×C4C2×D5511yescharacteristic
121C5#6694711yescharacteristic, complemented, Sylow
122C22—552no—
123C22—1101no—
124C22—1101no—
125C22—1101no—
126C22—1101no—
127C22—1101no—
128C22C22×D5511yescharacteristic
129C4—21no—
130C4—21no—
131C4—21no—
132C4—1101no—
133C4—1101no—
134C2—1102no—
135C2—2201no—
136C2#1172503111yescharacteristic
137C2D4×D5511yescharacteristic
138C2#1172503511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D55
commutator, socle, cosocleC22×C5×C11C23
FittingC5×C11×C4⋊C4C2
prime radicalC2×D220C2
hypercenterC4⋊C4D55
hypocenterC5×C11#123
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D55C2semidirect
3. C5×C11×C4⋊C4C2semidirect
4. #11724932C2semidirect
5. #11724932C2semidirect
6. #11724932C2semidirect
7. #11724930C2semidirect
32. C11×C4⋊C4D5semidirect
54. C5×C4⋊C4D11semidirect
59. C5×C11#123semidirect
102. C4⋊C4D55semidirect
106. C11#4040semidirect
121. C5#66947semidirect

Maximal subgroups

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

subgroupindex
C2×D2202
C2×C4×D552
C5×C11×C4⋊C42
#117249322
#117249302
#669475
#404011