Finite Group Databasebeta

← #13182874

Subgroups — #13182874

Order 1760.

188 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 54 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×C4×D55C211yesmaximal, characteristic, complemented
2C2×C11×D20C211yesmaximal, characteristic, complemented
3C2×#89169C212yesmaximal, complemented
4C5×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#11724885C212yesmaximal, complemented
6C22×D55C2211yescharacteristic
7C22×D5×C11C2212yes—
8C2×C4×C5×C11C2211yescharacteristic
9C2×Dic55C2211yescharacteristic
10C4×D55—22no—
11C11×D20—22no—
12C2×C5×Dic11C2212yes—
13#89169—24no—
14#66991—51nomaximal, Hall
15C22×C5×C11C2311yescharacteristic
16C2×D55—21no—
17C2×D55—21no—
18C2×D55D412yescomplemented
19C2×D5×C11—22no—
20C2×D5×C11—22no—
21C2×D5×C11—22no—
22C4×C5×C11D412yescomplemented
23Dic55—21no—
24C5×Dic11—22no—
25C2×D4×C11—51no—
26C2×C22⋊D11—52no—
27C2×C4×D11—51no—
28C22⋊Dic11—52no—
29C4⋊Dic11D511yescharacteristic, complemented
30#4041—111nomaximal, Hall
31C2×C5×C11C2×D411yescharacteristic
32C2×C5×C11C2×D411yescharacteristic
33C2×C5×C11#4111yescharacteristic
34D55—22no—
35D5×C11—42no—
36C23×C11—52no—
37C22×D11—51no—
38D4×C11—102no—
39C2×C4×C11C2×D511yescharacteristic
40C22⋊D11—104no—
41C2×Dic11—51no—
42C2×Dic11C2×D512yes—
43C4×D11—102no—
44C2×D20—112no—
45C2×D20D1111yescharacteristic, complemented
46C2×C4×D5—111no—
47C5×C4⋊C4—111no—
48#685—112no—
49C5×C11#12111yescharacteristic, complemented, Hall
50C22×C11—102no—
51C22×C11—102no—
52C22×C11—102no—
53C22×C11C22×D511yescharacteristic
54C2×D11—52no—
55C2×D11—101no—
56C2×D11—101no—
57C4×C11D2012yescomplemented
58Dic11—22no—
59Dic11—101no—
60C22×D5—111no—
61C22×D5C2×D1112yes—
62C2×C4×C5—112no—
63C2×C4×C5C2×D1111yescharacteristic
64C2×Dic5—111no—
65D20—22no—
66D20—224no—
67C4×D5—222no—
68#121—551noSylow
69C2×C11—202no—
70C2×C11C2×D2011yescharacteristic
71C2×C11D4×D511yescharacteristic
72C2×C11#71311yescharacteristic
73D11—102no—
74C22×C5C22×D1111yescharacteristic
75C2×D5—22no—
76C2×D5—22no—
77C2×D5—22no—
78C2×D5—112no—
79C2×D5—221no—
80C2×D5—221no—
81C4×C5—222no—
82C4×C5C22⋊D1112yescomplemented
83Dic5—221no—
84C2×D4—51no—
85C2×D4—552no—
86C22×C4—551no—
87C4⋊C4—111no—
88C22⋊C4—552no—
89C11#404111yescharacteristic, complemented, Sylow
90C2×C5D4×D1111yescharacteristic
91C2×C5#434111yescharacteristic
92C2×C5C2×C22⋊D1111yescharacteristic
93D5—42no—
94D5—222no—
95C23—52no—
96C23—551no—
97D4—102no—
98D4—1104no—
99C2×C4—112no—
100C2×C4—551no—
101C2×C4—1102no—
102C2×C4D5×D1111yescharacteristic
103C5#6699111yescharacteristic, complemented, Sylow
104C22—102no—
105C22—102no—
106C22—102no—
107C22—552no—
108C22—1101no—
109C22—1101no—
110C22C2×D5×D1111yescharacteristic
111C4—222no—
112C4—1101no—
113C4#8916912yescomplemented
114C2—202no—
115C2—1102no—
116C2#1172498511yescharacteristic
117C2#1172499411yescharacteristic
118C2C2×#8916911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, cosocleC22×C5×C11C23
FittingC2×C4×C5×C11C22
hypercenterC2×C4D5×D11
hypocenterC5×C11#121
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D55C2semidirect
2. C2×C11×D20C2semidirect
3. C2×#89169C2semidirect
4. C5×C4⋊Dic11C2semidirect
5. #11724885C2semidirect
18. C2×D55D4semidirect
22. C4×C5×C11D4semidirect
29. C4⋊Dic11D5semidirect
45. C2×D20D11semidirect
49. C5×C11#121semidirect
57. C4×C11D20semidirect
82. C4×C5C22⋊D11semidirect
89. C11#4041semidirect
103. C5#66991semidirect
113. C4#89169semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D552
C2×C11×D202
C2×#891692
C5×C4⋊Dic112
#117248852
#669915
#404111