Finite Group Databasebeta

← #66942⋊C5 #13182491

Subgroups — #66942⋊C5 #13182491

Order 1760.

112 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C4⋊C4×C11⋊C5C211yesmaximal, characteristic
2C4⋊(Dic11⋊C5)C211yesmaximal, characteristic
3(Dic11⋊C4)⋊C5C211yesmaximal, characteristic
4(Dic11⋊C4)⋊C5C211yesmaximal, characteristic
5(Dic11⋊C4)⋊C5C211yesmaximal, characteristic
6(Dic11⋊C4)⋊C5C211yesmaximal, characteristic
7C4×Dic11⋊C5C211yesmaximal, characteristic
8C2×C4×C11⋊C5C2211yescharacteristic
9C2×C4×C11⋊C5C2211yescharacteristic
10C2×C4×C11⋊C5C2211yescharacteristic
11C2×Dic11⋊C5C2211yescharacteristic
12C2×Dic11⋊C5C2211yescharacteristic
13C2×Dic11⋊C5C2211yescharacteristic
14C2×Dic11⋊C5C2211yescharacteristic
15#66942C511yesmaximal, characteristic, complemented, Hall
16C22×C11⋊C5C2311yescharacteristic
17C4×C11⋊C5—21no—
18C4×C11⋊C5—21no—
19C4×C11⋊C5—21no—
20Dic11⋊C5—21no—
21Dic11⋊C5—21no—
22Dic11⋊C5—21no—
23Dic11⋊C5Q812yes—
24C11×C4⋊C4C2×C511yescharacteristic
25C4⋊Dic11C2×C511yescharacteristic
26Dic11⋊C4C2×C511yescharacteristic
27Dic11⋊C4C2×C511yescharacteristic
28Dic11⋊C4C2×C511yescharacteristic
29Dic11⋊C4C2×C511yescharacteristic
30C4×Dic11C2×C511yescharacteristic
31C5×#125—111nomaximal, Hall
32C2×C11⋊C5C2×Q811yescharacteristic
33C2×C11⋊C5#4111yescharacteristic
34C2×C11⋊C5#4111yescharacteristic
35C2×C4×C11C22×C511yescharacteristic
36C2×C4×C11C22×C511yescharacteristic
37C2×C4×C11C22×C511yescharacteristic
38C2×Dic11C22×C511yescharacteristic
39C2×Dic11C22×C511yescharacteristic
40C2×Dic11C22×C511yescharacteristic
41C2×Dic11C22×C511yescharacteristic
42C5×C4⋊C4—111no—
43C5×C4⋊C4—111no—
44C5×C4⋊C4—111no—
45C5×C4⋊C4—111no—
46C5×C4⋊C4—111no—
47C5×C4⋊C4—111no—
48C42×C5—111no—
49C11⋊C5#12511yescharacteristic, complemented, Hall
50C22×C11C23×C511yescharacteristic
51C4×C11—21no—
52C4×C11—21no—
53C4×C11—21no—
54Dic11—21no—
55Dic11—21no—
56Dic11—21no—
57Dic11C5×Q812yes—
58C2×C4×C5—111no—
59C2×C4×C5—111no—
60C2×C4×C5—111no—
61C2×C4×C5—111no—
62C2×C4×C5—111no—
63C2×C4×C5—111no—
64C2×C4×C5—111no—
65#125—111noSylow
66C2×C11C2×C5×Q811yescharacteristic
67C2×C11C5×#4111yescharacteristic
68C2×C11C5×#4111yescharacteristic
69C22×C5—111no—
70C4×C5—112no—
71C4×C5—221no—
72C4×C5—221no—
73C4×C5—221no—
74C4×C5—221no—
75C4×C5—221no—
76C4×C5—221no—
77C4⋊C4—111no—
78C4⋊C4—111no—
79C4⋊C4—111no—
80C4⋊C4—111no—
81C4⋊C4—111no—
82C4⋊C4AGL(1,𝔽11)11yescharacteristic
83C42—111no—
84C11C5×#12511yescharacteristic, complemented, Sylow
85C2×C5—111no—
86C2×C5—111no—
87C2×C5—111no—
88C2×C4—111no—
89C2×C4—111no—
90C2×C4—111no—
91C2×C4—111no—
92C2×C4C2×AGL(1,𝔽11)11yescharacteristic
93C2×C4C2×AGL(1,𝔽11)11yescharacteristic
94C2×C4C2×AGL(1,𝔽11)11yescharacteristic
95C5—111noSylow
96C22C22×AGL(1,𝔽11)11yescharacteristic
97C4—21no—
98C4—21no—
99C4—21no—
100C4—112no—
101C4—221no—
102C4—221no—
103C4—221no—
104C2#4339⋊C511yescharacteristic
105C2#4341⋊C511yescharacteristic
106C2Q8×AGL(1,𝔽11)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×AGL(1,𝔽11)
commutator, socle, cosocleC22×C11C23×C5
FittingC11×C4⋊C4C2×C5
prime radicalC22×C11⋊C5C23
hypercenterC4⋊C4AGL(1,𝔽11)
hypocenterC11C5×#125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
15. #66942C5semidirect
49. C11⋊C5#125semidirect
84. C11C5×#125semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C11⋊C52
C4⋊(Dic11⋊C5)2
(Dic11⋊C4)⋊C52
C4×Dic11⋊C52
#669425
C5×#12511