Finite Group Databasebeta

← C11⋊C5×#518 #72248885

Subgroups — C11⋊C5×#518 #72248885

Order 3520.

676 conjugacy classes of subgroups; only the 363 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 363 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
1C22×D4×C11⋊C5C211yesmaximal, characteristic
2C4×D4×C11⋊C5C218yesmaximal, complemented
3#117×C11⋊C5C212yesmaximal, complemented
4C2×C22⋊C4×C11⋊C5C214yesmaximal, complemented
5C24×C11⋊C5C2212yes—
6C2×D4×C11⋊C5C418yescomplemented
7C2×D4×C11⋊C5C2214yes—
8C22×C4×C11⋊C5C2211yescharacteristic
9C22×C4×C11⋊C5C2218yescomplemented
10C4⋊C4×C11⋊C5C2214yescomplemented
11C22⋊C4×C11⋊C5C2214yes—
12C22⋊C4×C11⋊C5C2218yescomplemented
13C42×C11⋊C5C2214yescomplemented
14C11×#518C511yesmaximal, characteristic, complemented, Hall
15C23×C11⋊C5—44no—
16C23×C11⋊C5C2×C418yescomplemented
17C23×C11⋊C5C2311yescharacteristic
18C23×C11⋊C5C2314yes—
19D4×C11⋊C5C2×C4116yescomplemented
20C2×C4×C11⋊C5—48no—
21C2×C4×C11⋊C5C2×C414yescomplemented
22C2×C4×C11⋊C5C2318yes—
23C2×C4×C11⋊C5C2312yes—
24C22×D4×C11C2×C511yescharacteristic
25C4×D4×C11C2×C518yescomplemented
26C11×#117C2×C512yescomplemented
27C2×C11×C22⋊C4C2×C514yescomplemented
28C5×#518—111nomaximal, Hall
29C22×C11⋊C5—28no—
30C22×C11⋊C5—22no—
31C22×C11⋊C5—48no—
32C22×C11⋊C5C22×C412yes—
33C22×C11⋊C5C22×C418yes—
34C22×C11⋊C5C2411yescharacteristic
35C4×C11⋊C5—28no—
36C4×C11⋊C5C22×C414yes—
37C24×C11C22×C512yes—
38C2×D4×C11C4×C518yescomplemented
39C2×D4×C11C22×C514yes—
40C22×C4×C11C22×C511yescharacteristic
41C22×C4×C11C22×C518yescomplemented
42C11×C4⋊C4C22×C514yescomplemented
43C11×C22⋊C4C22×C514yes—
44C11×C22⋊C4C22×C518yescomplemented
45C42×C11C22×C514yescomplemented
46C22×C5×D4—111no—
47C4×C5×D4—118no—
48C5×#117—112no—
49C2×C5×C22⋊C4—114no—
50C2×C11⋊C5—22no—
51C2×C11⋊C5—28no—
52C2×C11⋊C5C23×C411yescharacteristic
53C2×C11⋊C5H(5,𝔽2)12yes—
54C23×C11—44no—
55C23×C11C2×C4×C518yescomplemented
56C23×C11C23×C511yescharacteristic
57C23×C11C23×C514yes—
58D4×C11C2×C4×C5116yescomplemented
59C2×C4×C11—48no—
60C2×C4×C11C2×C4×C514yescomplemented
61C2×C4×C11C23×C518yes—
62C2×C4×C11C23×C512yes—
63C24×C5—112no—
64C2×C5×D4—118no—
65C2×C5×D4—114no—
66C22×C4×C5—111no—
67C22×C4×C5—118no—
68C5×C4⋊C4—114no—
69C5×C22⋊C4—114no—
70C5×C22⋊C4—118no—
71C42×C5—114no—
72#518C11⋊C511yescharacteristic, direct product factor, Sylow
73C11⋊C5#51811yescharacteristic, direct product factor, Hall
74C22×C11—28no—
75C22×C11—22no—
76C22×C11—48no—
77C22×C11C22×C4×C512yes—
78C22×C11C22×C4×C518yes—
79C22×C11C24×C511yescharacteristic
80C4×C11—28no—
81C4×C11C22×C4×C514yes—
82C23×C5—118no—
83C23×C5—111no—
84C23×C5—114no—
85C23×C5—444no—
86C5×D4—1116no—
87C2×C4×C5—114no—
88C2×C4×C5—112no—
89C2×C4×C5—118no—
90C2×C4×C5—448no—
91C22×D4C2×C11⋊C511yescharacteristic
92C4×D4C2×C11⋊C518yescomplemented
93#117C2×C11⋊C512yescomplemented
94C2×C22⋊C4C2×C11⋊C514yescomplemented
95C2×C11—22no—
96C2×C11—28no—
97C2×C11C23×C4×C511yescharacteristic
98C2×C11C5×H(5,𝔽2)12yes—
99C22×C5—112no—
100C22×C5—118no—
101C22×C5—111no—
102C22×C5—228no—
103C22×C5—222no—
104C22×C5—448no—
105C4×C5—114no—
106C4×C5—228no—
107C24C22×C11⋊C512yes—
108C2×D4C4×C11⋊C518yescomplemented
109C2×D4C22×C11⋊C514yes—
110C22×C4C22×C11⋊C511yescharacteristic
111C22×C4C22×C11⋊C518yescomplemented
112C4⋊C4C22×C11⋊C514yescomplemented
113C22⋊C4C22×C11⋊C514yes—
114C22⋊C4C22×C11⋊C518yescomplemented
115C42C22×C11⋊C514yescomplemented
116C11C5×#51811yescharacteristic, complemented, Sylow
117C2×C5—111no—
118C2×C5—112no—
119C2×C5—222no—
120C2×C5—228no—
121C23—44no—
122C23C2×C4×C11⋊C518yescomplemented
123C23C23×C11⋊C511yescharacteristic
124C23C23×C11⋊C514yes—
125D4C2×C4×C11⋊C5116yescomplemented
126C2×C4—48no—
127C2×C4C2×C4×C11⋊C514yescomplemented
128C2×C4C23×C11⋊C518yes—
129C2×C4C23×C11⋊C512yes—
130C5—111noSylow
131C22—28no—
132C22—22no—
133C22—48no—
134C22C22×C4×C11⋊C512yes—
135C22C22×C4×C11⋊C518yes—
136C22C24×C11⋊C511yescharacteristic
137C4—28no—
138C4C22×C4×C11⋊C514yes—
139C2—22no—
140C2—28no—
141C2C23×C4×C11⋊C511yescharacteristic
142C2H(5,𝔽2)×C11⋊C512yes—
subgroupG/H
center, FrattiniC22C24×C11⋊C5
commutatorC2×C11C23×C4×C5
FittingC11×#518C5
socle, cosocleC22×C11C24×C5
prime radicalC22×D4×C11⋊C5C2
hypercenter#518C11⋊C5
hypocenterC11C5×#518
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C4×D4×C11⋊C5C2semidirect
3. #117×C11⋊C5C2semidirect
4. C2×C22⋊C4×C11⋊C5C2semidirect
6. C2×D4×C11⋊C5C4semidirect
9. C22×C4×C11⋊C5C22semidirect
10. C4⋊C4×C11⋊C5C22semidirect
12. C22⋊C4×C11⋊C5C22semidirect
13. C42×C11⋊C5C22semidirect
14. C11×#518C5semidirect
16. C23×C11⋊C5C2×C4semidirect
19. D4×C11⋊C5C2×C4semidirect
21. C2×C4×C11⋊C5C2×C4semidirect
25. C4×D4×C11C2×C5semidirect
26. C11×#117C2×C5semidirect
27. C2×C11×C22⋊C4C2×C5semidirect
38. C2×D4×C11C4×C5semidirect
41. C22×C4×C11C22×C5semidirect
42. C11×C4⋊C4C22×C5semidirect
44. C11×C22⋊C4C22×C5semidirect
45. C42×C11C22×C5semidirect
55. C23×C11C2×C4×C5semidirect
58. D4×C11C2×C4×C5semidirect
60. C2×C4×C11C2×C4×C5semidirect
72. #518C11⋊C5direct (N × H)
73. C11⋊C5#518direct (N × H)
92. C4×D4C2×C11⋊C5semidirect
93. #117C2×C11⋊C5semidirect
94. C2×C22⋊C4C2×C11⋊C5semidirect
108. C2×D4C4×C11⋊C5semidirect
111. C22×C4C22×C11⋊C5semidirect
112. C4⋊C4C22×C11⋊C5semidirect
114. C22⋊C4C22×C11⋊C5semidirect
115. C42C22×C11⋊C5semidirect
116. C11C5×#518semidirect
122. C23C2×C4×C11⋊C5semidirect
125. D4C2×C4×C11⋊C5semidirect
127. C2×C4C2×C4×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C11⋊C52
C4×D4×C11⋊C52
#117×C11⋊C52
C2×C22⋊C4×C11⋊C52
C11×#5185
C5×#51811