Finite Group Databasebeta

← C4×C11×C22⋊D5 #13183141

Subgroups — C4×C11×C22⋊D5 #13183141

Order 1760.

188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 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×C4×C5×C11C211yesmaximal, characteristic, complemented
2C2×C11×C22⋊D5C211yesmaximal, characteristic
3C2×C4×D5×C11C211yesmaximal, characteristic, complemented
4C11×C22⋊Dic5C211yesmaximal, characteristic, complemented
5C11×#685C211yesmaximal, characteristic, complemented
6C11×#683C211yesmaximal, characteristic, complemented
7C4×C11×Dic5C211yesmaximal, characteristic, complemented
8C23×C5×C11C2211yescharacteristic
9C22×D5×C11C2211yescharacteristic
10C2×C4×C5×C11—22no—
11C2×C4×C5×C11C2211yescharacteristic
12C2×C4×C5×C11C2211yescharacteristic
13C11×C22⋊D5C414yesdirect product factor
14C2×C11×Dic5C2211yescharacteristic
15C2×C11×Dic5C2211yescharacteristic
16C2×C11×Dic5C2211yescharacteristic
17C4×D5×C11—22no—
18C4×D4×C11—51nomaximal, Hall
19C22×C5×C11—21no—
20C22×C5×C11—21no—
21C22×C5×C11C2×C412yescomplemented
22C22×C5×C11C2311yescharacteristic
23C2×D5×C11—21no—
24C2×D5×C11—21no—
25C2×D5×C11C2×C412yescomplemented
26C4×C5×C11—21no—
27C4×C5×C11D412yescomplemented
28C11×Dic5—21no—
29C11×Dic5—21no—
30C11×Dic5C2×C412yescomplemented
31C2×D4×C11—51no—
32C22×C4×C11—51no—
33C22×C4×C11D511yescharacteristic, complemented
34C11×C4⋊C4—51no—
35C11×C22⋊C4—51no—
36C11×C22⋊C4—51no—
37C42×C11—51no—
38C4×C22⋊D5C1111yesmaximal, characteristic, direct product factor, Hall
39C2×C5×C11—22no—
40C2×C5×C11C22×C411yescharacteristic
41C2×C5×C11C2×D411yescharacteristic
42C2×C5×C11#4111yescharacteristic
43D5×C11—22no—
44C23×C11—51no—
45C23×C11C2×D511yescharacteristic
46D4×C11—54no—
47C2×C4×C11—22no—
48C2×C4×C11—51no—
49C2×C4×C11—51no—
50C2×C4×C11—51no—
51C2×C4×C11—102no—
52C2×C4×C11C2×D511yescharacteristic
53C2×C4×C11C2×D511yescharacteristic
54C22×C4×C5C2×C1111yescharacteristic, complemented
55C2×C22⋊D5C2×C1111yescharacteristic
56C2×C4×D5C2×C1111yescharacteristic, complemented
57C22⋊Dic5C2×C1111yescharacteristic, complemented
58#685C2×C1111yescharacteristic, complemented
59#683C2×C1111yescharacteristic, complemented
60C4×Dic5C2×C1111yescharacteristic, complemented
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11—21no—
63C22×C11—21no—
64C22×C11—52no—
65C22×C11—101no—
66C22×C11—101no—
67C22×C11C4×D512yescomplemented
68C22×C11C22×D511yescharacteristic
69C4×C11—21no—
70C4×C11—52no—
71C4×C11—101no—
72C4×C11—101no—
73C4×C11C22⋊D512yesdirect product factor
74C23×C5C22×C1111yescharacteristic
75C22×D5C22×C1111yescharacteristic
76C2×C4×C5—22no—
77C2×C4×C5C22×C1111yescharacteristic
78C2×C4×C5C22×C1111yescharacteristic
79C22⋊D5C4×C1114yesdirect product factor
80C2×Dic5C22×C1111yescharacteristic
81C2×Dic5C22×C1111yescharacteristic
82C2×Dic5C22×C1111yescharacteristic
83C4×D5—22no—
84C4×D4—51noSylow
85C2×C11—22no—
86C2×C11—102no—
87C2×C11C2×C4×D511yescharacteristic
88C2×C11#70911yescharacteristic
89C2×C11C2×C22⋊D511yescharacteristic
90C22×C5—21no—
91C22×C5—21no—
92C22×C5C2×C4×C1112yescomplemented
93C22×C5C23×C1111yescharacteristic
94C2×D5—21no—
95C2×D5—21no—
96C2×D5C2×C4×C1112yescomplemented
97C4×C5—21no—
98C4×C5D4×C1112yescomplemented
99Dic5—21no—
100Dic5—21no—
101Dic5C2×C4×C1112yescomplemented
102C2×D4—51no—
103C22×C4—51no—
104C22×C4D5×C1111yescharacteristic, complemented
105C4⋊C4—51no—
106C22⋊C4—51no—
107C22⋊C4—51no—
108C42—51no—
109C11C4×C22⋊D511yescharacteristic, direct product factor, Sylow
110C2×C5—22no—
111C2×C5C22×C4×C1111yescharacteristic
112C2×C5C2×D4×C1111yescharacteristic
113C2×C5C11×#4111yescharacteristic
114D5—22no—
115C23—51no—
116C23C2×D5×C1111yescharacteristic
117D4—54no—
118C2×C4—22no—
119C2×C4—51no—
120C2×C4—51no—
121C2×C4—51no—
122C2×C4—102no—
123C2×C4C2×D5×C1111yescharacteristic
124C2×C4C2×D5×C1111yescharacteristic
125C5C4×D4×C1111yescharacteristic, complemented, Sylow
126C22—21no—
127C22—21no—
128C22—52no—
129C22—101no—
130C22—101no—
131C22C4×D5×C1112yescomplemented
132C22C22×D5×C1111yescharacteristic
133C4—21no—
134C4—52no—
135C4—101no—
136C4—101no—
137C4C11×C22⋊D512yesdirect product factor
138C2—22no—
139C2—102no—
140C2C2×C4×D5×C1111yescharacteristic
141C2C11×#70911yescharacteristic
142C2C2×C11×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D5
commutatorC2×C5C22×C4×C11
FrattiniC22C22×D5×C11
FittingC22×C4×C5×C11C2
socleC22×C5×C11C23
prime radicalC2×C11×C22⋊D5C2
cosocleC22×C5C23×C11
hypercenterC22×C4×C11D5
hypocenterC5C4×D4×C11
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4×C11 ◁ C22×C4×C11

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×C11C2semidirect
3. C2×C4×D5×C11C2semidirect
4. C11×C22⋊Dic5C2semidirect
5. C11×#685C2semidirect
6. C11×#683C2semidirect
7. C4×C11×Dic5C2semidirect
13. C11×C22⋊D5C4direct (N × H)
21. C22×C5×C11C2×C4semidirect
25. C2×D5×C11C2×C4semidirect
27. C4×C5×C11D4semidirect
30. C11×Dic5C2×C4semidirect
33. C22×C4×C11D5semidirect
38. C4×C22⋊D5C11direct (N × H)
54. C22×C4×C5C2×C11semidirect
56. C2×C4×D5C2×C11semidirect
57. C22⋊Dic5C2×C11semidirect
58. #685C2×C11semidirect
59. #683C2×C11semidirect
60. C4×Dic5C2×C11semidirect
61. C5×C11C4×D4semidirect
67. C22×C11C4×D5semidirect
73. C4×C11C22⋊D5direct (N × H)
79. C22⋊D5C4×C11direct (N × H)
92. C22×C5C2×C4×C11semidirect
96. C2×D5C2×C4×C11semidirect
98. C4×C5D4×C11semidirect
101. Dic5C2×C4×C11semidirect
104. C22×C4D5×C11semidirect
109. C11C4×C22⋊D5direct (N × H)
125. C5C4×D4×C11semidirect
131. C22C4×D5×C11semidirect
137. C4C11×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×C112
C2×C11×C22⋊D52
C2×C4×D5×C112
C11×C22⋊Dic52
C11×#6852
C11×#6832
C4×C11×Dic52
C4×D4×C115
C4×C22⋊D511