Finite Group Databasebeta

← C5×(C22⋊D11)⋊C4 #13183009

Subgroups — C5×(C22⋊D11)⋊C4 #13183009

Order 1760.

188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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×C5×C22⋊D11C211yesmaximal, characteristic
2C22×C5×Dic11C211yesmaximal, characteristic, complemented
3C2×C4×C5×D11C211yesmaximal, characteristic, complemented
4C5×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C5×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6C5×Dic11⋊C4C211yesmaximal, characteristic, complemented
7C4×C5×Dic11C211yesmaximal, characteristic, complemented
8C23×C5×C11C2211yescharacteristic
9C22×C5×D11C2211yescharacteristic
10C2×C4×C5×C11C2211yescharacteristic
11C2×C4×C5×C11C2211yescharacteristic
12C5×C22⋊D11C414yescomplemented
13C2×C5×Dic11—22no—
14C2×C5×Dic11C2211yescharacteristic
15C2×C5×Dic11C2211yescharacteristic
16C2×C5×Dic11C2211yescharacteristic
17C4×C5×D11—22no—
18(C22⋊D11)⋊C4C511yesmaximal, characteristic, direct product factor, Hall
19C22×C5×C11—21no—
20C22×C5×C11—21no—
21C22×C5×C11C2×C412yescomplemented
22C22×C5×C11C2311yescharacteristic
23C2×C5×D11—21no—
24C2×C5×D11—21no—
25C2×C5×D11C2×C412yescomplemented
26C4×C5×C11—21no—
27C4×C5×C11—21no—
28C5×Dic11—21no—
29C5×Dic11C2×C412yescomplemented
30C5×Dic11D412yescomplemented
31C2×C22⋊D11C2×C511yescharacteristic
32C22×Dic11C2×C511yescharacteristic, complemented
33C2×C4×D11C2×C511yescharacteristic, complemented
34C11×C22⋊C4C2×C511yescharacteristic, complemented
35(C2×D11)⋊C4C2×C511yescharacteristic, complemented
36Dic11⋊C4C2×C511yescharacteristic, complemented
37C4×Dic11C2×C511yescharacteristic, complemented
38C4×C5×D4—111nomaximal, Hall
39C2×C5×C11—22no—
40C2×C5×C11C22×C411yescharacteristic
41C2×C5×C11C2×D411yescharacteristic
42C2×C5×C11#4111yescharacteristic
43C5×D11—22no—
44C23×C11C22×C511yescharacteristic
45C22×D11C22×C511yescharacteristic
46C2×C4×C11C22×C511yescharacteristic
47C2×C4×C11C22×C511yescharacteristic
48C22⋊D11C4×C514yescomplemented
49C2×Dic11—22no—
50C2×Dic11C22×C511yescharacteristic
51C2×Dic11C22×C511yescharacteristic
52C2×Dic11C22×C511yescharacteristic
53C4×D11—22no—
54C2×C5×D4—111no—
55C22×C4×C5—111no—
56C22×C4×C5—111no—
57C5×C4⋊C4—111no—
58C5×C22⋊C4—111no—
59C5×C22⋊C4D1111yescharacteristic, complemented
60C42×C5—111no—
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11—21no—
63C22×C11—21no—
64C22×C11C2×C4×C512yescomplemented
65C22×C11C23×C511yescharacteristic
66C2×D11—21no—
67C2×D11—21no—
68C2×D11C2×C4×C512yescomplemented
69C4×C11—21no—
70C4×C11—21no—
71Dic11—21no—
72Dic11C2×C4×C512yescomplemented
73Dic11C5×D412yescomplemented
74C23×C5—111no—
75C23×C5C2×D1111yescharacteristic
76C5×D4—114no—
77C2×C4×C5—111no—
78C2×C4×C5—111no—
79C2×C4×C5—111no—
80C2×C4×C5—222no—
81C2×C4×C5—222no—
82C2×C4×C5C2×D1111yescharacteristic
83C2×C4×C5C2×D1111yescharacteristic
84C4×D4—111noSylow
85C2×C11—22no—
86C2×C11C22×C4×C511yescharacteristic
87C2×C11C2×C5×D411yescharacteristic
88C2×C11C5×#4111yescharacteristic
89D11—22no—
90C22×C5—21no—
91C22×C5—21no—
92C22×C5—112no—
93C22×C5—221no—
94C22×C5—221no—
95C22×C5C4×D1112yescomplemented
96C22×C5C22×D1111yescharacteristic
97C4×C5—21no—
98C4×C5—21no—
99C4×C5—112no—
100C4×C5—112no—
101C4×C5—221no—
102C2×D4—111no—
103C22×C4—111no—
104C22×C4—111no—
105C4⋊C4—111no—
106C22⋊C4—111no—
107C22⋊C4C5×D1111yescharacteristic, complemented
108C42—111no—
109C11C4×C5×D411yescharacteristic, complemented, Sylow
110C2×C5—22no—
111C2×C5—222no—
112C2×C5C2×C4×D1111yescharacteristic
113C2×C5D4×D1111yescharacteristic
114C2×C5#434111yescharacteristic
115C23—111no—
116C23C2×C5×D1111yescharacteristic
117D4—114no—
118C2×C4—111no—
119C2×C4—111no—
120C2×C4—111no—
121C2×C4—222no—
122C2×C4—222no—
123C2×C4C2×C5×D1111yescharacteristic
124C2×C4C2×C5×D1111yescharacteristic
125C5(C22⋊D11)⋊C411yescharacteristic, direct product factor, Sylow
126C22—21no—
127C22—21no—
128C22—112no—
129C22—221no—
130C22—221no—
131C22C4×C5×D1112yescomplemented
132C22C22×C5×D1111yescharacteristic
133C4—21no—
134C4—21no—
135C4—112no—
136C4—112no—
137C4—221no—
138C2—22no—
139C2—222no—
140C2C2×C4×C5×D1111yescharacteristic
141C2C5×D4×D1111yescharacteristic
142C2C5×#434111yescharacteristic
subgroupG/H
centerC22×C5C22×D11
commutatorC2×C11C22×C4×C5
FrattiniC22C22×C5×D11
FittingC5×C11×C22⋊C4C2
socleC22×C5×C11C23
prime radicalC2×C5×C22⋊D11C2
cosocleC22×C11C23×C5
hypercenterC5×C22⋊C4D11
hypocenterC11C4×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C5 ◁ C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C5×Dic11C2semidirect
3. C2×C4×C5×D11C2semidirect
4. C5×C11×C22⋊C4C2semidirect
5. C5×(C2×D11)⋊C4C2semidirect
6. C5×Dic11⋊C4C2semidirect
7. C4×C5×Dic11C2semidirect
12. C5×C22⋊D11C4semidirect
18. (C22⋊D11)⋊C4C5direct (N × H)
21. C22×C5×C11C2×C4semidirect
25. C2×C5×D11C2×C4semidirect
29. C5×Dic11C2×C4semidirect
30. C5×Dic11D4semidirect
32. C22×Dic11C2×C5semidirect
33. C2×C4×D11C2×C5semidirect
34. C11×C22⋊C4C2×C5semidirect
35. (C2×D11)⋊C4C2×C5semidirect
36. Dic11⋊C4C2×C5semidirect
37. C4×Dic11C2×C5semidirect
48. C22⋊D11C4×C5semidirect
59. C5×C22⋊C4D11semidirect
61. C5×C11C4×D4semidirect
64. C22×C11C2×C4×C5semidirect
68. C2×D11C2×C4×C5semidirect
72. Dic11C2×C4×C5semidirect
73. Dic11C5×D4semidirect
95. C22×C5C4×D11semidirect
107. C22⋊C4C5×D11semidirect
109. C11C4×C5×D4semidirect
125. C5(C22⋊D11)⋊C4direct (N × H)
131. C22C4×C5×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C22⋊D112
C22×C5×Dic112
C2×C4×C5×D112
C5×C11×C22⋊C42
C5×(C2×D11)⋊C42
C5×Dic11⋊C42
C4×C5×Dic112
(C22⋊D11)⋊C45
C4×C5×D411