Finite Group Databasebeta

← C4×C22⋊D55 #13183227

Subgroups — C4×C22⋊D55 #13183227

Order 1760.

188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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×C22⋊D55C211yesmaximal, characteristic
3C2×C4×D55C211yesmaximal, characteristic, complemented
4C22⋊Dic55C211yesmaximal, characteristic, complemented
5#11724932C211yesmaximal, characteristic, complemented
6#11724930C211yesmaximal, characteristic, complemented
7C4×Dic55C211yesmaximal, characteristic, complemented
8C23×C5×C11C2211yescharacteristic
9C22×D55C2211yescharacteristic
10C2×C4×C5×C11—22no—
11C2×C4×C5×C11C2211yescharacteristic
12C2×C4×C5×C11C2211yescharacteristic
13C22⋊D55C414yesdirect product factor
14C2×Dic55C2211yescharacteristic
15C2×Dic55C2211yescharacteristic
16C2×Dic55C2211yescharacteristic
17C4×D55—22no—
18C4×C22⋊D11—51nomaximal, Hall
19C22×C5×C11—21no—
20C22×C5×C11—21no—
21C22×C5×C11C2×C412yescomplemented
22C22×C5×C11C2311yescharacteristic
23C2×D55—21no—
24C2×D55—21no—
25C2×D55C2×C412yescomplemented
26C4×C5×C11—21no—
27C4×C5×C11D412yescomplemented
28Dic55—21no—
29Dic55—21no—
30Dic55C2×C412yescomplemented
31C22×C4×C11D511yescharacteristic, complemented
32C2×C22⋊D11—51no—
33C2×C4×D11—51no—
34C22⋊Dic11—51no—
35(C2×D11)⋊C4—51no—
36Dic11⋊C4—51no—
37C4×Dic11—51no—
38C4×C22⋊D5—111nomaximal, Hall
39C2×C5×C11—22no—
40C2×C5×C11C22×C411yescharacteristic
41C2×C5×C11C2×D411yescharacteristic
42C2×C5×C11#4111yescharacteristic
43D55—22no—
44C23×C11C2×D511yescharacteristic
45C22×D11—51no—
46C2×C4×C11—22no—
47C2×C4×C11C2×D511yescharacteristic
48C2×C4×C11C2×D511yescharacteristic
49C22⋊D11—54no—
50C2×Dic11—51no—
51C2×Dic11—51no—
52C2×Dic11—51no—
53C4×D11—102no—
54C22×C4×C5D1111yescharacteristic, complemented
55C2×C22⋊D5—111no—
56C2×C4×D5—111no—
57C22⋊Dic5—111no—
58#685—111no—
59#683—111no—
60C4×Dic5—111no—
61C5×C11C4×D411yescharacteristic, complemented, Hall
62C22×C11—21no—
63C22×C11—21no—
64C22×C11C4×D512yescomplemented
65C22×C11C22×D511yescharacteristic
66C2×D11—52no—
67C2×D11—101no—
68C2×D11—101no—
69C4×C11—21no—
70C4×C11C22⋊D512yescomplemented
71Dic11—52no—
72Dic11—101no—
73Dic11—101no—
74C23×C5C2×D1111yescharacteristic
75C22×D5—111no—
76C2×C4×C5—22no—
77C2×C4×C5C2×D1111yescharacteristic
78C2×C4×C5C2×D1111yescharacteristic
79C22⋊D5—114no—
80C2×Dic5—111no—
81C2×Dic5—111no—
82C2×Dic5—111no—
83C4×D5—222no—
84C4×D4—551noSylow
85C2×C11—22no—
86C2×C11C2×C4×D511yescharacteristic
87C2×C11#70911yescharacteristic
88C2×C11C2×C22⋊D511yescharacteristic
89D11—102no—
90C22×C5—21no—
91C22×C5—21no—
92C22×C5C4×D1112yescomplemented
93C22×C5C22×D1111yescharacteristic
94C2×D5—112no—
95C2×D5—221no—
96C2×D5—221no—
97C4×C5—21no—
98C4×C5C22⋊D1112yescomplemented
99Dic5—112no—
100Dic5—221no—
101Dic5—221no—
102C2×D4—551no—
103C22×C4—551no—
104C22×C4D5511yescharacteristic, complemented
105C4⋊C4—551no—
106C22⋊C4—551no—
107C22⋊C4—551no—
108C42—551no—
109C11C4×C22⋊D511yescharacteristic, complemented, Sylow
110C2×C5—22no—
111C2×C5C2×C4×D1111yescharacteristic
112C2×C5#433911yescharacteristic
113C2×C5C2×C22⋊D1111yescharacteristic
114D5—222no—
115C23—551no—
116C23C2×D5511yescharacteristic
117D4—554no—
118C2×C4—22no—
119C2×C4—551no—
120C2×C4—551no—
121C2×C4—551no—
122C2×C4—1102no—
123C2×C4C2×D5511yescharacteristic
124C2×C4C2×D5511yescharacteristic
125C5C4×C22⋊D1111yescharacteristic, complemented, Sylow
126C22—21no—
127C22—21no—
128C22—552no—
129C22—1101no—
130C22—1101no—
131C22C4×D5512yescomplemented
132C22C22×D5511yescharacteristic
133C4—21no—
134C4—552no—
135C4—1101no—
136C4—1101no—
137C4C22⋊D5512yesdirect product factor
138C2—22no—
139C2—1102no—
140C2C2×C4×D5511yescharacteristic
141C2#1172503111yescharacteristic
142C2C2×C22⋊D5511yescharacteristic
subgroupG/H
centerC2×C4C2×D55
commutatorC2×C5×C11C22×C4
FrattiniC22C22×D55
FittingC22×C4×C5×C11C2
socle, cosocleC22×C5×C11C23
prime radicalC2×C22⋊D55C2
hypercenterC22×C4D55
hypocenterC5×C11C4×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×C11C2semidirect
3. C2×C4×D55C2semidirect
4. C22⋊Dic55C2semidirect
5. #11724932C2semidirect
6. #11724930C2semidirect
7. C4×Dic55C2semidirect
13. C22⋊D55C4direct (N × H)
21. C22×C5×C11C2×C4semidirect
25. C2×D55C2×C4semidirect
27. C4×C5×C11D4semidirect
30. Dic55C2×C4semidirect
31. C22×C4×C11D5semidirect
54. C22×C4×C5D11semidirect
61. C5×C11C4×D4semidirect
64. C22×C11C4×D5semidirect
70. C4×C11C22⋊D5semidirect
92. C22×C5C4×D11semidirect
98. C4×C5C22⋊D11semidirect
104. C22×C4D55semidirect
109. C11C4×C22⋊D5semidirect
125. C5C4×C22⋊D11semidirect
131. C22C4×D55semidirect
137. C4C22⋊D55direct (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×C22⋊D552
C2×C4×D552
C22⋊Dic552
#117249322
#117249302
C4×Dic552
C4×C22⋊D115
C4×C22⋊D511