Finite Group Databasebeta

← #13182893

Subgroups — #13182893

Order 1760.

260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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×D5×D11C211yesmaximal, characteristic, complemented
2C2×D220C211yesmaximal, characteristic, complemented
3C2×#89169C211yesmaximal, characteristic, complemented
4C2×#89168C211yesmaximal, characteristic, complemented
5C11×#685C211yesmaximal, characteristic, complemented
6C5×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#11724886C211yesmaximal, characteristic, complemented
8C22×D55C2211yescharacteristic
9C22×D55C2211yescharacteristic, complemented
10C22×D5×C11C2211yescharacteristic
11C22×C5×D11C2211yescharacteristic
12C2×D5×D11—22no—
13C2×D5×D11—22no—
14C2×D5×D11—22no—
15C2×C4×C5×C11C2211yescharacteristic, complemented
16D220—22no—
17C2×C11×Dic5C2211yescharacteristic, complemented
18C2×C5×Dic11C2211yescharacteristic, complemented
19#89169—22no—
20#89168—22no—
21#66935—51nomaximal, Hall
22C22×C5×C11C2311yescharacteristic
23C2×D55—21no—
24C2×D55—21no—
25C2×D55—21no—
26C2×D55—21no—
27C2×D55—21no—
28C2×D55D412yescomplemented
29C2×D5×C11—21no—
30C2×D5×C11—21no—
31C2×D5×C11D412yescomplemented
32C2×C5×D11—21no—
33C2×C5×D11—21no—
34C2×C5×D11D412yescomplemented
35D5×D11—28no—
36C4×C5×C11—21no—
37C5×Dic11—21no—
38C11×Dic5—21no—
39C23×D11—51no—
40C2×C22⋊D11—51no—
41C2×D44—51no—
42C2×D44—51no—
43C11×C22⋊C4—51no—
44(C2×D11)⋊C4—51no—
45(C2×D11)⋊C4D511yescharacteristic, complemented
46#4028—111nomaximal, Hall
47C2×C5×C11C2×D411yescharacteristic
48C2×C5×C11C2×D411yescharacteristic
49C2×C5×C11C2×D411yescharacteristic
50D55—22no—
51D55—41no—
52C5×D11—22no—
53D5×C11—22no—
54C23×C11—51no—
55C22×D11—51no—
56C22×D11—51no—
57C22×D11—102no—
58C22×D11—102no—
59C22×D11—102no—
60C22×D11C2×D511yescharacteristic
61C2×C4×C11—51no—
62C2×C4×C11C2×D511yescharacteristic, complemented
63C22⋊D11—102no—
64C2×Dic11C2×D511yescharacteristic, complemented
65D44—102no—
66D44—102no—
67C23×D5—111no—
68C2×C22⋊D5—111no—
69C2×D20—111no—
70C2×D20—111no—
71C5×C22⋊C4—111no—
72#685—111no—
73#685D1111yescharacteristic, complemented
74C5×C11#12011yescharacteristic, complemented, Hall
75C22×C11—52no—
76C22×C11—101no—
77C22×C11—101no—
78C22×C11C22×D511yescharacteristic
79C2×D11—21no—
80C2×D11—21no—
81C2×D11—52no—
82C2×D11—108no—
83C2×D11—101no—
84C2×D11—101no—
85C2×D11—101no—
86C2×D11—101no—
87C2×D11—101no—
88C2×D11D2012yescomplemented
89C4×C11—21no—
90C4×C11—101no—
91Dic11—21no—
92C23×C5—111no—
93C22×D5—111no—
94C22×D5—111no—
95C22×D5—222no—
96C22×D5—222no—
97C22×D5—222no—
98C22×D5C2×D1111yescharacteristic
99C2×C4×C5—111no—
100C2×C4×C5C2×D1111yescharacteristic, complemented
101C22⋊D5—222no—
102C2×Dic5C2×D1111yescharacteristic, complemented
103D20—222no—
104D20—222no—
105#120—551noSylow
106C2×C11—102no—
107C2×C11C2×D2011yescharacteristic
108C2×C11D4×D511yescharacteristic
109C2×C11D4×D511yescharacteristic
110D11—22no—
111D11—102no—
112D11—201no—
113C22×C5—112no—
114C22×C5—221no—
115C22×C5—221no—
116C22×C5C22×D1111yescharacteristic
117C2×D5—21no—
118C2×D5—21no—
119C2×D5—112no—
120C2×D5—228no—
121C2×D5—221no—
122C2×D5—221no—
123C2×D5—221no—
124C2×D5—221no—
125C2×D5—221no—
126C2×D5D4412yescomplemented
127C4×C5—21no—
128C4×C5—221no—
129Dic5—21no—
130C24—551no—
131C2×D4—551no—
132C2×D4—551no—
133C2×D4—551no—
134C22⋊C4—51no—
135C22⋊C4—111no—
136C22⋊C4—551no—
137C11#402811yescharacteristic, complemented, Sylow
138C2×C5—222no—
139C2×C5C2×D4411yescharacteristic
140C2×C5D4×D1111yescharacteristic
141C2×C5D4×D1111yescharacteristic
142D5—22no—
143D5—222no—
144D5—441no—
145C23—51no—
146C23—111no—
147C23—551no—
148C23—551no—
149C23—1102no—
150C23—1102no—
151C23—1102no—
152D4—1102no—
153D4—1102no—
154D4—1102no—
155C2×C4—51no—
156C2×C4—111no—
157C2×C4D5×D1111yescharacteristic, complemented
158C5#6693511yescharacteristic, complemented, Sylow
159C22—52no—
160C22—101no—
161C22—101no—
162C22—112no—
163C22—221no—
164C22—221no—
165C22—552no—
166C22—1108no—
167C22—1101no—
168C22—1101no—
169C22—1101no—
170C22—1101no—
171C22—1101no—
172C22C2×D5×D1111yescharacteristic
173C4—21no—
174C4—101no—
175C4—221no—
176C2—102no—
177C2—222no—
178C2—1102no—
179C2—2201no—
180C2D11×D2011yescharacteristic
181C2D5×D4411yescharacteristic
182C2#1172500711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×D11
commutator, socle, cosocleC22×C5×C11C23
FittingC2×C4×C5×C11C22
hypercenterC2×C4D5×D11
hypocenterC5×C11#120
LCSG ▷ C22×C5×C11 ▷ C5×C11
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×D11C2semidirect
2. C2×D220C2semidirect
3. C2×#89169C2semidirect
4. C2×#89168C2semidirect
5. C11×#685C2semidirect
6. C5×(C2×D11)⋊C4C2semidirect
7. #11724886C2semidirect
9. C22×D55C22semidirect
15. C2×C4×C5×C11C22semidirect
17. C2×C11×Dic5C22semidirect
18. C2×C5×Dic11C22semidirect
28. C2×D55D4semidirect
31. C2×D5×C11D4semidirect
34. C2×C5×D11D4semidirect
45. (C2×D11)⋊C4D5semidirect
62. C2×C4×C11C2×D5semidirect
64. C2×Dic11C2×D5semidirect
73. #685D11semidirect
74. C5×C11#120semidirect
88. C2×D11D20semidirect
100. C2×C4×C5C2×D11semidirect
102. C2×Dic5C2×D11semidirect
126. C2×D5D44semidirect
137. C11#4028semidirect
157. C2×C4D5×D11semidirect
158. C5#66935semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D112
C2×D2202
C2×#891692
C2×#891682
C11×#6852
C5×(C2×D11)⋊C42
#117248862
#669355
#402811