Finite Group Databasebeta

← #11751319

Subgroups — #11751319

Order 960.

376 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 91 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×C3×C5×D4C211yesmaximal, characteristic
2C2×#6716C212yesmaximal, complemented
3#91813C211yesmaximal, characteristic, complemented
4#91116C212yesmaximal, complemented
5#91114C211yesmaximal, characteristic, complemented
6#65507—31nomaximal, Hall
7C24×C3×C5—21no—
8C2×C3×C5×D4—24no—
9C2×C3×C5×D4—21no—
10C2×C3×C5×D4C2212yes—
11C22×C3×C4×C5C2211yescharacteristic
12C2×Dic30C2211yescharacteristic, complemented
13#6719—21no—
14#6716—24no—
15C4⋊Dic15C2211yescharacteristic, complemented
16#6712—21no—
17C2×C3⋊#168C2212yescomplemented
18#5218—51nomaximal, Hall
19C22×C5×D4D311yescharacteristic
20C2×#687—32no—
21#4070—31no—
22#3964—32no—
23C22⋊#168—31no—
24C23×C3×C5—24no—
25C23×C3×C5—22no—
26C23×C3×C5—42no—
27C23×C3×C5—42no—
28C23×C3×C5D411yescharacteristic
29C3×C5×D4—24no—
30C3×C5×D4—22no—
31C3×C5×D4D414yes—
32C2×C3×C4×C5—22no—
33C2×C3×C4×C5D411yescharacteristic
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36C2×Dic15—21no—
37Dic30—22no—
38C3⋊#168—22no—
39C22×C3×D4D511yescharacteristic
40C2×#214—52no—
41#924—51no—
42#832—52no—
43#830—51no—
44C24×C5—21no—
45C2×C5×D4—24no—
46C2×C5×D4—21no—
47C2×C5×D4C2×D312yes—
48C22×C4×C5C2×D311yescharacteristic
49C2×Dic10—31no—
50C22⋊Dic5—61no—
51#687—64no—
52C4⋊Dic5—31no—
53#683—61no—
54C2×#168—32no—
55#450—151noSylow
56C22×C3×C5—21no—
57C22×C3×C5—21no—
58C22×C3×C5—24no—
59C22×C3×C5—48no—
60C22×C3×C5—42no—
61C22×C3×C5—42no—
62C22×C3×C5SD1612yescomplemented
63C22×C3×C5C2×D411yescharacteristic
64C3×C4×C5—21no—
65C3×C4×C5C2×D412yes—
66Dic15—41no—
67Dic15—41no—
68C24×C3—21no—
69C2×C3×D4—24no—
70C2×C3×D4—21no—
71C2×C3×D4C2×D512yes—
72C22×C3×C4C2×D511yescharacteristic
73C2×Dic6—51no—
74#217—101no—
75#214—104no—
76C4⋊Dic3—51no—
77Dic3⋊C4—101no—
78C2×C3⋊C8—52no—
79C23×C5—24no—
80C23×C5—22no—
81C23×C5—42no—
82C23×C5—42no—
83C23×C5#6711yescharacteristic
84C5×D4—24no—
85C5×D4—22no—
86C5×D4#6714yes—
87C2×C4×C5—22no—
88C2×C4×C5#6711yescharacteristic
89C2×C4×C5C22×D311yescharacteristic
90C2×Dic5—61no—
91C2×Dic5—61no—
92Dic10—62no—
93#168—62no—
94C22×D4D1511yescharacteristic
95C2×SD16—152no—
96C22⋊Q8—151no—
97#102—152no—
98C22⋊C8—151no—
99C2×C3×C5—22no—
100C2×C3×C5—44no—
101C2×C3×C5#12011yescharacteristic
102C2×C3×C5C2×SD1611yescharacteristic
103C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
104C23×C3—24no—
105C23×C3—22no—
106C23×C3—42no—
107C23×C3—42no—
108C23×C3C22⋊D511yescharacteristic
109C3×D4—24no—
110C3×D4—22no—
111C3×D4C22⋊D514yes—
112C2×C3×C4—22no—
113C2×C3×C4C22⋊D511yescharacteristic
114C2×C3×C4C22×D511yescharacteristic
115C2×Dic3—101no—
116C2×Dic3—101no—
117Dic6—102no—
118C3⋊C8—102no—
119C22×C5—21no—
120C22×C5—21no—
121C22×C5—24no—
122C22×C5—48no—
123C22×C5—42no—
124C22×C5—42no—
125C22×C5#21412yescomplemented
126C22×C5C2×#6711yescharacteristic
127C4×C5—21no—
128C4×C5C2×#6712yes—
129Dic5—121no—
130Dic5—121no—
131C24—21no—
132C2×Q8—151no—
133C2×D4—24no—
134C2×D4—21no—
135C2×D4C2×D1512yes—
136C22×C4C2×D1511yescharacteristic
137SD16—304no—
138C2×C8—152no—
139C4⋊C4—151no—
140C4⋊C4—301no—
141C22⋊C4—301no—
142C3×C5#45011yescharacteristic, complemented, Hall
143C22×C3—21no—
144C22×C3—21no—
145C22×C3—24no—
146C22×C3—48no—
147C22×C3—42no—
148C22×C3—42no—
149C22×C3#68712yescomplemented
150C22×C3C2×C22⋊D511yescharacteristic
151C3×C4—21no—
152C3×C4C2×C22⋊D512yes—
153Dic3—201no—
154Dic3—201no—
155C2×C5—22no—
156C2×C5—44no—
157C2×C5#93211yescharacteristic
158C2×C5C2×#21411yescharacteristic
159C2×C5#95311yescharacteristic
160C23—24no—
161C23—22no—
162C23—42no—
163C23—42no—
164C23#122011yescharacteristic
165Q8—302no—
166D4—24no—
167D4—22no—
168D4#122014yes—
169C2×C4—22no—
170C2×C4—301no—
171C2×C4—301no—
172C2×C4#122011yescharacteristic
173C2×C4C22×D1511yescharacteristic
174C8—302no—
175C2×C3—22no—
176C2×C3—44no—
177C2×C3#407811yescharacteristic
178C2×C3C2×#68711yescharacteristic
179C2×C3#409911yescharacteristic
180C5#521811yescharacteristic, complemented, Sylow
181C22—21no—
182C22—21no—
183C22—24no—
184C22—48no—
185C22—42no—
186C22—42no—
187C22#671612yescomplemented
188C22C2×#122011yescharacteristic
189C4—21no—
190C4—601no—
191C4—601no—
192C4C2×#122012yes—
193C3#6550711yescharacteristic, complemented, Sylow
194C2—22no—
195C2—44no—
196C2#9182111yescharacteristic
197C2C2×#671611yescharacteristic
198C2#9184211yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
Fitting, prime radicalC22×C3×C5×D4C2
socleC22×C3×C5C2×D4
hypercenterC22×D4D15
hypocenterC3×C5#450
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#6716C2semidirect
3. #91813C2semidirect
4. #91116C2semidirect
5. #91114C2semidirect
12. C2×Dic30C22semidirect
15. C4⋊Dic15C22semidirect
17. C2×C3⋊#168C22semidirect
62. C22×C3×C5SD16semidirect
125. C22×C5#214semidirect
142. C3×C5#450semidirect
149. C22×C3#687semidirect
180. C5#5218semidirect
187. C22#6716semidirect
193. C3#65507semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×D42
C2×#67162
#918132
#911162
#911142
#655073
#52185