Finite Group Databasebeta

← #14284337

Subgroups — #14284337

Order 1920.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×C3×C5×#124C211yesmaximal, characteristic
2#11751027C212yesmaximal, complemented
3#11746361C214yesmaximal, complemented
4#10602512—31nomaximal, Hall
5C22×C3×C5×Q8C411yescharacteristic
6C22×C3×C5×D4C411yescharacteristic
7C3×C5×#124—22no—
8C3×C5×#124C412yes—
9C3×C5×#124C2212yes—
10C2×C3×C5×C22⋊C4—22no—
11C2×C3×C42×C5C2211yescharacteristic
12#91114—22no—
13C4⋊(C3⋊#168)—22no—
14#91087C2214yescomplemented
15#71719—51nomaximal, Hall
16C2×C5×#124D311yescharacteristic
17#65215—32no—
18#64760—34no—
19C24×C3×C5—21no—
20C2×C3×C5×Q8—21no—
21C2×C3×C5×Q8—42no—
22C2×C3×C5×Q8C2×C412yes—
23C2×C3×C5×D4—21no—
24C2×C3×C5×D4—42no—
25C2×C3×C5×D4C2×C412yes—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5D412yes—
29C3×C5×C22⋊C4—24no—
30C3×C5×C22⋊C4—24no—
31C3×C42×C5C2×C411yescharacteristic
32C3×C42×C5D412yes—
33C3×C42×C5C2311yescharacteristic
34C2×C3⋊#168—24no—
35C2×C3×#124D511yescharacteristic
36#4926—52no—
37#4540—54no—
38C22×C5×Q8Dic311yescharacteristic
39C22×C5×D4Dic311yescharacteristic
40C5×#124—22no—
41C5×#124Dic312yes—
42C5×#124C2×D312yes—
43C2×C5×C22⋊C4—22no—
44C2×C42×C5C2×D311yescharacteristic
45C22⋊#168—62no—
46C4⋊#168—62no—
47#3935—34no—
48#1533—151noSylow
49C23×C3×C5—22no—
50C23×C3×C5—44no—
51C23×C3×C5—42no—
52C23×C3×C5C22⋊C411yescharacteristic
53C3×C5×Q8—42no—
54C3×C5×Q8—42no—
55C3×C5×D4—42no—
56C3×C5×D4—42no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—42no—
60C2×C3×C4×C5—42no—
61C2×C3×C4×C5C22⋊C412yes—
62C2×C3×C4×C5C22⋊C411yescharacteristic
63C2×C3×C4×C5C22×C411yescharacteristic
64C2×C3×C4×C5C2×D412yes—
65C3⋊#168—44no—
66C22×C3×Q8Dic511yescharacteristic
67C22×C3×D4Dic511yescharacteristic
68C3×#124—22no—
69C3×#124Dic512yes—
70C3×#124C2×D512yes—
71C2×C3×C22⋊C4—22no—
72C2×C3×C42C2×D511yescharacteristic
73#830—102no—
74C4⋊(C3⋊C8)—102no—
75#803—54no—
76C24×C5—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—42no—
79C2×C5×Q8C2×Dic312yes—
80C2×C5×D4—21no—
81C2×C5×D4—42no—
82C2×C5×D4C2×Dic312yes—
83C22×C4×C5—21no—
84C22×C4×C5C2×Dic311yescharacteristic
85C22×C4×C5#6712yes—
86C5×C22⋊C4—24no—
87C5×C22⋊C4—24no—
88C42×C5C2×Dic311yescharacteristic
89C42×C5#6712yes—
90C42×C5C22×D311yescharacteristic
91C2×#168—64no—
92C2×#124D1511yescharacteristic
93#432—152no—
94#329—154no—
95C22×C3×C5—22no—
96C22×C3×C5—42no—
97C22×C3×C5—44no—
98C22×C3×C5—84no—
99C22×C3×C5#10012yes—
100C22×C3×C5C2×C22⋊C411yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—21no—
103C3×C4×C5—22no—
104C3×C4×C5—22no—
105C3×C4×C5—42no—
106C24×C3—21no—
107C2×C3×Q8—21no—
108C2×C3×Q8—42no—
109C2×C3×Q8C2×Dic512yes—
110C2×C3×D4—21no—
111C2×C3×D4—42no—
112C2×C3×D4C2×Dic512yes—
113C22×C3×C4—21no—
114C22×C3×C4C2×Dic511yescharacteristic
115C22×C3×C4C22⋊D512yes—
116C3×C22⋊C4—24no—
117C3×C22⋊C4—24no—
118C3×C42C2×Dic511yescharacteristic
119C3×C42C22⋊D512yes—
120C3×C42C22×D511yescharacteristic
121C2×C3⋊C8—104no—
122C23×C5—22no—
123C23×C5—44no—
124C23×C5—42no—
125C23×C5#21711yescharacteristic
126C5×Q8—42no—
127C5×Q8—42no—
128C5×D4—42no—
129C5×D4—42no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—42no—
133C2×C4×C5—42no—
134C2×C4×C5#21712yes—
135C2×C4×C5#21711yescharacteristic
136C2×C4×C5C22×Dic311yescharacteristic
137C2×C4×C5C2×#6712yes—
138#168—124no—
139C22×Q8Dic1511yescharacteristic
140C22×D4Dic1511yescharacteristic
141#124—22no—
142#124Dic1512yes—
143#124C2×D1512yes—
144C2×C22⋊C4—22no—
145C2×C42C2×D1511yescharacteristic
146C4⋊C8—302no—
147C22⋊C8—302no—
148#97—154no—
149C2×C3×C5—22no—
150C2×C3×C5—82no—
151C2×C3×C5C2×#10011yescharacteristic
152C2×C3×C5#42112yes—
153C23×C3—22no—
154C23×C3—44no—
155C23×C3—42no—
156C23×C3C22⋊Dic511yescharacteristic
157C3×Q8—42no—
158C3×Q8—42no—
159C3×D4—42no—
160C3×D4—42no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4C22⋊Dic512yes—
166C2×C3×C4C22⋊Dic511yescharacteristic
167C2×C3×C4C22×Dic511yescharacteristic
168C2×C3×C4C2×C22⋊D512yes—
169C3⋊C8—204no—
170C22×C5—22no—
171C22×C5—42no—
172C22×C5—44no—
173C22×C5—84no—
174C22×C5#83312yes—
175C22×C5C2×#21711yescharacteristic
176C4×C5—21no—
177C4×C5—21no—
178C4×C5—22no—
179C4×C5—22no—
180C4×C5—42no—
181C24—21no—
182C2×Q8—21no—
183C2×Q8—42no—
184C2×Q8C2×Dic1512yes—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4C2×Dic1512yes—
188C22×C4—21no—
189C22×C4C2×Dic1511yescharacteristic
190C22×C4#122012yes—
191C2×C8—304no—
192C22⋊C4—24no—
193C22⋊C4—24no—
194C42C2×Dic1511yescharacteristic
195C42#122012yes—
196C42C22×D1511yescharacteristic
197C3×C5#153311yescharacteristic, complemented, Hall
198C22×C3—22no—
199C22×C3—42no—
200C22×C3—44no—
201C22×C3—84no—
202C22×C3#396512yes—
203C22×C3C2×C22⋊Dic511yescharacteristic
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—22no—
207C3×C4—22no—
208C3×C4—42no—
209C2×C5—22no—
210C2×C5—82no—
211C2×C5C2×#83311yescharacteristic
212C2×C5#523612yes—
213C23—22no—
214C23—44no—
215C23—42no—
216C23#671911yescharacteristic
217Q8—42no—
218Q8—42no—
219D4—42no—
220D4—42no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4#671912yes—
226C2×C4#671911yescharacteristic
227C2×C4C22×Dic1511yescharacteristic
228C2×C4C2×#122012yes—
229C8—604no—
230C2×C3—22no—
231C2×C3—82no—
232C2×C3C2×#396511yescharacteristic
233C2×C3#6552512yes—
234C5#7171911yescharacteristic, complemented, Sylow
235C22—22no—
236C22—42no—
237C22—44no—
238C22—84no—
239C22#9111712yes—
240C22C2×#671911yescharacteristic
241C4—21no—
242C4—21no—
243C4—22no—
244C4—22no—
245C4—42no—
246C3#1060251211yescharacteristic, complemented, Sylow
247C2—22no—
248C2—82no—
249C2C2×#9111711yescharacteristic
250C2#1175133712yes—
subgroupG/H
centerC22C2×#6719
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC2×C3×C5×#124C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C4
cosocleC3×C42×C5C23
hypercenterC2×#124D15
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #11751027C2semidirect
3. #11746361C2semidirect
14. #91087C22semidirect
197. C3×C5#1533semidirect
234. C5#71719semidirect
246. C3#10602512semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1242
#117510272
#117463612
#106025123
#717195