Finite Group Databasebeta

← #14284341

Subgroups — #14284341

Order 1920.

496 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 105 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×#4093C211yesmaximal, characteristic
2#11752416C212yesmaximal, complemented
3#11746798C214yesmaximal, complemented
4#10604961—31nomaximal, Hall
5C22×C3×C5×Q8C411yescharacteristic
6C22×C3×D20C411yescharacteristic
7C3×#4093—22no—
8C3×#4093C412yes—
9C3×#4093C2212yes—
10C2×C3×#685—22no—
11C2×C3×C4×Dic5C2211yescharacteristic
12#91241—22no—
13#91233—22no—
14#91231C2214yescomplemented
15#71719—51nomaximal, Hall
16C2×#4093D311yescharacteristic
17#65757—32no—
18#64927—34no—
19C23×C3×D5—21no—
20C2×C3×C5×Q8—21no—
21C2×C3×C5×Q8—42no—
22C2×C3×C5×Q8C2×C412yes—
23C22×C3×C4×C5—21no—
24C22×C3×C4×C5C2×C411yescharacteristic
25C22×C3×Dic5D412yes—
26C2×C3×D20—21no—
27C2×C3×D20—42no—
28C2×C3×D20C2×C412yes—
29C2×C3⋊#170—24no—
30C3×#685—24no—
31C3×#685—24no—
32C3×C4×Dic5C2×C411yescharacteristic
33C3×C4×Dic5D412yes—
34C3×C4×Dic5C2311yescharacteristic
35C2×C3×#124—51no—
36#4926—52no—
37#4540—54no—
38C22×C5×Q8Dic311yescharacteristic
39C22×D20Dic311yescharacteristic
40#4093—22no—
41#4093Dic312yes—
42#4093C2×D312yes—
43C2×#685—22no—
44C2×C4×Dic5C2×D311yescharacteristic
45C22⋊#170—62no—
46#4004—62no—
47#4002—34no—
48#1533—151noSylow
49C23×C3×C5C22⋊C411yescharacteristic
50C22×C3×D5—22no—
51C22×C3×D5—44no—
52C22×C3×D5—42no—
53C3×C5×Q8—42no—
54C3×C5×Q8—42no—
55C2×C3×C4×C5—22no—
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5—42no—
58C2×C3×C4×C5C22⋊C411yescharacteristic
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×Dic5—42no—
61C2×C3×Dic5C22⋊C412yes—
62C2×C3×Dic5C2×D412yes—
63C3×D20—42no—
64C3×D20—42no—
65C3⋊#170—44no—
66C22×C3×Q8AGL(1,𝔽5)11yescharacteristic
67C22×C3×D4—51no—
68C3×#124—52no—
69C3×#124—52no—
70C3×#124—102no—
71C2×C3×C22⋊C4—102no—
72C2×C3×C42—51no—
73#830—102no—
74C4⋊(C3⋊C8)—102no—
75#803—54no—
76C23×D5—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—42no—
79C2×C5×Q8C2×Dic312yes—
80C22×C4×C5—21no—
81C22×C4×C5C2×Dic311yescharacteristic
82C22×Dic5#6712yes—
83C2×D20—21no—
84C2×D20—42no—
85C2×D20C2×Dic312yes—
86C2×#170—64no—
87#685—24no—
88#685—24no—
89C4×Dic5C2×Dic311yescharacteristic
90C4×Dic5#6712yes—
91C4×Dic5C22×D311yescharacteristic
92C2×#124—51no—
93#432—152no—
94#329—154no—
95C22×C3×C5—22no—
96C22×C3×C5#10012yes—
97C22×C3×C5C2×C22⋊C411yescharacteristic
98C2×C3×D5—42no—
99C2×C3×D5—44no—
100C2×C3×D5—84no—
101C3×C4×C5—21no—
102C3×C4×C5—21no—
103C3×C4×C5—42no—
104C3×Dic5—22no—
105C3×Dic5—22no—
106C24×C3—101no—
107C2×C3×Q8—21no—
108C2×C3×Q8—42no—
109C2×C3×Q8C2×AGL(1,𝔽5)12yes—
110C2×C3×D4—52no—
111C2×C3×D4—101no—
112C2×C3×D4—202no—
113C22×C3×C4—21no—
114C22×C3×C4—52no—
115C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
116C3×C22⋊C4—104no—
117C3×C22⋊C4—104no—
118C3×C42—52no—
119C3×C42—51no—
120C3×C42—51no—
121C2×C3⋊C8—104no—
122C23×C5#21711yescharacteristic
123C22×D5—22no—
124C22×D5—44no—
125C22×D5—42no—
126C5×Q8—42no—
127C5×Q8—42no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—42no—
131C2×C4×C5#21711yescharacteristic
132C2×C4×C5C22×Dic311yescharacteristic
133C2×Dic5—42no—
134C2×Dic5#21712yes—
135C2×Dic5C2×#6712yes—
136D20—42no—
137D20—42no—
138#170—124no—
139C22×Q8ΓL(1,𝔽16)11yescharacteristic
140C22×D4—51no—
141#124—52no—
142#124—52no—
143#124—102no—
144C2×C22⋊C4—102no—
145C2×C42—51no—
146C4⋊C8—302no—
147C22⋊C8—302no—
148#97—154no—
149C2×C3×C5—22no—
150C2×C3×C5C2×#10011yescharacteristic
151C2×C3×C5#42112yes—
152C3×D5—82no—
153C23×C3—102no—
154C23×C3—204no—
155C23×C3—202no—
156C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
157C3×Q8—42no—
158C3×Q8—42no—
159C3×D4—202no—
160C3×D4—202no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—42no—
164C2×C3×C4—52no—
165C2×C3×C4—52no—
166C2×C3×C4—202no—
167C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
169C3⋊C8—204no—
170C22×C5—22no—
171C22×C5#83312yes—
172C22×C5C2×#21711yescharacteristic
173C2×D5—42no—
174C2×D5—44no—
175C2×D5—84no—
176C4×C5—21no—
177C4×C5—21no—
178C4×C5—42no—
179Dic5—22no—
180Dic5—22no—
181C24—101no—
182C2×Q8—21no—
183C2×Q8—42no—
184C2×Q8C2×ΓL(1,𝔽16)12yes—
185C2×D4—52no—
186C2×D4—101no—
187C2×D4—202no—
188C22×C4—21no—
189C22×C4—52no—
190C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
191C2×C8—304no—
192C22⋊C4—104no—
193C22⋊C4—104no—
194C42—52no—
195C42—51no—
196C42—51no—
197C3×C5#153311yescharacteristic, complemented, Hall
198C22×C3—22no—
199C22×C3—202no—
200C22×C3—204no—
201C22×C3—404no—
202C22×C3#401312yes—
203C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—42no—
207C3×C4—102no—
208C3×C4—102no—
209C2×C5—22no—
210C2×C5C2×#83311yescharacteristic
211C2×C5#523612yes—
212D5—82no—
213C23—102no—
214C23—204no—
215C23—202no—
216C23#676311yescharacteristic
217Q8—42no—
218Q8—42no—
219D4—202no—
220D4—202no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—52no—
225C2×C4—52no—
226C2×C4—202no—
227C2×C4#676311yescharacteristic
228C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
229C8—604no—
230C2×C3—22no—
231C2×C3—402no—
232C2×C3#6578412yes—
233C2×C3C2×#401311yescharacteristic
234C5#7171911yescharacteristic, complemented, Sylow
235C22—22no—
236C22—202no—
237C22—204no—
238C22—404no—
239C22#9124212yes—
240C22C2×#676311yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—102no—
245C4—102no—
246C3#1060496111yescharacteristic, complemented, Sylow
247C2—22no—
248C2—402no—
249C2#1175244312yes—
250C2C2×#9124211yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC22×C3×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C4
cosocleC3×C4×Dic5C23
hypercenterC22×Q8ΓL(1,𝔽16)
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #11752416C2semidirect
3. #11746798C2semidirect
14. #91231C22semidirect
197. C3×C5#1533semidirect
234. C5#71719semidirect
246. C3#10604961semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40932
#117524162
#117467982
#106049613
#717195