Finite Group Databasebeta

← #14289048

Subgroups — #14289048

Order 1920.

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

normal subgroups only

This group has 480 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
1#11756493C211yesmaximal, characteristic, complemented
2C3×C5×#492C211yesmaximal, characteristic, complemented
3#11751173C212yesmaximal, complemented
4#11746367C211yesmaximal, characteristic, complemented
5#11746280C212yesmaximal, complemented
6#10602058—31nomaximal, Hall
7C2×C3×C5×SD16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×#127C2211yescharacteristic
10#91836—22no—
11C2×#6715—22no—
12#91784—22no—
13#91781—22no—
14C4×D60C2212yes—
15C3×C4×C5×C8C2211yescharacteristic
16#91116—22no—
17C4⋊(C3⋊#168)C2212yes—
18#71265—51nomaximal, Hall
19#66068—31no—
20C5×#492D311yescharacteristic, complemented
21#65361—32no—
22#64766—31no—
23#64679—32no—
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4—21no—
27C2×D60—22no—
28C2×D60D412yes—
29C2×C4×D15—22no—
30C3×C5×SD16—44no—
31C2×C3×C5×C8—21no—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6715—44no—
35#6714—24no—
36#6714—22no—
37C4⋊Dic15D412yes—
38C4×Dic15—22no—
39C2×C3⋊#168—22no—
40#5734—51no—
41C3×#492D511yescharacteristic, complemented
42#5072—52no—
43#4546—51no—
44#4459—52no—
45C2×C5×SD16—22no—
46C5×C4⋊Q8C2×D311yescharacteristic
47C5×#127C2×D311yescharacteristic
48#4093—62no—
49C2×#686—62no—
50#4041—62no—
51#4038—62no—
52C4×D20—32no—
53C4×C5×C8C2×D311yescharacteristic
54#3964—62no—
55C4⋊#168—32no—
56#1624—151noSylow
57C23×C3×C5—41no—
58C22×D15—22no—
59C3×C5×Q8—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C3×C5×D4—42no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×C3×C4×C5C2×D412yes—
66C2×Dic15—22no—
67D60—22no—
68D60—22no—
69D60—82no—
70C4×D15—42no—
71C4×D15—42no—
72C3×C5×C8—22no—
73C3⋊#168—42no—
74C2×C3×SD16—22no—
75C3×C4⋊Q8C2×D511yescharacteristic
76C3×#127C2×D511yescharacteristic
77#947—102no—
78C2×#213—102no—
79#895—102no—
80#892—102no—
81C4×D12—52no—
82C3×C4×C8C2×D511yescharacteristic
83#832—102no—
84C4⋊(C3⋊C8)—52no—
85C2×C5×Q8#6712yes—
86C2×C5×D4—22no—
87C2×C5×D4—21no—
88C2×D20—32no—
89C2×D20—62no—
90C2×C4×D5—62no—
91C5×SD16—44no—
92C2×C5×C8—21no—
93C5×C4⋊C4—22no—
94C42×C5C22×D311yescharacteristic
95#686—124no—
96#685—64no—
97#685—62no—
98C4⋊Dic5—32no—
99C4×Dic5—62no—
100C2×#168—62no—
101#555—151no—
102#492D1511yescharacteristic, complemented
103#459—152no—
104#333—151no—
105D4⋊C8—152no—
106C22×C3×C5—82no—
107C22×C3×C5—81no—
108C22×C3×C5#12011yescharacteristic
109C2×D15—42no—
110C2×D15—42no—
111C2×D15—42no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5#13512yes—
115C3×C4×C5AGL(1,ℤ/8)12yes—
116Dic15—42no—
117C2×C3×Q8C22⋊D512yes—
118C2×C3×D4—22no—
119C2×C3×D4—21no—
120C2×D12—52no—
121C2×D12—102no—
122C2×C4×D3—102no—
123C3×SD16—44no—
124C2×C3×C8—21no—
125C3×C4⋊C4—22no—
126C3×C42C22×D511yescharacteristic
127#213—204no—
128(C2×D3)⋊C4—104no—
129(C2×D3)⋊C4—102no—
130C4⋊Dic3—52no—
131C4×Dic3—102no—
132C2×C3⋊C8—102no—
133C23×C5—41no—
134C22×D5—62no—
135C5×Q8—42no—
136C5×D4—42no—
137C5×D4—42no—
138C5×D4—42no—
139C2×C4×C5—22no—
140C2×C4×C5D3×D412yes—
141C2×C4×C5C2×#6711yescharacteristic
142C2×Dic5—62no—
143D20—62no—
144D20—62no—
145D20—242no—
146C4×D5—122no—
147C4×D5—122no—
148C5×C8—22no—
149#168—122no—
150C2×SD16—22no—
151C2×D8—302no—
152C4⋊Q8C2×D1511yescharacteristic
153#127C2×D1511yescharacteristic
154#124—302no—
155#121—302no—
156C4×D4—152no—
157#117—302no—
158C4⋊C8—152no—
159#102—302no—
160C4×C8C2×D1511yescharacteristic
161C2×C3×C5—161no—
162C2×C3×C5#44912yes—
163C2×C3×C5#45311yescharacteristic
164D15—82no—
165C23×C3—41no—
166C22×D3—102no—
167C3×Q8—42no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—42no—
171C2×C3×C4—22no—
172C2×C3×C4D4×D512yes—
173C2×C3×C4C2×C22⋊D511yescharacteristic
174C2×Dic3—102no—
175D12—102no—
176D12—102no—
177D12—402no—
178C4×D3—202no—
179C4×D3—202no—
180C3×C8—22no—
181C3⋊C8—202no—
182C22×C5—82no—
183C22×C5—81no—
184C22×C5#93711yescharacteristic
185C2×D5—122no—
186C2×D5—122no—
187C2×D5—122no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5#91412yes—
191C4×C5#91612yes—
192Dic5—122no—
193C2×Q8#122012yes—
194C2×D4—22no—
195C2×D4—21no—
196C2×D4—152no—
197C2×D4—302no—
198C22×C4—302no—
199SD16—44no—
200D8—604no—
201C2×C8—21no—
202C2×C8—302no—
203C4⋊C4—22no—
204C4⋊C4—152no—
205C22⋊C4—304no—
206C22⋊C4—302no—
207C42—302no—
208C42C22×D1511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3—81no—
211C22×C3—82no—
212C22×C3#408311yescharacteristic
213C2×D3—202no—
214C2×D3—202no—
215C2×D3—202no—
216C3×C4—21no—
217C3×C4—42no—
218C3×C4#406012yes—
219C3×C4#406212yes—
220Dic3—202no—
221C2×C5—161no—
222C2×C5#507711yescharacteristic
223C2×C5#517212yes—
224D5—242no—
225C23—41no—
226C23—302no—
227Q8—42no—
228D4—42no—
229D4—42no—
230D4—42no—
231D4—302no—
232D4—302no—
233D4—1202no—
234C2×C4—22no—
235C2×C4—302no—
236C2×C4—602no—
237C2×C4—602no—
238C2×C4D4×D1512yes—
239C2×C4C2×#122011yescharacteristic
240C8—22no—
241C8—602no—
242C2×C3—161no—
243C2×C3#6536611yescharacteristic
244C2×C3#6546112yes—
245D3—402no—
246C5#7126511yescharacteristic, complemented, Sylow
247C22—81no—
248C22—82no—
249C22—602no—
250C22—602no—
251C22—602no—
252C22#9182611yescharacteristic
253C4—21no—
254C4—42no—
255C4—602no—
256C4#9180312yes—
257C4#9180512yes—
258C3#1060205811yescharacteristic, complemented, Sylow
259C2—161no—
260C2—1202no—
261C2#1175117811yescharacteristic
262C2#1175127312yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#492C2
socleC22×C3×C5#120
hypercenter#492D15
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #11756493C2semidirect
2. C3×C5×#492C2semidirect
3. #11751173C2semidirect
4. #11746367C2semidirect
5. #11746280C2semidirect
20. C5×#492D3semidirect
41. C3×#492D5semidirect
102. #492D15semidirect
209. C3×C5#1624semidirect
246. C5#71265semidirect
258. C3#10602058semidirect

Maximal subgroups

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

subgroupindex
#117564932
C3×C5×#4922
#117511732
#117463672
#117462802
#106020583
#712655