Finite Group Databasebeta

← #14285439

Subgroups — #14285439

Order 1920.

508 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 102 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#11756484C211yesmaximal, characteristic
2#11747015C212yesmaximal, complemented
3C5×#4546C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745854C212yesmaximal, complemented
6#10599282—31nomaximal, Hall
7C2×#6821C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9#91836C412yes—
10#91784—22no—
11#91782—22no—
12#91763C2211yescharacteristic
13C42×D15C2211yescharacteristic
14C2×#6651—22no—
15C5×C4⋊(C3⋊C8)C2212yes—
16C3×C4⋊#168C2212yes—
17#90983—22no—
18#68489—51nomaximal, Hall
19#66059—31no—
20#65126—32no—
21C5×#333—31no—
22#64766D311yescharacteristic, complemented
23#64705—32no—
24C2×C3×C5×Q8C2×C412yes—
25#6821—44no—
26C2×D60—22no—
27C2×D60—22no—
28C2×D60C2×C412yes—
29C2×C4×D15—22no—
30C2×C4×D15C2×C411yescharacteristic
31C2×C4×D15D412yes—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6714—24no—
35C4×Dic15C2×C411yescharacteristic
36C4×Dic15D412yes—
37C2×C5×C3⋊C8—22no—
38C2×C3×#168—22no—
39#6651—44no—
40#5725—51no—
41#4837—52no—
42C3×#333—51no—
43#4546D511yescharacteristic, complemented
44#4485—52no—
45C2×#713—32no—
46C5×C4⋊Q8C2×D311yescharacteristic
47#4093—32no—
48C2×#676—62no—
49#4041—62no—
50#4039—62no—
51#4020—31no—
52C42×D5—31no—
53C5×C4⋊C8—32no—
54#3946—62no—
55C4⋊#168C2×D312yes—
56#1560—151noSylow
57C22×D15—22no—
58C22×D15C22⋊C411yescharacteristic
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C2×Dic15C22⋊C412yes—
64C2×Dic15C22⋊C411yescharacteristic
65D60—42no—
66D60—44no—
67D60—42no—
68D60—42no—
69C4×D15—22no—
70C4×D15—22no—
71C4×D15—22no—
72C4×D15—44no—
73C3×#168—42no—
74C5×C3⋊C8—42no—
75C2×#239—52no—
76C3×C4⋊Q8C2×D511yescharacteristic
77#947—52no—
78C2×ΓL(1,𝔽25)—102no—
79#895—102no—
80#893—102no—
81#874—51no—
82C42×D3—51no—
83C3×C4⋊C8—52no—
84Dic3⋊C8—102no—
85C4⋊(C3⋊C8)C2×D512yes—
86C2×C5×Q8C4×D312yes—
87#713—124no—
88C2×D20—32no—
89C2×D20—62no—
90C2×D20—62no—
91C2×C4×D5—31no—
92C2×C4×D5—32no—
93C2×C4×D5—62no—
94C2×C5×C8—62no—
95C5×C4⋊C4—22no—
96C42×C5C22×D311yescharacteristic
97#685—64no—
98C4×Dic5—31no—
99C4×Dic5—32no—
100C2×#168—22no—
101#676—124no—
102#532—151no—
103#423—152no—
104#333—31no—
105#333—51no—
106#331—152no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×D15—21no—
109C2×D15—22no—
110C2×D15—42no—
111C2×D15—44no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5AGL(1,ℤ/8)12yes—
115C3×C4×C5#13712yes—
116Dic15—22no—
117Dic15#10012yes—
118C2×C3×Q8C4×D512yes—
119#239—204no—
120C2×D12—52no—
121C2×D12—102no—
122C2×D12—102no—
123C2×C4×D3—51no—
124C2×C4×D3—52no—
125C2×C4×D3—102no—
126C2×C3×C8—102no—
127C3×C4⋊C4—22no—
128C3×C42C22×D511yescharacteristic
129(C2×D3)⋊C4—104no—
130C4×Dic3—51no—
131C4×Dic3—52no—
132C2×C3⋊C8—22no—
133ΓL(1,𝔽25)—204no—
134C22×D5—31no—
135C22×D5—62no—
136C5×Q8—42no—
137C2×C4×C5—22no—
138C2×C4×C5C2×C4×D311yescharacteristic
139C2×C4×C5D3×D412yes—
140C2×Dic5—31no—
141C2×Dic5—32no—
142D20—122no—
143D20—124no—
144D20—122no—
145D20—122no—
146C4×D5—62no—
147C4×D5—62no—
148C4×D5—62no—
149C4×D5—124no—
150C5×C8—122no—
151#168—42no—
152C2×#41—152no—
153C2×M16—302no—
154C4⋊Q8D3×D511yescharacteristic
155#127—151no—
156#124—152no—
157#121—302no—
158C4×D4—302no—
159C2×C42—151no—
160C4⋊C8—32no—
161C4⋊C8—52no—
162C4⋊C8—302no—
163C2×C3×C5C2×#10011yescharacteristic
164C2×C3×C5#41712yes—
165D15—41no—
166D15—82no—
167C22×D3—51no—
168C22×D3—102no—
169C3×Q8—42no—
170C2×C3×C4—22no—
171C2×C3×C4C2×C4×D511yescharacteristic
172C2×C3×C4D4×D512yes—
173C2×Dic3—51no—
174C2×Dic3—52no—
175D12—202no—
176D12—204no—
177D12—202no—
178D12—202no—
179C4×D3—102no—
180C4×D3—102no—
181C4×D3—102no—
182C4×D3—204no—
183C3×C8—202no—
184C3⋊C8—42no—
185C22×C5D3×C22⋊C411yescharacteristic
186C2×D5—61no—
187C2×D5—62no—
188C2×D5—122no—
189C2×D5—124no—
190C4×C5—21no—
191C4×C5—42no—
192C4×C5#91412yes—
193C4×C5#91812yes—
194Dic5—32no—
195Dic5—62no—
196#41—604no—
197C2×Q8#120012yes—
198C2×D4—152no—
199C2×D4—302no—
200C2×D4—302no—
201C22×C4—151no—
202C22×C4—152no—
203C22×C4—302no—
204M16—604no—
205C2×C8—62no—
206C2×C8—102no—
207C4⋊C4—22no—
208C22⋊C4—304no—
209C42—151no—
210C42—152no—
211C42C2×D3×D511yescharacteristic
212C3×C5#156011yescharacteristic, complemented, Hall
213C22×C3D5×C22⋊C411yescharacteristic
214C2×D3—101no—
215C2×D3—102no—
216C2×D3—202no—
217C2×D3—204no—
218C3×C4—21no—
219C3×C4—42no—
220C3×C4#406012yes—
221C3×C4#406412yes—
222Dic3—52no—
223Dic3—102no—
224C2×C5D3×#10011yescharacteristic
225C2×C5#480312yes—
226D5—121no—
227D5—242no—
228C23—151no—
229C23—302no—
230Q8—42no—
231D4—602no—
232D4—604no—
233D4—602no—
234D4—602no—
235C2×C4—22no—
236C2×C4—151no—
237C2×C4—152no—
238C2×C4—302no—
239C2×C4—302no—
240C2×C4—302no—
241C2×C4—604no—
242C2×C4C2×#120011yescharacteristic
243C2×C4#679012yes—
244C8—122no—
245C8—202no—
246C2×C3D5×#10011yescharacteristic
247C2×C3#6509212yes—
248D3—201no—
249D3—402no—
250C5#6848911yescharacteristic, complemented, Sylow
251C22—301no—
252C22—302no—
253C22—602no—
254C22—604no—
255C22#9156111yescharacteristic
256C4—21no—
257C4—42no—
258C4—152no—
259C4—302no—
260C4#9150612yes—
261C4#9151212yes—
262C3#1059928211yescharacteristic, complemented, Sylow
263C2—601no—
264C2—1202no—
265C2#1174912711yescharacteristic
266C2#1174920512yes—
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756484C2
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1560
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11747015C2semidirect
3. C5×#4546C2semidirect
4. C3×#64766C2semidirect
5. #11745854C2semidirect
22. #64766D3semidirect
43. #4546D5semidirect
212. C3×C5#1560semidirect
250. C5#68489semidirect
262. C3#10599282semidirect

Maximal subgroups

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

subgroupindex
#117564842
#117470152
C5×#45462
C3×#647662
#117458542
#105992823
#684895