Finite Group Databasebeta

← #14284707

Subgroups — #14284707

Order 1920.

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

normal subgroups only

This group has 492 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
1#11756484C211yesmaximal, characteristic
2#11750934C212yesmaximal, complemented
3C3×C5×#333C211yesmaximal, characteristic, complemented
4#11746367C211yesmaximal, characteristic, complemented
5#11746306C212yesmaximal, complemented
6#10599275—31nomaximal, Hall
7C2×#6821C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9#91836C412yes—
10#91784—22no—
11#91782—22no—
12#91763C2211yescharacteristic
13C42×D15C2211yescharacteristic
14C3×C5×C4⋊C8C2212yes—
15#91104—22no—
16C8×Dic15—22no—
17C4⋊(C3⋊#168)C2212yes—
18#68482—51nomaximal, Hall
19#66059—31no—
20#65122—32no—
21C5×#333D311yescharacteristic, complemented
22#64766—31no—
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—
32C2×C3×C5×C8—22no—
33C3×C5×C4⋊C4—22no—
34C3×C42×C5C2311yescharacteristic
35#6714—24no—
36C4×Dic15C2×C411yescharacteristic
37C4×Dic15D412yes—
38C2×C3⋊#168—22no—
39#5725—51no—
40#4833—52no—
41C3×#333D511yescharacteristic, complemented
42#4546—51no—
43#4485—52no—
44C2×#713—32no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4093—32no—
47#4041—62no—
48#4039—62no—
49#4020—31no—
50C42×D5—31no—
51C5×C4⋊C8C2×D312yes—
52#3952—62no—
53C8×Dic5—62no—
54C4⋊#168—32no—
55#1543—151noSylow
56C22×D15—22no—
57C22×D15C22⋊C411yescharacteristic
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15C22⋊C412yes—
63C2×Dic15C22⋊C411yescharacteristic
64D60—42no—
65D60—44no—
66D60—42no—
67D60—42no—
68C4×D15—22no—
69C4×D15—22no—
70C4×D15—22no—
71C4×D15—44no—
72C3×C5×C8—42no—
73C3⋊#168—42no—
74C2×#239—52no—
75C3×C4⋊Q8C2×D511yescharacteristic
76#947—52no—
77#895—102no—
78#893—102no—
79#874—51no—
80C42×D3—51no—
81C3×C4⋊C8C2×D512yes—
82(C2×D3)⋊C8—102no—
83C8×Dic3—102no—
84C4⋊(C3⋊C8)—52no—
85C2×C5×Q8C4×D312yes—
86#713—124no—
87C2×D20—32no—
88C2×D20—62no—
89C2×D20—62no—
90C2×C4×D5—31no—
91C2×C4×D5—32no—
92C2×C4×D5—62no—
93C2×C5×C8—22no—
94C5×C4⋊C4—22no—
95C42×C5C22×D311yescharacteristic
96#685—64no—
97C4×Dic5—31no—
98C4×Dic5—32no—
99C2×#168—62no—
100#532—151no—
101#431—152no—
102#333—151no—
103#333D1511yescharacteristic, complemented
104#331—152no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×D15—21no—
107C2×D15—22no—
108C2×D15—42no—
109C2×D15—44no—
110C3×C4×C5—21no—
111C3×C4×C5—42no—
112C3×C4×C5#13512yes—
113C3×C4×C5#13512yes—
114Dic15—22no—
115Dic15#10012yes—
116C2×C3×Q8C4×D512yes—
117#239—204no—
118C2×D12—52no—
119C2×D12—102no—
120C2×D12—102no—
121C2×C4×D3—51no—
122C2×C4×D3—52no—
123C2×C4×D3—102no—
124C2×C3×C8—22no—
125C3×C4⋊C4—22no—
126C3×C42C22×D511yescharacteristic
127(C2×D3)⋊C4—104no—
128C4×Dic3—51no—
129C4×Dic3—52no—
130C2×C3⋊C8—102no—
131C22×D5—31no—
132C22×D5—62no—
133C5×Q8—42no—
134C2×C4×C5—22no—
135C2×C4×C5C2×C4×D311yescharacteristic
136C2×C4×C5D3×D412yes—
137C2×Dic5—31no—
138C2×Dic5—32no—
139D20—122no—
140D20—124no—
141D20—122no—
142D20—122no—
143C4×D5—62no—
144C4×D5—62no—
145C4×D5—62no—
146C4×D5—124no—
147C5×C8—42no—
148#168—122no—
149C2×#41—152no—
150C4⋊Q8C2×D1511yescharacteristic
151#127—151no—
152#124—152no—
153#121—302no—
154C4×D4—302no—
155C2×C42—151no—
156C4⋊C8—152no—
157C4⋊C8C2×D1512yes—
158C22⋊C8—302no—
159C4×C8—302no—
160C2×C3×C5C2×#10011yescharacteristic
161C2×C3×C5#41612yes—
162D15—41no—
163D15—82no—
164C22×D3—51no—
165C22×D3—102no—
166C3×Q8—42no—
167C2×C3×C4—22no—
168C2×C3×C4C2×C4×D511yescharacteristic
169C2×C3×C4D4×D512yes—
170C2×Dic3—51no—
171C2×Dic3—52no—
172D12—202no—
173D12—204no—
174D12—202no—
175D12—202no—
176C4×D3—102no—
177C4×D3—102no—
178C4×D3—102no—
179C4×D3—204no—
180C3×C8—42no—
181C3⋊C8—202no—
182C22×C5D3×C22⋊C411yescharacteristic
183C2×D5—61no—
184C2×D5—62no—
185C2×D5—122no—
186C2×D5—124no—
187C4×C5—21no—
188C4×C5—42no—
189C4×C5#91612yes—
190C4×C5#91912yes—
191Dic5—32no—
192Dic5—62no—
193#41—604no—
194C2×Q8C4×D1512yes—
195C2×D4—152no—
196C2×D4—302no—
197C2×D4—302no—
198C22×C4—151no—
199C22×C4—152no—
200C22×C4—302no—
201C2×C8—22no—
202C2×C8—302no—
203C4⋊C4—22no—
204C22⋊C4—304no—
205C42—151no—
206C42—152no—
207C42C22×D1511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3D5×C22⋊C411yescharacteristic
210C2×D3—101no—
211C2×D3—102no—
212C2×D3—202no—
213C2×D3—204no—
214C3×C4—21no—
215C3×C4—42no—
216C3×C4#406212yes—
217C3×C4#406512yes—
218Dic3—52no—
219Dic3—102no—
220C2×C5D3×#10011yescharacteristic
221C2×C5#480412yes—
222D5—121no—
223D5—242no—
224C23—151no—
225C23—302no—
226Q8—42no—
227D4—602no—
228D4—604no—
229D4—602no—
230D4—602no—
231C2×C4—22no—
232C2×C4—151no—
233C2×C4—152no—
234C2×C4—302no—
235C2×C4—302no—
236C2×C4—302no—
237C2×C4—604no—
238C2×C4C2×C4×D1511yescharacteristic
239C2×C4D4×D1512yes—
240C8—42no—
241C8—602no—
242C2×C3D5×#10011yescharacteristic
243C2×C3#6509312yes—
244D3—201no—
245D3—402no—
246C5#6848211yescharacteristic, complemented, Sylow
247C22—301no—
248C22—302no—
249C22—602no—
250C22—604no—
251C22C22⋊C4×D1511yescharacteristic
252C4—21no—
253C4—42no—
254C4—152no—
255C4—302no—
256C4#9180512yes—
257C4#9180812yes—
258C3#1059927511yescharacteristic, complemented, Sylow
259C2—601no—
260C2—1202no—
261C2D15×#10011yescharacteristic
262C2#1175090512yes—
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756484C2
cosocleC3×C42×C5C23
hypercenter#333D15
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #11750934C2semidirect
3. C3×C5×#333C2semidirect
4. #11746367C2semidirect
5. #11746306C2semidirect
21. C5×#333D3semidirect
41. C3×#333D5semidirect
103. #333D15semidirect
208. C3×C5#1543semidirect
246. C5#68482semidirect
258. C3#10599275semidirect

Maximal subgroups

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

subgroupindex
#117564842
#117509342
C3×C5×#3332
#117463672
#117463062
#105992753
#684825