Finite Group Databasebeta

← #14285350

Subgroups — #14285350

Order 1920.

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

normal subgroups only

This group has 456 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
1D15×C4⋊Q8C211yesmaximal, characteristic
2#11746867C212yesmaximal
3C5×#4546C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745863C212yesmaximal, complemented
6#10599280—31nomaximal, Hall
7C2×Q8×D15C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9#91833C412yes—
10C4⋊C4×D15—22no—
11#91777—22no—
12C42×D15C2211yescharacteristic
13#91758C2211yescharacteristic
14C5×C4⋊(C3⋊C8)C2212yes—
15C3×C4⋊#168C2212yes—
16#90957—22no—
17#90954—22no—
18#68487—51nomaximal, Hall
19D5×C4⋊Q8—31no—
20#65124—32no—
21C5×#333—31no—
22#64766D311yescharacteristic, complemented
23#64701—32no—
24C2×C3×C5×Q8C2×C412yes—
25Q8×D15—44no—
26C2×C4×D15—22no—
27C2×C4×D15C2×C411yescharacteristic
28C2×C4×D15D412yes—
29C2×Dic30—22no—
30C2×Dic30C2×C412yes—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C4⋊Dic15—22no—
34#6712—24no—
35C4×Dic15C2×C411yescharacteristic
36C4×Dic15D412yes—
37C2×C5×C3⋊C8—22no—
38C2×C3×#168—22no—
39D3×C4⋊Q8—51no—
40#4835—52no—
41C3×#333—51no—
42#4546D511yescharacteristic, complemented
43#4481—52no—
44C2×Q8×D5—32no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4090—32no—
47D5×C4⋊C4—62no—
48#4034—62no—
49C42×D5—31no—
50#4015—31no—
51C5×C4⋊C8—32no—
52#3952—62no—
53#3947—62no—
54C4⋊#168C2×D312yes—
55#1558—151noSylow
56C22×D15C22⋊C411yescharacteristic
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×Dic15—22no—
62C2×Dic15C22⋊C412yes—
63C2×Dic15C22⋊C411yescharacteristic
64C4×D15—22no—
65C4×D15—22no—
66C4×D15—22no—
67C4×D15—44no—
68Dic30—44no—
69Dic30—42no—
70C3×#168—42no—
71C5×C3⋊C8—42no—
72C2×D3×Q8—52no—
73C3×C4⋊Q8C2×D511yescharacteristic
74#944—52no—
75D3×C4⋊C4—102no—
76#888—102no—
77C42×D3—51no—
78#869—51no—
79C3×C4⋊C8—52no—
80(C2×D3)⋊C8—102no—
81#815—102no—
82C4⋊(C3⋊C8)C2×D512yes—
83C2×C5×Q8C4×D312yes—
84Q8×D5—124no—
85C2×C4×D5—31no—
86C2×C4×D5—32no—
87C2×C4×D5—62no—
88C2×Dic10—32no—
89C2×Dic10—62no—
90C2×C5×C8—62no—
91C5×C4⋊C4—22no—
92C42×C5C22×D311yescharacteristic
93C4⋊Dic5—62no—
94#683—64no—
95C4×Dic5—31no—
96C4×Dic5—32no—
97C2×#168—22no—
98C2×C4⋊Q8—151no—
99#432—152no—
100#333—31no—
101#333—51no—
102#333—152no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C2×D15—22no—
105C2×D15#10012yes—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13712yes—
109C3×C4×C5#13712yes—
110Dic15—21no—
111Dic15—22no—
112Dic15—42no—
113C2×C3×Q8C4×D512yes—
114D3×Q8—204no—
115C2×C4×D3—51no—
116C2×C4×D3—52no—
117C2×C4×D3—102no—
118C2×Dic6—52no—
119C2×Dic6—102no—
120C2×C3×C8—102no—
121C3×C4⋊C4—22no—
122C3×C42C22×D511yescharacteristic
123C4⋊Dic3—102no—
124Dic3⋊C4—104no—
125C4×Dic3—51no—
126C4×Dic3—52no—
127C2×C3⋊C8—22no—
128C22×D5—31no—
129C5×Q8—42no—
130C2×C4×C5—22no—
131C2×C4×C5C2×C4×D311yescharacteristic
132C2×C4×C5D3×D412yes—
133C2×Dic5—32no—
134C2×Dic5—31no—
135C2×Dic5—62no—
136C4×D5—62no—
137C4×D5—62no—
138C4×D5—62no—
139C4×D5—124no—
140Dic10—124no—
141Dic10—122no—
142C5×C8—122no—
143#168—42no—
144C22×Q8—152no—
145C4⋊Q8—152no—
146C4⋊Q8—151no—
147C4⋊Q8—302no—
148C4⋊Q8D3×D511yescharacteristic
149C2×C4⋊C4—302no—
150C2×C42—151no—
151C4⋊C8—32no—
152C4⋊C8—52no—
153C22⋊C8—302no—
154#97—302no—
155C2×C3×C5C2×#10011yescharacteristic
156C2×C3×C5#41912yes—
157D15—22no—
158C22×D3—51no—
159C3×Q8—42no—
160C2×C3×C4—22no—
161C2×C3×C4C2×C4×D511yescharacteristic
162C2×C3×C4D4×D512yes—
163C2×Dic3—52no—
164C2×Dic3—51no—
165C2×Dic3—102no—
166C4×D3—102no—
167C4×D3—102no—
168C4×D3—102no—
169C4×D3—204no—
170Dic6—204no—
171Dic6—202no—
172C3×C8—202no—
173C3⋊C8—42no—
174C22×C5D3×C22⋊C411yescharacteristic
175C2×D5—32no—
176C2×D5—62no—
177C4×C5—21no—
178C4×C5—42no—
179C4×C5#91512yes—
180C4×C5#91812yes—
181Dic5—61no—
182Dic5—62no—
183Dic5—122no—
184C2×Q8—152no—
185C2×Q8—302no—
186C2×Q8—604no—
187C2×Q8#120012yes—
188C22×C4—151no—
189C22×C4—152no—
190C22×C4—302no—
191C2×C8—62no—
192C2×C8—102no—
193C4⋊C4—22no—
194C4⋊C4—304no—
195C4⋊C4—302no—
196C42—151no—
197C42—152no—
198C42C2×D3×D511yescharacteristic
199C3×C5#155811yescharacteristic, complemented, Hall
200C22×C3D5×C22⋊C411yescharacteristic
201C2×D3—52no—
202C2×D3—102no—
203C3×C4—21no—
204C3×C4—42no—
205C3×C4#406112yes—
206C3×C4#406412yes—
207Dic3—101no—
208Dic3—102no—
209Dic3—202no—
210C2×C5D3×#10011yescharacteristic
211C2×C5#480212yes—
212D5—62no—
213C23—151no—
214Q8—42no—
215Q8—602no—
216Q8—604no—
217C2×C4—22no—
218C2×C4—152no—
219C2×C4—151no—
220C2×C4—302no—
221C2×C4—302no—
222C2×C4—302no—
223C2×C4—302no—
224C2×C4—604no—
225C2×C4C2×#120011yescharacteristic
226C2×C4#679012yes—
227C8—122no—
228C8—202no—
229C2×C3D5×#10011yescharacteristic
230C2×C3#6509112yes—
231D3—102no—
232C5#6848711yescharacteristic, complemented, Sylow
233C22—152no—
234C22—302no—
235C22#9156111yescharacteristic
236C4—21no—
237C4—42no—
238C4—301no—
239C4—302no—
240C4—602no—
241C4#9152212yes—
242C4#9152412yes—
243C3#1059928011yescharacteristic, complemented, Sylow
244C2—302no—
245C2#1174912711yescharacteristic
246C2#1174921812yes—
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1558
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
3. C5×#4546C2semidirect
4. C3×#64766C2semidirect
5. #11745863C2semidirect
22. #64766D3semidirect
42. #4546D5semidirect
199. C3×C5#1558semidirect
232. C5#68487semidirect
243. C3#10599280semidirect

Maximal subgroups

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

subgroupindex
D15×C4⋊Q82
#117468672
C5×#45462
C3×#647662
#117458632
#105992803
#684875