Finite Group Databasebeta

← #14284639

Subgroups — #14284639

Order 1920.

512 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 122 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#11747000C212yesmaximal
3C5×#4546C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745863C212yesmaximal, complemented
6D5×#333—31nomaximal, Hall
7C2×Q8×D15C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9#91833C412yes—
10C4⋊C4×D15—22no—
11#91777—22no—
12C42×D15C2211yescharacteristic
13#91758C2211yescharacteristic
14C2×#6648—22no—
15C5×C4⋊(C3⋊C8)C2212yes—
16C3×C4⋊#168C2212yes—
17#90983—22no—
18D3×#333—51nomaximal, Hall
19D5×C4⋊Q8—31no—
20D5×C4⋊C8—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—
39#6648—44no—
40D3×C4⋊Q8—51no—
41D3×C4⋊C8—52no—
42C3×#333—51no—
43#4546D511yescharacteristic, complemented
44#4481—52no—
45C2×Q8×D5—32no—
46C5×C4⋊Q8C2×D311yescharacteristic
47#4090—32no—
48C2×C8×D5—62no—
49D5×C4⋊C4—62no—
50#4034—62no—
51C42×D5—31no—
52#4015—31no—
53C5×C4⋊C8—32no—
54#3946—62no—
55C4⋊#168C2×D312yes—
56C2×#333—151noSylow
57C22×D15C22⋊C411yescharacteristic
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—22no—
63C2×Dic15C22⋊C411yescharacteristic
64C2×Dic15C22⋊C412yes—
65C4×D15—22no—
66C4×D15—44no—
67C4×D15SD1614yes—
68C4×D15Q1614yes—
69Dic30—44no—
70Dic30—42no—
71C3×#168—42no—
72C5×C3⋊C8—42no—
73C2×D3×Q8—52no—
74C3×C4⋊Q8C2×D511yescharacteristic
75#944—52no—
76C2×D3×C8—102no—
77D3×C4⋊C4—102no—
78#888—102no—
79C42×D3—51no—
80#869—51no—
81C3×C4⋊C8—52no—
82Dic3⋊C8—102no—
83C4⋊(C3⋊C8)C2×D512yes—
84C2×C5×Q8C4×D312yes—
85Q8×D5—124no—
86C2×C4×D5—32no—
87C2×C4×D5—31no—
88C2×C4×D5—62no—
89C2×Dic10—32no—
90C2×Dic10—62no—
91C2×C5×C8—62no—
92C5×C4⋊C4—22no—
93C42×C5C22×D311yescharacteristic
94C4⋊Dic5—62no—
95#683—64no—
96C4×Dic5—31no—
97C4×Dic5—32no—
98C2×#168—22no—
99C8×D5—124no—
100C2×C4⋊Q8—151no—
101C2×C4⋊C8—152no—
102#333—31no—
103#333—51no—
104#333—152no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×D15#10012yes—
107C2×D15#10314yes—
108C3×C4×C5—21no—
109C3×C4×C5—42no—
110C3×C4×C5C2×SD1612yes—
111C3×C4×C5C2×Q1612yes—
112Dic15—21no—
113Dic15—42no—
114Dic15#10314yes—
115C2×C3×Q8C4×D512yes—
116D3×Q8—204no—
117C2×C4×D3—52no—
118C2×C4×D3—51no—
119C2×C4×D3—102no—
120C2×Dic6—52no—
121C2×Dic6—102no—
122C2×C3×C8—102no—
123C3×C4⋊C4—22no—
124C3×C42C22×D511yescharacteristic
125C4⋊Dic3—102no—
126Dic3⋊C4—104no—
127C4×Dic3—51no—
128C4×Dic3—52no—
129C2×C3⋊C8—22no—
130D3×C8—204no—
131C22×D5—31no—
132C5×Q8—42no—
133C2×C4×C5—22no—
134C2×C4×C5C2×C4×D311yescharacteristic
135C2×C4×C5D3×D412yes—
136C2×Dic5—32no—
137C2×Dic5—31no—
138C2×Dic5—62no—
139C4×D5—34no—
140C4×D5—34no—
141C4×D5—62no—
142C4×D5—124no—
143Dic10—124no—
144Dic10—122no—
145C5×C8—122no—
146#168—42no—
147C22×Q8—152no—
148C22×C8—302no—
149C4⋊Q8—152no—
150C4⋊Q8—151no—
151C4⋊Q8—302no—
152C4⋊Q8D3×D511yescharacteristic
153C2×C4⋊C4—302no—
154C2×C42—151no—
155C4⋊C8—32no—
156C4⋊C8—52no—
157C4⋊C8—302no—
158C2×C3×C5C2×#10011yescharacteristic
159C2×C3×C5C2×#10312yes—
160D15#33314yescomplemented
161C22×D3—51no—
162C3×Q8—42no—
163C2×C3×C4—22no—
164C2×C3×C4C2×C4×D511yescharacteristic
165C2×C3×C4D4×D512yes—
166C2×Dic3—52no—
167C2×Dic3—51no—
168C2×Dic3—102no—
169C4×D3—54no—
170C4×D3—54no—
171C4×D3—102no—
172C4×D3—204no—
173Dic6—204no—
174Dic6—202no—
175C3×C8—202no—
176C3⋊C8—42no—
177C22×C5D3×C22⋊C411yescharacteristic
178C2×D5—32no—
179C2×D5—34no—
180C4×C5—21no—
181C4×C5—42no—
182C4×C5D3×SD1612yes—
183C4×C5D3×Q1612yes—
184Dic5—34no—
185Dic5—61no—
186Dic5—122no—
187C2×Q8—152no—
188C2×Q8—302no—
189C2×Q8—604no—
190C2×Q8#120012yes—
191C22×C4—152no—
192C22×C4—151no—
193C22×C4—302no—
194C2×C8—62no—
195C2×C8—102no—
196C2×C8—604no—
197C4⋊C4—22no—
198C4⋊C4—304no—
199C4⋊C4—302no—
200C42—151no—
201C42—152no—
202C42C2×D3×D511yescharacteristic
203C3×C5C2×#33311yescharacteristic, complemented, Hall
204C22×C3D5×C22⋊C411yescharacteristic
205C2×D3—52no—
206C2×D3—54no—
207C3×C4—21no—
208C3×C4—42no—
209C3×C4D5×SD1612yes—
210C3×C4D5×Q1612yes—
211Dic3—54no—
212Dic3—101no—
213Dic3—202no—
214C2×C5D3×#10011yescharacteristic
215C2×C5D3×#10312yes—
216D5—34no—
217C23—151no—
218Q8—42no—
219Q8—602no—
220Q8—604no—
221C2×C4—22no—
222C2×C4—152no—
223C2×C4—154no—
224C2×C4—154no—
225C2×C4—151no—
226C2×C4—302no—
227C2×C4—302no—
228C2×C4—604no—
229C2×C4C2×#120011yescharacteristic
230C2×C4#679012yes—
231C8—122no—
232C8—202no—
233C2×C3D5×#10011yescharacteristic
234C2×C3D5×#10312yes—
235D3—54no—
236C5D3×#33311yescharacteristic, complemented, Sylow
237C22—152no—
238C22—154no—
239C22#9156111yescharacteristic
240C4—21no—
241C4—42no—
242C4—154no—
243C4—301no—
244C4—602no—
245C4#9150512yes—
246C4#9151112yes—
247C3D5×#33311yescharacteristic, complemented, Sylow
248C2—154no—
249C2#1174912711yescharacteristic
250C2#1174920312yes—
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×C5C2×#333
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
43. #4546D5semidirect
160. D15#333semidirect
203. C3×C5C2×#333semidirect
236. C5D3×#333semidirect
247. C3D5×#333semidirect

Maximal subgroups

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

subgroupindex
D15×C4⋊Q82
#117470002
C5×#45462
C3×#647662
#117458632
D5×#3333
D3×#3335