Finite Group Databasebeta

← #14283900

Subgroups — #14283900

Order 1920.

464 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 94 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×#125C211yesmaximal, characteristic
2#11746983C212yesmaximal
3C5×#4543C211yesmaximal, characteristic, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745851C212yesmaximal, complemented
6D5×#330—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C4⋊C4×D15—22no—
9C4⋊C4×D15C412yes—
10#91779C412yes—
11#91778—22no—
12C42×D15C2211yescharacteristic
13#91759C2211yescharacteristic
14C2×#6648—22no—
15C5×#803C2212yes—
16C3×#3935C2212yes—
17#90954—22no—
18D3×#330—51nomaximal, Hall
19D5×#125—31no—
20D5×#97—32no—
21C5×#330—31no—
22#64763D311yescharacteristic, complemented
23#64685—32no—
24C2×C4×D15—22no—
25C2×C4×D15C2×C411yescharacteristic
26C2×C4×D15D412yes—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4C2×C412yes—
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15—22no—
31C4⋊Dic15C2×C412yes—
32#6712—22no—
33#6712—22no—
34#6712—22no—
35C4×Dic15C2×C411yescharacteristic
36C4×Dic15D412yes—
37C2×C5×C3⋊C8—22no—
38C2×C3×#168—22no—
39#6648—28no—
40D3×#125—51no—
41D3×#97—52no—
42C3×#330—51no—
43#4543D511yescharacteristic, complemented
44#4465—52no—
45C5×#125C2×D311yescharacteristic
46C2×C8×D5—62no—
47D5×C4⋊C4—32no—
48D5×C4⋊C4—62no—
49#4036—32no—
50#4035—62no—
51C42×D5—31no—
52#4016—31no—
53C5×#97—32no—
54#3947—62no—
55#3935C2×D312yes—
56C2×#330—151noSylow
57C22×D15C22⋊C411yescharacteristic
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—24no—
66C4×D15—44no—
67C3×#168—24no—
68C5×C3⋊C8—24no—
69C3×#125C2×D511yescharacteristic
70C2×D3×C8—102no—
71D3×C4⋊C4—52no—
72D3×C4⋊C4—102no—
73#890—52no—
74#889—102no—
75C42×D3—51no—
76#870—51no—
77C3×#97—52no—
78#815—102no—
79#803C2×D512yes—
80C2×C4×D5—31no—
81C2×C4×D5—32no—
82C2×C4×D5—62no—
83C2×C5×C8—62no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4C4×D312yes—
86C42×C5C22×D311yescharacteristic
87C4⋊Dic5—32no—
88C4⋊Dic5—62no—
89#683—62no—
90#683—62no—
91#683—62no—
92C4×Dic5—31no—
93C4×Dic5—32no—
94C2×#168—22no—
95C8×D5—68no—
96C2×#125—151no—
97C2×#97—152no—
98#330—31no—
99#330—51no—
100#330—152no—
101C22×C3×C5C2×C22⋊C411yescharacteristic
102C2×D15#10112yes—
103C2×D15#10414yes—
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107Dic15—21no—
108Dic15—22no—
109Dic15—42no—
110C2×C4×D3—51no—
111C2×C4×D3—52no—
112C2×C4×D3—102no—
113C2×C3×C8—102no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4C4×D512yes—
116C3×C42C22×D511yescharacteristic
117C4⋊Dic3—52no—
118C4⋊Dic3—102no—
119Dic3⋊C4—102no—
120Dic3⋊C4—102no—
121Dic3⋊C4—102no—
122C4×Dic3—51no—
123C4×Dic3—52no—
124C2×C3⋊C8—22no—
125D3×C8—108no—
126C22×D5—31no—
127C2×C4×C5—22no—
128C2×C4×C5C2×C4×D311yescharacteristic
129C2×C4×C5D3×D412yes—
130C2×Dic5—31no—
131C2×Dic5—32no—
132C2×Dic5—62no—
133C4×D5—64no—
134C4×D5—62no—
135C4×D5—124no—
136C5×C8—64no—
137#168—24no—
138C22×C8—302no—
139#125—152no—
140#125—151no—
141#125—302no—
142#125D3×D511yescharacteristic
143C2×C4⋊C4—152no—
144C2×C4⋊C4—302no—
145C2×C42—151no—
146#97—32no—
147#97—52no—
148#97—302no—
149C2×C3×C5C2×#10111yescharacteristic
150C2×C3×C5C2×#10412yes—
151D15#33014yescomplemented
152C22×D3—51no—
153C2×C3×C4—22no—
154C2×C3×C4C2×C4×D511yescharacteristic
155C2×C3×C4D4×D512yes—
156C2×Dic3—51no—
157C2×Dic3—52no—
158C2×Dic3—102no—
159C4×D3—104no—
160C4×D3—102no—
161C4×D3—204no—
162C3×C8—104no—
163C3⋊C8—24no—
164C22×C5D3×C22⋊C411yescharacteristic
165C2×D5—32no—
166C2×D5—34no—
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—42no—
170Dic5—61no—
171Dic5—62no—
172Dic5—122no—
173C22×C4—151no—
174C22×C4—152no—
175C22×C4—302no—
176C2×C8—62no—
177C2×C8—102no—
178C2×C8—308no—
179C4⋊C4—22no—
180C4⋊C4—152no—
181C4⋊C4—302no—
182C4⋊C4—302no—
183C4⋊C4—302no—
184C4⋊C4—302no—
185C4⋊C4#120012yes—
186C42—151no—
187C42—152no—
188C42C2×D3×D511yescharacteristic
189C3×C5C2×#33011yescharacteristic, complemented, Hall
190C22×C3D5×C22⋊C411yescharacteristic
191C2×D3—52no—
192C2×D3—54no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196Dic3—101no—
197Dic3—102no—
198Dic3—202no—
199C2×C5D3×#10111yescharacteristic
200C2×C5D3×#10412yes—
201D5—34no—
202C23—151no—
203C2×C4—22no—
204C2×C4—152no—
205C2×C4—151no—
206C2×C4—304no—
207C2×C4—302no—
208C2×C4—302no—
209C2×C4—604no—
210C2×C4C2×#120011yescharacteristic
211C2×C4#679012yes—
212C8—64no—
213C8—104no—
214C2×C3D5×#10111yescharacteristic
215C2×C3D5×#10412yes—
216D3—54no—
217C5D3×#33011yescharacteristic, complemented, Sylow
218C22—154no—
219C22—152no—
220C22#9156111yescharacteristic
221C4—22no—
222C4—21no—
223C4—42no—
224C4—302no—
225C4—301no—
226C4—602no—
227C3D5×#33011yescharacteristic, complemented, Sylow
228C2—154no—
229C2#1174937311yescharacteristic
230C2#1174943012yes—
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5C2×#330
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C5×#4543C2semidirect
4. C3×#64763C2semidirect
5. #11745851C2semidirect
22. #64763D3semidirect
43. #4543D5semidirect
151. D15#330semidirect
189. C3×C5C2×#330semidirect
217. C5D3×#330semidirect
227. C3D5×#330semidirect

Maximal subgroups

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

subgroupindex
D15×#1252
#117469832
C5×#45432
C3×#647632
#117458512
D5×#3303
D3×#3305