Finite Group Databasebeta

← #14308949

Subgroups — #14308949

Order 1920.

492 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 123 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#11756259C211yesmaximal, characteristic
2C3×C5×#391C211yesmaximal, characteristic
3#11751326C212yesmaximal
4#11746351C211yesmaximal, characteristic
5#11746344C212yesmaximal
6#10600466—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C3×C42×C5C2211yescharacteristic
10#91815C2212yes—
11#91813—22no—
12C2×#6710C2212yes—
13#91779—22no—
14#91777—22no—
15C3×C5×#95—22no—
16#91119—22no—
17#91119—22no—
18#69673—51nomaximal, Hall
19#65834—31no—
20C5×#391D311yescharacteristic
21#65514—32no—
22#64750—31no—
23#64743—32no—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8—22no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8Q812yescomplemented
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×Dic30—22no—
33C3×C5×C4⋊C4—22no—
34C3×C42×C5—22no—
35#6719—22no—
36C4⋊Dic15—22no—
37C4⋊Dic15D412yes—
38C4⋊Dic15D412yes—
39#6712—24no—
40C4×Dic15—22no—
41#6710—22no—
42#6710—22no—
43C2×C3⋊#168—22no—
44#5500—51no—
45C3×#391D511yescharacteristic
46#5225—52no—
47#4530—51no—
48#4523—52no—
49C22×C5×Q8C2×D311yescharacteristic
50C2×C5×C4⋊C4C2×D311yescharacteristic
51C2×C42×C5C2×D311yescharacteristic
52#4072—32no—
53#4070—62no—
54C2×#681—32no—
55#4036—62no—
56#4034—62no—
57C5×#95—22no—
58#3967—62no—
59#3967—62no—
60#2028—151noSylow
61C23×C3×C5C2×D411yescharacteristic
62C3×C5×Q8—24no—
63C3×C5×Q8—42no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—22no—
66C2×C3×C4×C5—22no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—41no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5C2×D412yes—
73C2×C3×C4×C5C2×Q811yescharacteristic
74C2×C3×C4×C5#4112yes—
75C2×C3×C4×C5#4111yescharacteristic
76C2×Dic15—22no—
77C2×Dic15—22no—
78Dic30—82no—
79C3⋊#168—42no—
80C22×C3×Q8C2×D511yescharacteristic
81C2×C3×C4⋊C4C2×D511yescharacteristic
82C2×C3×C42C2×D511yescharacteristic
83#926—52no—
84#924—102no—
85C2×#208—52no—
86#890—102no—
87#888—102no—
88C3×#95—22no—
89#835—102no—
90#835—102no—
91C2×C5×Q8—21no—
92C2×C5×Q8—22no—
93C2×C5×Q8—22no—
94C2×C5×Q8Dic612yescomplemented
95C22×C4×C5—21no—
96C22×C4×C5—21no—
97C22×C4×C5#6712yes—
98C22×C4×C5C22×D311yescharacteristic
99C2×Dic10—62no—
100C5×C4⋊C4—22no—
101C42×C5—22no—
102C22⋊Dic5—62no—
103C4⋊Dic5—32no—
104C4⋊Dic5—32no—
105C4⋊Dic5—62no—
106#683—64no—
107C4×Dic5—62no—
108#681—62no—
109#681—62no—
110C2×#168—62no—
111#544—151no—
112#419—152no—
113#391D1511yescharacteristic
114#343—151no—
115#339—152no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5#12011yescharacteristic
119C22×C3×C5C22⋊Q811yescharacteristic
120C22×C3×C5#12411yescharacteristic
121C3×C4×C5—42no—
122C3×C4×C5—42no—
123C3×C4×C5—42no—
124C3×C4×C5C22⋊Q812yes—
125C3×C4×C5#12412yes—
126Dic15—42no—
127Dic15—42no—
128C2×C3×Q8—21no—
129C2×C3×Q8—22no—
130C2×C3×Q8—22no—
131C2×C3×Q8Dic1012yescomplemented
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4C22⋊D512yes—
135C22×C3×C4C22×D511yescharacteristic
136C2×Dic6—102no—
137C3×C4⋊C4—22no—
138C3×C42—22no—
139#217—102no—
140C4⋊Dic3—52no—
141C4⋊Dic3—52no—
142C4⋊Dic3—102no—
143Dic3⋊C4—104no—
144C4×Dic3—102no—
145#208—102no—
146#208—102no—
147C2×C3⋊C8—102no—
148C23×C5C2×#6711yescharacteristic
149C5×Q8—24no—
150C5×Q8—42no—
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—22no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—42no—
159C2×C4×C5C2×Dic611yescharacteristic
160C2×C4×C5#23511yescharacteristic
161C2×C4×C5D3×D412yes—
162C2×C4×C5#23712yes—
163C2×Dic5—62no—
164C2×Dic5—62no—
165Dic10—242no—
166#168—122no—
167C22×Q8C2×D1511yescharacteristic
168C2×M16—152no—
169C4⋊Q8—302no—
170#125—302no—
171C22⋊Q8—302no—
172#117—152no—
173C2×C4⋊C4C2×D1511yescharacteristic
174C2×C42C2×D1511yescharacteristic
175#103—302no—
176#103—302no—
177#95—22no—
178C2×C3×C5—21no—
179C2×C3×C5—21no—
180C2×C3×C5#39311yescharacteristic
181C2×C3×C5#45511yescharacteristic
182C2×C3×C5#45611yescharacteristic
183C23×C3C2×C22⋊D511yescharacteristic
184C3×Q8—24no—
185C3×Q8—42no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—42no—
194C2×C3×C4C2×Dic1011yescharacteristic
195C2×C3×C4#70911yescharacteristic
196C2×C3×C4D4×D512yes—
197C2×C3×C4#71112yes—
198C2×Dic3—102no—
199C2×Dic3—102no—
200Dic6—402no—
201C3⋊C8—202no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#92411yescharacteristic
205C22×C5#93611yescharacteristic
206C22×C5#93711yescharacteristic
207C4×C5—42no—
208C4×C5—42no—
209C4×C5—42no—
210C4×C5#87812yes—
211C4×C5#88512yes—
212Dic5—122no—
213Dic5—122no—
214C2×Q8—21no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—302no—
218C2×Q8Dic3012yescomplemented
219C22×C4—21no—
220C22×C4—21no—
221C22×C4#122012yes—
222C22×C4C22×D1511yescharacteristic
223M16—302no—
224M16—302no—
225C2×C8—302no—
226C4⋊C4—22no—
227C4⋊C4—152no—
228C4⋊C4—152no—
229C4⋊C4—302no—
230C4⋊C4—304no—
231C22⋊C4—302no—
232C42—22no—
233C42—302no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#407011yescharacteristic
238C22×C3#408211yescharacteristic
239C22×C3#408311yescharacteristic
240C3×C4—42no—
241C3×C4—42no—
242C3×C4—42no—
243C3×C4#402412yes—
244C3×C4#403112yes—
245Dic3—202no—
246Dic3—202no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#494711yescharacteristic
250C2×C5#506111yescharacteristic
251C2×C5#509511yescharacteristic
252C23C2×#122011yescharacteristic
253Q8—24no—
254Q8—42no—
255Q8—1202no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—302no—
265C2×C4—302no—
266C2×C4C2×Dic3011yescharacteristic
267C2×C4#681711yescharacteristic
268C2×C4D4×D1512yes—
269C2×C4#681912yes—
270C8—602no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6523611yescharacteristic
274C2×C3#6535011yescharacteristic
275C2×C3#6538411yescharacteristic
276C5#6967311yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9181311yescharacteristic
280C22#9182511yescharacteristic
281C22#9182611yescharacteristic
282C4—42no—
283C4—42no—
284C4—42no—
285C4—602no—
286C4—602no—
287C4#9176712yes—
288C4#9177412yes—
289C3#1060046611yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1175104811yescharacteristic
293C2#1175116211yescharacteristic
294C2#1175119611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#391C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#391D15
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
27. C2×C3×C5×Q8Q8semidirect
94. C2×C5×Q8Dic6semidirect
131. C2×C3×Q8Dic10semidirect
218. C2×Q8Dic30semidirect
234. C3×C5#2028semidirect
276. C5#69673semidirect
289. C3#10600466semidirect

Maximal subgroups

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

subgroupindex
#117562592
C3×C5×#3912
#117513262
#117463512
#117463442
#106004663
#696735