Finite Group Databasebeta

← #14308952

Subgroups — #14308952

Order 1920.

492 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 117 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
2#11751221C212yesmaximal
3#11751074C211yesmaximal, characteristic
4C3×C5×#343C211yesmaximal, characteristic
5#11746376C212yesmaximal
6#10599791—31nomaximal, Hall
7C22×Dic30C2211yescharacteristic
8C2×C3×C5×M16C2212yes—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10#91815C2212yes—
11#91813—22no—
12C2×C4×Dic15C2211yescharacteristic
13#91779—22no—
14#91777—22no—
15#91115—22no—
16#91100—22no—
17#91100—22no—
18#68998—51nomaximal, Hall
19#65834—31no—
20#65409—32no—
21#65263—31no—
22C5×#343D311yescharacteristic
23#64775—32no—
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C22×Dic15—21no—
27C22×Dic15—21no—
28C2×Dic30—22no—
29C2×Dic30—22no—
30C2×Dic30—21no—
31C2×Dic30—22no—
32C2×Dic30Q812yescomplemented
33C3×C5×M16—22no—
34C3×C5×M16—22no—
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—22no—
37#6719—22no—
38C4⋊Dic15—22no—
39C4⋊Dic15D412yes—
40C4⋊Dic15D412yes—
41#6712—24no—
42C4×Dic15—22no—
43C4×Dic15—22no—
44#5500—51no—
45#5120—52no—
46#4973—51no—
47C3×#343D511yescharacteristic
48#4555—52no—
49C22×Dic10—31no—
50C2×C5×M16C2×D312yes—
51C2×C5×C4⋊C4C2×D311yescharacteristic
52#4072—32no—
53#4070—62no—
54C2×C4×Dic5—31no—
55#4036—62no—
56#4034—62no—
57#3963—62no—
58#3948—62no—
59#3948—62no—
60#2028—151noSylow
61C23×C3×C5C2×D411yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5C2×D412yes—
65C2×C3×C4×C5C2×Q811yescharacteristic
66C2×C3×C4×C5#4112yes—
67C2×C3×C4×C5#4111yescharacteristic
68C2×Dic15—22no—
69C2×Dic15—22no—
70C2×Dic15—22no—
71C2×Dic15—22no—
72C2×Dic15—41no—
73C2×Dic15—41no—
74C2×Dic15—41no—
75C2×Dic15—41no—
76Dic30—24no—
77Dic30—42no—
78Dic30—82no—
79C3×C5×C8—42no—
80C22×Dic6—51no—
81C2×C3×M16C2×D512yes—
82C2×C3×C4⋊C4C2×D511yescharacteristic
83#926—52no—
84#924—102no—
85C2×C4×Dic3—51no—
86#890—102no—
87#888—102no—
88C3⋊#95—102no—
89#816—102no—
90#816—102no—
91C22×C4×C5D1212yes—
92C22×C4×C5C22×D311yescharacteristic
93C22×Dic5—61no—
94C22×Dic5—61no—
95C2×Dic10—32no—
96C2×Dic10—62no—
97C2×Dic10—62no—
98C2×Dic10—61no—
99C2×Dic10—62no—
100C5×M16—22no—
101C5×M16—22no—
102C2×C5×C8—22no—
103C5×C4⋊C4—22no—
104C22⋊Dic5—62no—
105C4⋊Dic5—32no—
106C4⋊Dic5—32no—
107C4⋊Dic5—62no—
108#683—64no—
109C4×Dic5—62no—
110C4×Dic5—62no—
111#544—151no—
112#419—152no—
113#391—151no—
114#343D1511yescharacteristic
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×C5C22⋊Q812yes—
123C3×C4×C5#12412yes—
124Dic15—42no—
125Dic15—42no—
126Dic15—42no—
127Dic15—42no—
128C22×C3×C4D2012yes—
129C22×C3×C4C22×D511yescharacteristic
130C22×Dic3—101no—
131C22×Dic3—101no—
132C2×Dic6—52no—
133C2×Dic6—102no—
134C2×Dic6—102no—
135C2×Dic6—101no—
136C2×Dic6—102no—
137C3×M16—22no—
138C3×M16—22no—
139C2×C3×C8—22no—
140C3×C4⋊C4—22no—
141#217—102no—
142C4⋊Dic3—52no—
143C4⋊Dic3—52no—
144C4⋊Dic3—102no—
145Dic3⋊C4—104no—
146C4×Dic3—102no—
147C4×Dic3—102no—
148C23×C5C2×D1211yescharacteristic
149C2×C4×C5—22no—
150C2×C4×C5—42no—
151C2×C4×C5#23512yes—
152C2×C4×C5D3×D412yes—
153C2×C4×C5#23711yescharacteristic
154C2×C4×C5D3×Q811yescharacteristic
155C2×Dic5—62no—
156C2×Dic5—62no—
157C2×Dic5—62no—
158C2×Dic5—62no—
159C2×Dic5—121no—
160C2×Dic5—121no—
161C2×Dic5—121no—
162C2×Dic5—121no—
163Dic10—64no—
164Dic10—122no—
165Dic10—242no—
166C5×C8—42no—
167C22×Q8—151no—
168C2×M16C2×D1512yes—
169C4⋊Q8—302no—
170#125—302no—
171C22⋊Q8—302no—
172#117—152no—
173C2×C4⋊C4C2×D1511yescharacteristic
174C2×C42—151no—
175#103—302no—
176#103—302no—
177#95—302no—
178C2×C3×C5—21no—
179C2×C3×C5—21no—
180C2×C3×C5#39311yescharacteristic
181C2×C3×C5#45511yescharacteristic
182C2×C3×C5#45611yescharacteristic
183C23×C3C2×D2011yescharacteristic
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4#70912yes—
187C2×C3×C4D4×D512yes—
188C2×C3×C4#71111yescharacteristic
189C2×C3×C4Q8×D511yescharacteristic
190C2×Dic3—102no—
191C2×Dic3—102no—
192C2×Dic3—102no—
193C2×Dic3—102no—
194C2×Dic3—201no—
195C2×Dic3—201no—
196C2×Dic3—201no—
197C2×Dic3—201no—
198Dic6—104no—
199Dic6—202no—
200Dic6—402no—
201C3×C8—42no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#87511yescharacteristic
205C22×C5#88211yescharacteristic
206C22×C5#89711yescharacteristic
207C4×C5—42no—
208C4×C5#88512yes—
209C4×C5#89612yes—
210Dic5—122no—
211Dic5—122no—
212Dic5—122no—
213Dic5—122no—
214C2×Q8—152no—
215C2×Q8—302no—
216C2×Q8—301no—
217C2×Q8—302no—
218C2×Q8—302no—
219C22×C4—301no—
220C22×C4—301no—
221C22×C4D6012yes—
222C22×C4C22×D1511yescharacteristic
223M16—22no—
224M16—22no—
225C2×C8—22no—
226C4⋊C4—22no—
227C4⋊C4—152no—
228C4⋊C4—152no—
229C4⋊C4—302no—
230C4⋊C4—304no—
231C22⋊C4—302no—
232C42—302no—
233C42—302no—
234C3×C5#202811yescharacteristic, complemented, Hall
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#402111yescharacteristic
238C22×C3#402811yescharacteristic
239C22×C3#404311yescharacteristic
240C3×C4—42no—
241C3×C4#403112yes—
242C3×C4#404212yes—
243Dic3—202no—
244Dic3—202no—
245Dic3—202no—
246Dic3—202no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#467311yescharacteristic
250C2×C5#474611yescharacteristic
251C2×C5#475211yescharacteristic
252C23C2×D6011yescharacteristic
253Q8—304no—
254Q8—602no—
255Q8—1202no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—302no—
259C2×C4—302no—
260C2×C4—302no—
261C2×C4—302no—
262C2×C4—601no—
263C2×C4—601no—
264C2×C4—601no—
265C2×C4—601no—
266C2×C4#681712yes—
267C2×C4D4×D1512yes—
268C2×C4#681911yescharacteristic
269C2×C4Q8×D1511yescharacteristic
270C8—42no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6496211yescharacteristic
274C2×C3#6503511yescharacteristic
275C2×C3#6504111yescharacteristic
276C5#6899811yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9176411yescharacteristic
280C22#9177111yescharacteristic
281C22#9178611yescharacteristic
282C4—42no—
283C4—602no—
284C4—602no—
285C4—602no—
286C4—602no—
287C4#9177412yes—
288C4#9178512yes—
289C3#1059979111yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1175077411yescharacteristic
293C2#1175084711yescharacteristic
294C2#1175085311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#343C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#343D15
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
32. C2×Dic30Q8semidirect
234. C3×C5#2028semidirect
276. C5#68998semidirect
289. C3#10599791semidirect

Maximal subgroups

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

subgroupindex
#117562592
#117512212
#117510742
C3×C5×#3432
#117463762
#105997913
#689985