Finite Group Databasebeta

← #14301485

Subgroups — #14301485

Order 1920.

648 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C3×C5×#519C211yesmaximal, characteristic
2C2×#91833C211yesmaximal, characteristic
3C2×#91120C211yesmaximal, characteristic
4#11751105C212yesmaximal
5#11746353C212yesmaximal
6#10602453—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×Dic30C2211yescharacteristic
9C3×C4×C5×Q8—24no—
10C3×C5×#117—22no—
11C3×C5×#117C2212yes—
12#91833—22no—
13#91833C414yescomplemented
14C2×#6712—22no—
15C2×C4×Dic15C2211yescharacteristic
16C2×#6710C2212yes—
17#91120—22no—
18#91094—24no—
19#71660—51nomaximal, Hall
20C5×#519D311yescharacteristic
21C2×#4090—31no—
22C2×#3968—31no—
23#65293—32no—
24#64752—32no—
25C2×C3×C5×Q8—22no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8C2×C412yes—
28C2×C3×C5×Q8D412yes—
29C22×C3×C4×C5D412yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—21no—
32C22×Dic15—21no—
33C2×Dic30—22no—
34C2×Dic30—22no—
35C2×Dic30—21no—
36C2×Dic30C2×C412yes—
37C3×C5×C4⋊C4—24no—
38C3×C5×C4⋊C4D414yes—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5—24no—
41C3×C42×C5—22no—
42#6712—28no—
43C4×Dic15—21no—
44C4×Dic15C2×C412yes—
45#6710—22no—
46#6710—22no—
47C2×C3⋊#168—22no—
48C3×#519D511yescharacteristic
49C2×#944—51no—
50C2×#836—51no—
51#5004—52no—
52#4532—52no—
53C22×C5×Q8C2×D311yescharacteristic
54C22×Dic10—31no—
55C4×C5×Q8—24no—
56C5×#117—22no—
57C5×#117C2×D312yes—
58#4090—34no—
59#4090—62no—
60C2×#683—62no—
61C2×C4×Dic5—31no—
62C2×#681—32no—
63#3968—62no—
64#3942—64no—
65#1886—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C3×C5×Q8—24no—
68C3×C5×Q8—24no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—24no—
72C2×C3×C4×C5C22⋊C414yes—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×Dic15—24no—
78C2×Dic15—22no—
79C2×Dic15—22no—
80C2×Dic15—41no—
81C2×Dic15—41no—
82Dic30—24no—
83Dic30—42no—
84C3⋊#168—42no—
85C22×C3×Q8C2×D511yescharacteristic
86C22×Dic6—51no—
87C3×C4×Q8—24no—
88C3×#117—22no—
89C3×#117C2×D512yes—
90#944—54no—
91#944—102no—
92C2×Dic3⋊C4—102no—
93C2×C4×Dic3—51no—
94C2×#208—52no—
95#836—102no—
96#810—104no—
97C2×C5×Q8—22no—
98C2×C5×Q8—22no—
99C2×C5×Q8C4×D312yes—
100C2×C5×Q8D1212yes—
101C22×C4×C5#6712yes—
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—61no—
104C22×Dic5—61no—
105C2×Dic10—32no—
106C2×Dic10—62no—
107C2×Dic10—62no—
108C2×Dic10—61no—
109C5×C4⋊C4—24no—
110C5×C4⋊C4#6714yes—
111C5×C22⋊C4—22no—
112C42×C5—24no—
113C42×C5—22no—
114#683—68no—
115C4×Dic5—32no—
116C4×Dic5—61no—
117#681—62no—
118#681—62no—
119C2×#168—62no—
120C2×C4⋊Q8—151no—
121#519D1511yescharacteristic
122#419—152no—
123C2×#101—151no—
124#339—152no—
125C22×C3×C5—22no—
126C22×C3×C5C2×C22⋊C411yescharacteristic
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5#12311yescharacteristic
129C3×C4×C5—24no—
130C3×C4×C5—44no—
131C3×C4×C5C4×D412yes—
132C3×C4×C5#12112yes—
133Dic15—24no—
134Dic15—42no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8C4×D512yes—
138C2×C3×Q8D2012yes—
139C22×C3×C4C22⋊D512yes—
140C22×C3×C4C22×D511yescharacteristic
141C22×Dic3—101no—
142C22×Dic3—101no—
143C2×Dic6—52no—
144C2×Dic6—102no—
145C2×Dic6—102no—
146C2×Dic6—101no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4C22⋊D514yes—
149C3×C22⋊C4—22no—
150C3×C42—24no—
151C3×C42—22no—
152Dic3⋊C4—108no—
153C4×Dic3—52no—
154C4×Dic3—101no—
155#208—102no—
156#208—102no—
157C2×C3⋊C8—102no—
158C23×C5C2×#6711yescharacteristic
159C5×Q8—24no—
160C5×Q8—24no—
161C2×C4×C5—22no—
162C2×C4×C5—22no—
163C2×C4×C5—24no—
164C2×C4×C5(C2×D3)⋊C414yes—
165C2×C4×C5C2×C4×D311yescharacteristic
166C2×C4×C5C2×D1211yescharacteristic
167C2×C4×C5#23512yes—
168C2×C4×C5C2×#6712yes—
169C2×Dic5—64no—
170C2×Dic5—62no—
171C2×Dic5—62no—
172C2×Dic5—121no—
173C2×Dic5—121no—
174Dic10—64no—
175Dic10—122no—
176#168—122no—
177C22×Q8—151no—
178C22×Q8C2×D1511yescharacteristic
179C2×M16—152no—
180C4⋊Q8—154no—
181C4⋊Q8—302no—
182C4×Q8—24no—
183#117—22no—
184#117C2×D1512yes—
185C2×C4⋊C4—302no—
186C2×C42—151no—
187#103—304no—
188#101—302no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#38611yescharacteristic
192C2×C3×C5#45612yes—
193C23×C3C2×C22⋊D511yescharacteristic
194C3×Q8—24no—
195C3×Q8—24no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—24no—
199C2×C3×C4#68514yes—
200C2×C3×C4C2×C4×D511yescharacteristic
201C2×C3×C4C2×D2011yescharacteristic
202C2×C3×C4#70912yes—
203C2×C3×C4C2×C22⋊D512yes—
204C2×Dic3—104no—
205C2×Dic3—102no—
206C2×Dic3—102no—
207C2×Dic3—201no—
208C2×Dic3—201no—
209Dic6—104no—
210Dic6—202no—
211C3⋊C8—202no—
212C22×C5—22no—
213C22×C5C2×(C2×D3)⋊C411yescharacteristic
214C22×C5#92911yescharacteristic
215C22×C5#95311yescharacteristic
216C4×C5—24no—
217C4×C5—44no—
218C4×C5C4×#6712yes—
219C4×C5#93012yes—
220Dic5—64no—
221Dic5—122no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—152no—
225C2×Q8—301no—
226C2×Q8—302no—
227C2×Q8—302no—
228C2×Q8C4×D1512yes—
229C2×Q8D6012yes—
230C22×C4—301no—
231C22×C4—301no—
232C22×C4#122012yes—
233C22×C4C22×D1511yescharacteristic
234M16—302no—
235M16—302no—
236C2×C8—302no—
237C4⋊C4—24no—
238C4⋊C4—308no—
239C4⋊C4#122014yes—
240C22⋊C4—22no—
241C42—24no—
242C42—22no—
243C42—152no—
244C42—301no—
245C3×C5#188611yescharacteristic, complemented, Hall
246C22×C3—22no—
247C22×C3C2×#68511yescharacteristic
248C22×C3#407511yescharacteristic
249C22×C3#409911yescharacteristic
250C3×C4—24no—
251C3×C4—44no—
252C3×C4C4×C22⋊D512yes—
253C3×C4#407612yes—
254Dic3—104no—
255Dic3—202no—
256C2×C5—21no—
257C2×C5—21no—
258C2×C5#521311yescharacteristic
259C2×C5#524612yes—
260C23C2×#122011yescharacteristic
261Q8—24no—
262Q8—24no—
263Q8—304no—
264Q8—602no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—304no—
269C2×C4—302no—
270C2×C4—302no—
271C2×C4—601no—
272C2×C4—601no—
273C2×C4#671414yes—
274C2×C4C2×C4×D1511yescharacteristic
275C2×C4C2×D6011yescharacteristic
276C2×C4#681712yes—
277C2×C4C2×#122012yes—
278C8—602no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3#6550211yescharacteristic
282C2×C3#6553512yes—
283C5#7166011yescharacteristic, complemented, Sylow
284C22—22no—
285C22C2×#671411yescharacteristic
286C22#9181811yescharacteristic
287C22#9184211yescharacteristic
288C4—24no—
289C4—44no—
290C4—304no—
291C4—602no—
292C4C4×#122012yes—
293C4#9181912yes—
294C3#1060245311yescharacteristic, complemented, Sylow
295C2—21no—
296C2—21no—
297C2#1175131411yescharacteristic
298C2#1175134712yes—
subgroupG/H
centerC22#91842
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#519C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenter#519D15
hypocenterC3×C5#1886
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
13. #91833C4semidirect
245. C3×C5#1886semidirect
283. C5#71660semidirect
294. C3#10602453semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5192
C2×#918332
C2×#911202
#117511052
#117463532
#106024533
#716605