Finite Group Databasebeta

← #14308961

Subgroups — #14308961

Order 1920.

492 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 120 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×#65834C211yesmaximal, characteristic
2C5×#4973C211yesmaximal, characteristic
3#11748407C212yesmaximal
4#11746351C211yesmaximal, characteristic
5#11745974C212yesmaximal
6#10600466—31nomaximal, Hall
7C22×C5×Dic6C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6710C2212yes—
10C2×C4×C5×Dic3C2211yescharacteristic
11C3×#4072C2212yes—
12C3×#4070—22no—
13C3×#4036—22no—
14C3×#4034—22no—
15C5×C3⋊#95—22no—
16#90972—22no—
17#90972—22no—
18#71905—51nomaximal, Hall
19#65834D311yescharacteristic
20C5×#391—31no—
21#65514—32no—
22#64750—31no—
23#64743—32no—
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5C2311yescharacteristic
26C22×C5×Dic3—21no—
27C22×C5×Dic3—21no—
28C2×C5×Dic6—22no—
29C2×C5×Dic6—22no—
30C2×C5×Dic6—21no—
31C2×C5×Dic6Q812yescomplemented
32C2×C3×Dic10—22no—
33C3×C5×C4⋊C4—22no—
34#6710—22no—
35#6710—22no—
36C2×C3⋊#168—22no—
37C4×C5×Dic3—22no—
38C3×C22⋊Dic5—22no—
39C3×C4⋊Dic5—22no—
40C3×C4⋊Dic5D412yes—
41C3×C4⋊Dic5D412yes—
42C3×#683—24no—
43C3×C4×Dic5—22no—
44C3×#544—51no—
45#5004—52no—
46#4973D511yescharacteristic
47#4532—52no—
48#4530—51no—
49C22×C5×Q8—31no—
50C2×C5×C4⋊C4C2×D311yescharacteristic
51C2×C42×C5—31no—
52#4072C2×D312yes—
53#4070—22no—
54C2×#681—32no—
55#4036—22no—
56#4034—22no—
57C5×#95—62no—
58#3967—62no—
59#3967—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×C5×Dic3—22no—
69C2×C5×Dic3—22no—
70C2×C5×Dic3—41no—
71C2×C5×Dic3—41no—
72C2×C5×Dic3—41no—
73C2×C5×Dic3—41no—
74C5×Dic6—24no—
75C5×Dic6—42no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—22no—
78C3×Dic10—82no—
79C3⋊#168—42no—
80C22×Dic6C2×D511yescharacteristic
81C3×C4⋊Q8—102no—
82C3×#125—102no—
83C3×C22⋊Q8—102no—
84C3×#117—52no—
85C2×C3×C4⋊C4C2×D511yescharacteristic
86C2×C4×Dic3C2×D511yescharacteristic
87C2×#208—52no—
88C3⋊#95—22no—
89#810—102no—
90#810—102no—
91C2×C5×Q8—32no—
92C2×C5×Q8—61no—
93C2×C5×Q8—62no—
94C2×C5×Q8—62no—
95C22×C4×C5—61no—
96C22×C4×C5—61no—
97C22×C4×C5#6712yes—
98C22×C4×C5C22×D311yescharacteristic
99C2×Dic10—22no—
100C5×C4⋊C4—22no—
101C42×C5—62no—
102C22⋊Dic5—22no—
103C4⋊Dic5—22no—
104C4⋊Dic5#6712yes—
105C4⋊Dic5#6712yes—
106#683—24no—
107C4×Dic5—22no—
108#681—62no—
109#681—62no—
110C2×#168—62no—
111#544—51no—
112#419—152no—
113#391—31no—
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×C5C22⋊Q812yes—
123C3×C4×C5#12412yes—
124C3×Dic5—42no—
125C3×Dic5—42no—
126C5×Dic3—42no—
127C5×Dic3—42no—
128C2×C3×Q8—102no—
129C22×C3×C4C22⋊D512yes—
130C22×C3×C4C22×D511yescharacteristic
131C22×Dic3—21no—
132C22×Dic3—21no—
133C2×Dic6—22no—
134C2×Dic6—22no—
135C2×Dic6—21no—
136C2×Dic6Dic1012yescomplemented
137C3×C4⋊C4—22no—
138C3×C4⋊C4—52no—
139C3×C4⋊C4—52no—
140C3×C4⋊C4—104no—
141C3×C4⋊C4—102no—
142C3×C22⋊C4—102no—
143C3×C42—102no—
144C4×Dic3—22no—
145#208—102no—
146#208—102no—
147C2×C3⋊C8—102no—
148C23×C5C2×#6711yescharacteristic
149C5×Q8—64no—
150C5×Q8—122no—
151C2×C4×C5—22no—
152C2×C4×C5—42no—
153C2×C4×C5—62no—
154C2×C4×C5—62no—
155C2×C4×C5—121no—
156C2×C4×C5—121no—
157C2×C4×C5—121no—
158C2×C4×C5—121no—
159C2×C4×C5D3×Q811yescharacteristic
160C2×C4×C5#23912yes—
161C2×C4×C5#23911yescharacteristic
162C2×C4×C5C2×#6712yes—
163C2×Dic5—22no—
164C2×Dic5—22no—
165Dic10—82no—
166#168—122no—
167C22×Q8—31no—
168C2×M16—152no—
169C4⋊Q8—102no—
170#125—102no—
171C22⋊Q8—102no—
172#117—52no—
173C2×C4⋊C4D3×D511yescharacteristic
174C2×C42—31no—
175#103—302no—
176#103—302no—
177#95—62no—
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—402no—
185C2×C3×C4—22no—
186C2×C3×C4—42no—
187C2×C3×C4—102no—
188C2×C3×C4—102no—
189C2×C3×C4C2×Dic1011yescharacteristic
190C2×C3×C4#70911yescharacteristic
191C2×C3×C4D4×D512yes—
192C2×C3×C4#71112yes—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—41no—
196C2×Dic3—41no—
197C2×Dic3—41no—
198C2×Dic3—41no—
199Dic6—24no—
200Dic6—42no—
201C3⋊C8—202no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#94611yescharacteristic
205C22×C5#94711yescharacteristic
206C22×C5#95311yescharacteristic
207C4×C5—42no—
208C4×C5—122no—
209C4×C5—122no—
210C4×C5#94612yes—
211C4×C5#94712yes—
212Dic5—42no—
213Dic5—42no—
214C2×Q8—32no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8—62no—
218C2×Q8—102no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4#120112yes—
222C22×C4C2×D3×D511yescharacteristic
223M16—302no—
224M16—302no—
225C2×C8—302no—
226C4⋊C4—22no—
227C4⋊C4—52no—
228C4⋊C4—52no—
229C4⋊C4—102no—
230C4⋊C4—104no—
231C22⋊C4—102no—
232C42—62no—
233C42—102no—
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—202no—
242C3×C4—202no—
243C3×C4#402412yes—
244C3×C4#403112yes—
245Dic3—42no—
246Dic3—42no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5#523111yescharacteristic
250C2×C5#524211yescharacteristic
251C2×C5#524611yescharacteristic
252C23C2×#120111yescharacteristic
253Q8—64no—
254Q8—122no—
255Q8—402no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—62no—
259C2×C4—62no—
260C2×C4—102no—
261C2×C4—102no—
262C2×C4—121no—
263C2×C4—121no—
264C2×C4—121no—
265C2×C4—121no—
266C2×C4D3×Dic1011yescharacteristic
267C2×C4#676812yes—
268C2×C4#676911yescharacteristic
269C2×C4D5×#6712yes—
270C8—602no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#6523611yescharacteristic
274C2×C3#6535011yescharacteristic
275C2×C3#6538411yescharacteristic
276C5#7190511yescharacteristic, complemented, Sylow
277C22—21no—
278C22—21no—
279C22#9136911yescharacteristic
280C22#9137011yescharacteristic
281C22#9156311yescharacteristic
282C4—42no—
283C4—122no—
284C4—122no—
285C4—202no—
286C4—202no—
287C4#9132612yes—
288C4#9141012yes—
289C3#1060046611yescharacteristic, complemented, Sylow
290C2—21no—
291C2—21no—
292C2#1174874611yescharacteristic
293C2#1174914411yescharacteristic
294C2#1174939011yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2028
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. C2×C5×Dic6Q8semidirect
136. C2×Dic6Dic10semidirect
234. C3×C5#2028semidirect
276. C5#71905semidirect
289. C3#10600466semidirect

Maximal subgroups

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

subgroupindex
C3×#658342
C5×#49732
#117484072
#117463512
#117459742
#106004663
#719055