Finite Group Databasebeta

← #14280939

Subgroups — #14280939

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4033C211yesmaximal, characteristic
2#11748316C212yesmaximal
3#11746349C211yesmaximal, characteristic
4C5×#4528C211yesmaximal, characteristic
5#11745951C212yesmaximal
6#10598918—31nomaximal, Hall
7C22×C3×Dic10C411yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C3×#683C411yescharacteristic
10C2×C3×#683C2211yescharacteristic
11C2×C3×C4×Dic5C411yescharacteristic
12C2×C3×C4×Dic5C411yescharacteristic
13C2×C3×C4×Dic5C2211yescharacteristic
14C3×#4033—22no—
15C3×#4033—22no—
16#91114C2212yes—
17C5×#830C2212yes—
18#90982—22no—
19Dic5×C3⋊C8—22no—
20#71624—51nomaximal, Hall
21C2×#4033D311yescharacteristic
22#65007—32no—
23C5×#324—31no—
24#64748—31no—
25#64689—32no—
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×C3×Dic5C2×C411yescharacteristic
30C22×C3×Dic5C2×C411yescharacteristic
31C22×C3×Dic5C2×C411yescharacteristic
32C22×C3×Dic5C2×C411yescharacteristic
33C2×C3×Dic10—22no—
34C2×C3×Dic10—22no—
35C2×C3×Dic10C814yescomplemented
36C3×C5×C4⋊C4—22no—
37C2×C3⋊#168—22no—
38C2×C5×C3⋊C8—22no—
39C3×#683—22no—
40C3×#683—22no—
41C3×C4×Dic5—21no—
42C3×C4×Dic5—21no—
43C3×C4×Dic5—21no—
44C3×C4×Dic5—21no—
45C3×C4×Dic5D412yes—
46C3×C4×Dic5D412yes—
47C2×C3×C4×Q8—51no—
48#4925—52no—
49#4528—51no—
50#4528—52no—
51#4528D511yescharacteristic
52C22×Dic10Dic311yescharacteristic
53C2×C5×C4⋊C4C2×D311yescharacteristic
54C2×#683Dic311yescharacteristic
55C2×#683C2×D311yescharacteristic
56C2×C4×Dic5Dic311yescharacteristic
57C2×C4×Dic5Dic311yescharacteristic
58C2×C4×Dic5C2×D311yescharacteristic
59#4033—22no—
60#4033—22no—
61C5×C22⋊C8—32no—
62C22⋊#168—32no—
63#3946—62no—
64C8×Dic5—62no—
65#1461—151noSylow
66C23×C3×C5C22×C411yescharacteristic
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×C812yes—
73C2×C3×C4×C5C2×D412yes—
74C2×C3×Dic5—21no—
75C2×C3×Dic5—21no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—21no—
78C2×C3×Dic5—41no—
79C2×C3×Dic5C22⋊C411yescharacteristic
80C2×C3×Dic5C22⋊C412yes—
81C2×C3×Dic5C22⋊C411yescharacteristic
82C2×C3×Dic5C2×C812yes—
83C2×C3×Dic5C2×C812yes—
84C2×C3×Dic5M1612yes—
85C3×Dic10—28no—
86C3⋊#168—42no—
87C5×C3⋊C8—42no—
88C22×C3×Q8—51no—
89C3×C4×Q8—102no—
90C3×C4×Q8—102no—
91C2×C3×C4⋊C4—51no—
92C2×C3×C4⋊C4—51no—
93C2×C3×C4⋊C4C2×D511yescharacteristic
94C2×C3×C42—51no—
95C2×C3×C42—51no—
96C2×C3×C42—51no—
97#830—52no—
98#830C2×D512yes—
99C4⋊(C3⋊C8)—102no—
100C4×C3⋊C8—102no—
101C22×C4×C5C2×Dic311yescharacteristic
102C22×C4×C5C2×Dic311yescharacteristic
103C22×C4×C5C22×D311yescharacteristic
104C22×Dic5C2×Dic311yescharacteristic
105C22×Dic5C2×Dic311yescharacteristic
106C22×Dic5C2×Dic311yescharacteristic
107C22×Dic5C2×Dic311yescharacteristic
108C2×Dic10—22no—
109C2×Dic10—22no—
110C2×Dic10C3⋊C814yescomplemented
111C2×C5×C8—62no—
112C5×C4⋊C4—22no—
113#683—22no—
114#683—22no—
115C4×Dic5—21no—
116C4×Dic5—21no—
117C4×Dic5—21no—
118C4×Dic5—21no—
119C4×Dic5#6712yes—
120C4×Dic5#6712yes—
121C2×#168—62no—
122C2×C4×Q8—51no—
123#431—152no—
124#324—31no—
125#324—152no—
126#324—151no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C22×C3×C5C22×C811yescharacteristic
131C22×C3×C5C2×M1611yescharacteristic
132C3×C4×C5—22no—
133C3×C4×C5—22no—
134C3×C4×C5—41no—
135C3×Dic5—22no—
136C3×Dic5—21no—
137C3×Dic5—41no—
138C3×Dic5C22⋊C814yes—
139C3×Dic5#10112yes—
140C2×C3×Q8—54no—
141C2×C3×Q8—102no—
142C2×C3×Q8—102no—
143C22×C3×C4—51no—
144C22×C3×C4—51no—
145C22×C3×C4—51no—
146C22×C3×C4—51no—
147C22×C3×C4C4×D511yescharacteristic
148C22×C3×C4C4×D511yescharacteristic
149C22×C3×C4C22×D511yescharacteristic
150C3×C4⋊C4—22no—
151C3×C4⋊C4—102no—
152C3×C4⋊C4—102no—
153C3×C42—52no—
154C3×C42—52no—
155C3×C42—101no—
156C3×C42—101no—
157C3×C42—101no—
158C3×C42—101no—
159C2×C3⋊C8—22no—
160C2×C3⋊C8—102no—
161C23×C5C22×Dic311yescharacteristic
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5C2×C3⋊C812yes—
168C2×C4×C5C2×#6712yes—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—22no—
172C2×Dic5—21no—
173C2×Dic5—41no—
174C2×Dic5C2×C3⋊C812yes—
175C2×Dic5C2×C3⋊C812yes—
176C2×Dic5#20812yes—
177C2×Dic5#21711yescharacteristic
178C2×Dic5#21712yes—
179C2×Dic5#21711yescharacteristic
180Dic10—28no—
181C5×C8—122no—
182#168—122no—
183C22×Q8—51no—
184C4×Q8—102no—
185C4×Q8—102no—
186C2×C4⋊C4—51no—
187C2×C4⋊C4—51no—
188C2×C4⋊C4D3×D511yescharacteristic
189C2×C42—51no—
190C2×C42—51no—
191C2×C42—51no—
192C4⋊C8—302no—
193C22⋊C8—32no—
194C22⋊C8—152no—
195C4×C8—302no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5C2×C22⋊C811yescharacteristic
199C2×C3×C5#41011yescharacteristic
200C2×C3×C5C2×#10111yescharacteristic
201C23×C3C2×C4×D511yescharacteristic
202C3×Q8—108no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—51no—
209C2×C3×C4—52no—
210C2×C3×C4—52no—
211C2×C3×C4—52no—
212C2×C3×C4—51no—
213C2×C3×C4—52no—
214C2×C3×C4—102no—
215C2×C3×C4—101no—
216C2×C3×C4—101no—
217C2×C3×C4—101no—
218C2×C3×C4—201no—
219C2×C3×C4C8×D512yes—
220C2×C3×C4D4×D512yes—
221C3⋊C8—42no—
222C3⋊C8—202no—
223C22×C5—21no—
224C22×C5—21no—
225C22×C5C22×C3⋊C811yescharacteristic
226C22×C5C2×#20811yescharacteristic
227C22×C5C2×#21711yescharacteristic
228C4×C5—22no—
229C4×C5—22no—
230C4×C5—41no—
231Dic5—22no—
232Dic5—21no—
233Dic5—41no—
234Dic5#83014yes—
235Dic5#83612yes—
236C2×Q8—54no—
237C2×Q8—102no—
238C2×Q8—102no—
239C22×C4—51no—
240C22×C4—51no—
241C22×C4—51no—
242C22×C4—51no—
243C22×C4D5×Dic311yescharacteristic
244C22×C4D5×Dic311yescharacteristic
245C22×C4C2×D3×D511yescharacteristic
246C2×C8—62no—
247C2×C8—302no—
248C4⋊C4—22no—
249C4⋊C4—102no—
250C4⋊C4—102no—
251C42—52no—
252C42—52no—
253C42—101no—
254C42—101no—
255C42—101no—
256C42—101no—
257C3×C5#146111yescharacteristic, complemented, Hall
258C22×C3—21no—
259C22×C3—21no—
260C22×C3D5×C22⋊C411yescharacteristic
261C22×C3C2×C8×D511yescharacteristic
262C22×C3D5×M1611yescharacteristic
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—41no—
266C3×C4—52no—
267C3×C4—54no—
268C3×C4—101no—
269C3×C4—102no—
270C3×C4—201no—
271C2×C5—21no—
272C2×C5—21no—
273C2×C5C2×#83011yescharacteristic
274C2×C5C2×#83611yescharacteristic
275C2×C5#524011yescharacteristic
276C23C2×D5×Dic311yescharacteristic
277Q8—108no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—52no—
284C2×C4—52no—
285C2×C4—51no—
286C2×C4—52no—
287C2×C4—52no—
288C2×C4—51no—
289C2×C4—102no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—101no—
293C2×C4—201no—
294C2×C4D5×C3⋊C812yes—
295C2×C4D5×#6712yes—
296C8—122no—
297C8—602no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3D5×C22⋊C811yescharacteristic
301C2×C3#6502911yescharacteristic
302C2×C3D5×#10111yescharacteristic
303C5#7162411yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22C2×D5×C3⋊C811yescharacteristic
307C22D5×#20811yescharacteristic
308C22D5×#21711yescharacteristic
309C4—22no—
310C4—22no—
311C4—41no—
312C4—54no—
313C4—52no—
314C4—102no—
315C4—101no—
316C4—201no—
317C3#1059891811yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2D5×#83011yescharacteristic
321C2#1174917211yescharacteristic
322C2D5×#83611yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1461
LCSG ▷ C22×C3×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
35. C2×C3×Dic10C8semidirect
110. C2×Dic10C3⋊C8semidirect
257. C3×C5#1461semidirect
303. C5#71624semidirect
317. C3#10598918semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40332
#117483162
#117463492
C5×#45282
#117459512
#105989183
#716245