Finite Group Databasebeta

← #14284188

Subgroups — #14284188

Order 1920.

512 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
1C3×C5×#532C211yesmaximal, characteristic
2#11751027C211yesmaximal, characteristic, complemented
3C2×#91087C211yesmaximal, characteristic, complemented
4#11746361C214yesmaximal, complemented
5#10602591—31nomaximal, Hall
6C2×C3×C5×#41C412yes—
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×C5×#127C411yescharacteristic
9C3×C5×#124C2212yes—
10C3×C5×#121—21no—
11C3×C5×#121—21no—
12C3×C4×C5×D4—21no—
13C3×C4×C5×D4—21no—
14C2×C3×C42×C5C2211yescharacteristic
15C22×C3⋊#168—21no—
16#91114—21no—
17C4⋊(C3⋊#168)—21no—
18#91087—21no—
19#91087C2212yes—
20#91087C2212yes—
21#71798—51nomaximal, Hall
22C5×#532D311yescharacteristic
23#65215—31no—
24C2×#3935—31no—
25#64760—34no—
26C3×C5×#41—44no—
27C2×C3×C5×Q8C2×C412yes—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—21no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4C2×C412yes—
32C22×C3×C4×C5—22no—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C22⋊C4—22no—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2×C411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C3×C42×C5D411yescharacteristic
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—24no—
45C2×C3⋊#168—22no—
46C2×C3⋊#168—22no—
47C3×#532D511yescharacteristic
48#4926—51no—
49C2×#803—51no—
50#4540—54no—
51C2×C5×#41Dic312yes—
52C5×C4⋊Q8Dic311yescharacteristic
53C5×#127Dic311yescharacteristic
54C5×#124C2×D312yes—
55C5×#121—21no—
56C5×#121—21no—
57C4×C5×D4—21no—
58C4×C5×D4—21no—
59C2×C42×C5C2×D311yescharacteristic
60C22×#168—61no—
61C22⋊#168—61no—
62C4⋊#168—61no—
63#3935—32no—
64#3935—32no—
65#3935—61no—
66#1530—151noSylow
67C23×C3×C5—22no—
68C23×C3×C5C22⋊C411yescharacteristic
69C3×C5×Q8—42no—
70C3×C5×D4—42no—
71C3×C5×D4—42no—
72C3×C5×D4—44no—
73C3×C5×D4—42no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—44no—
79C2×C3×C4×C5C22⋊C411yescharacteristic
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C3⋊#168—24no—
86C3⋊#168—42no—
87C2×C3×#41Dic512yes—
88C3×C4⋊Q8Dic511yescharacteristic
89C3×#127Dic511yescharacteristic
90C3×#124C2×D512yes—
91C3×#121—21no—
92C3×#121—21no—
93C3×C4×D4—21no—
94C3×C4×D4—21no—
95C2×C3×C42C2×D511yescharacteristic
96C22×C3⋊C8—101no—
97#830—101no—
98C4⋊(C3⋊C8)—101no—
99#803—52no—
100#803—52no—
101#803—101no—
102C5×#41—44no—
103C2×C5×Q8C2×Dic312yes—
104C2×C5×D4—22no—
105C2×C5×D4—21no—
106C2×C5×D4—21no—
107C2×C5×D4C2×Dic312yes—
108C22×C4×C5—22no—
109C22×C4×C5C2×Dic311yescharacteristic
110C22×C4×C5#6711yescharacteristic
111C22×C4×C5#6711yescharacteristic
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—22no—
116C42×C5C2×Dic311yescharacteristic
117C42×C5#6711yescharacteristic
118C42×C5#6711yescharacteristic
119C42×C5C22×D311yescharacteristic
120C2×#168—64no—
121C2×#168—62no—
122C2×#168—62no—
123#532D1511yescharacteristic
124#432—151no—
125C2×#97—151no—
126#329—154no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5—42no—
130C22×C3×C5—42no—
131C22×C3×C5—42no—
132C22×C3×C5#10012yes—
133C22×C3×C5C2×C22⋊C411yescharacteristic
134C3×C4×C5—21no—
135C3×C4×C5—21no—
136C3×C4×C5—21no—
137C3×C4×C5—21no—
138C3×C4×C5—21no—
139C3×C4×C5—42no—
140C3×C4×C5#10412yes—
141C3×#41—44no—
142C2×C3×Q8C2×Dic512yes—
143C2×C3×D4—22no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4C2×Dic512yes—
147C22×C3×C4—22no—
148C22×C3×C4C2×Dic511yescharacteristic
149C22×C3×C4C22⋊D511yescharacteristic
150C22×C3×C4C22⋊D511yescharacteristic
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—22no—
155C3×C42C2×Dic511yescharacteristic
156C3×C42C22⋊D511yescharacteristic
157C3×C42C22⋊D511yescharacteristic
158C3×C42C22×D511yescharacteristic
159C2×C3⋊C8—104no—
160C2×C3⋊C8—102no—
161C2×C3⋊C8—102no—
162C23×C5—22no—
163C23×C5#21711yescharacteristic
164C5×Q8—42no—
165C5×D4—42no—
166C5×D4—42no—
167C5×D4—44no—
168C5×D4—42no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—22no—
172C2×C4×C5—41no—
173C2×C4×C5—44no—
174C2×C4×C5#21711yescharacteristic
175C2×C4×C5#21711yescharacteristic
176C2×C4×C5#21711yescharacteristic
177C2×C4×C5C22×Dic311yescharacteristic
178C2×C4×C5C2×#6711yescharacteristic
179C2×C4×C5C2×#6711yescharacteristic
180#168—64no—
181#168—122no—
182C2×#41Dic1512yes—
183C22×C8—301no—
184C4⋊Q8Dic1511yescharacteristic
185#127Dic1511yescharacteristic
186#124C2×D1512yes—
187#121—21no—
188#121—21no—
189C4×D4—21no—
190C4×D4—21no—
191C2×C42C2×D1511yescharacteristic
192C4⋊C8—301no—
193C22⋊C8—301no—
194#97—152no—
195#97—152no—
196#97—301no—
197C2×C3×C5—22no—
198C2×C3×C5—82no—
199C2×C3×C5C2×#10011yescharacteristic
200C2×C3×C5C2×#10411yescharacteristic
201C2×C3×C5#42111yescharacteristic
202C23×C3—22no—
203C23×C3C22⋊Dic511yescharacteristic
204C3×Q8—42no—
205C3×D4—42no—
206C3×D4—42no—
207C3×D4—44no—
208C3×D4—42no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—41no—
213C2×C3×C4—44no—
214C2×C3×C4C22⋊Dic511yescharacteristic
215C2×C3×C4C22⋊Dic511yescharacteristic
216C2×C3×C4C22⋊Dic511yescharacteristic
217C2×C3×C4C22×Dic511yescharacteristic
218C2×C3×C4C2×C22⋊D511yescharacteristic
219C2×C3×C4C2×C22⋊D511yescharacteristic
220C3⋊C8—104no—
221C3⋊C8—202no—
222C22×C5—21no—
223C22×C5—21no—
224C22×C5—42no—
225C22×C5—42no—
226C22×C5—42no—
227C22×C5#83312yes—
228C22×C5C2×#21711yescharacteristic
229C4×C5—21no—
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—42no—
235C4×C5#83712yes—
236#41—44no—
237C2×Q8C2×Dic1512yes—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C2×Dic1512yes—
242C22×C4—22no—
243C22×C4C2×Dic1511yescharacteristic
244C22×C4#122011yescharacteristic
245C22×C4#122011yescharacteristic
246C2×C8—304no—
247C2×C8—302no—
248C2×C8—302no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C42C2×Dic1511yescharacteristic
254C42#122011yescharacteristic
255C42#122011yescharacteristic
256C42C22×D1511yescharacteristic
257C3×C5#153011yescharacteristic, complemented, Hall
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3#396512yes—
264C22×C3C2×C22⋊Dic511yescharacteristic
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—42no—
271C3×C4#396912yes—
272C2×C5—22no—
273C2×C5—82no—
274C2×C5C2×#83311yescharacteristic
275C2×C5C2×#83711yescharacteristic
276C2×C5#523611yescharacteristic
277C23—22no—
278C23#671911yescharacteristic
279Q8—42no—
280D4—42no—
281D4—42no—
282D4—44no—
283D4—42no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—44no—
289C2×C4#671911yescharacteristic
290C2×C4#671911yescharacteristic
291C2×C4#671911yescharacteristic
292C2×C4C22×Dic1511yescharacteristic
293C2×C4C2×#122011yescharacteristic
294C2×C4C2×#122011yescharacteristic
295C8—304no—
296C8—602no—
297C2×C3—22no—
298C2×C3—82no—
299C2×C3C2×#396511yescharacteristic
300C2×C3C2×#396911yescharacteristic
301C2×C3#6552511yescharacteristic
302C5#7179811yescharacteristic, complemented, Sylow
303C22—21no—
304C22—21no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22#9111712yes—
309C22C2×#671911yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4#9112112yes—
317C3#1060259111yescharacteristic, complemented, Sylow
318C2—22no—
319C2—82no—
320C2C2×#9111711yescharacteristic
321C2C2×#9112111yescharacteristic
322C2#1175133711yescharacteristic
subgroupG/H
centerC22C2×#6719
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#532C2
socleC22×C3×C5C2×C22⋊C4
cosocleC3×C42×C5C23
hypercenter#532D15
hypocenterC3×C5#1530
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
2. #11751027C2semidirect
3. C2×#91087C2semidirect
4. #11746361C2semidirect
257. C3×C5#1530semidirect
302. C5#71798semidirect
317. C3#10602591semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5322
#117510272
C2×#910872
#117463612
#106025913
#717985