Finite Group Databasebeta

← #14283285

Subgroups — #14283285

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2#11751312C211yesmaximal, characteristic, complemented
3C5×#5207C211yesmaximal, characteristic, complemented
4#11745955C214yesmaximal, complemented
5#10600771—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×C22⋊D5—21no—
8C22×C3×D20C411yescharacteristic, complemented
9C2×#6719—21no—
10C2×C5×#208—21no—
11C3×#4076—21no—
12C3×#4076—21no—
13C3×#4076C412yescomplemented
14C3×#4076C2212yes—
15C2×C3×#685—21no—
16C2×C3×C4⋊Dic5C411yescharacteristic, complemented
17#91115—21no—
18#91115C2212yescomplemented
19C5×#830—21no—
20C5×#830C2212yescomplemented
21#71674—51nomaximal, Hall
22C2×#4076D311yescharacteristic
23C5×#407—31no—
24#65500—31no—
25#64690—34no—
26C24×C3×C5D411yescharacteristic
27C23×C3×D5—21no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—22no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—44no—
39C22×C3×Dic5—21no—
40C2×C3×D20—21no—
41C2×C3×D20—42no—
42C2×C3×D20C2×C412yes—
43#6719—42no—
44C5×#208—42no—
45C2×C5×C3⋊C8—22no—
46C3×#685—22no—
47C3×#685—22no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5C2×C412yes—
50C2×C3×#121—51no—
51#5211—51no—
52#5207D511yescharacteristic, complemented
53#4537—54no—
54C23×C4×C5C2×D311yescharacteristic
55C22×C22⋊D5—21no—
56C22×D20Dic311yescharacteristic, complemented
57C2×C5×M16—61no—
58C2×C22⋊Dic5—61no—
59#4076—21no—
60#4076—21no—
61#4076Dic312yescomplemented
62#4076C2×D312yes—
63C2×#685—21no—
64C2×C4⋊Dic5Dic311yescharacteristic, complemented
65C5×C22⋊C8—32no—
66C5×C22⋊C8—61no—
67#3963—32no—
68#3963—61no—
69#1510—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—42no—
78C22×C3×D5—42no—
79C22×C3×D5—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—42no—
91C2×Dic15—42no—
92C2×Dic15—42no—
93C3×C22⋊D5—44no—
94C3×C22⋊D5—44no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—42no—
97C3×D20—42no—
98C3×D20—42no—
99C5×C3⋊C8—42no—
100C22×C3×D4—51no—
101C22×C3×D4—101no—
102C23×C3×C4C2×D511yescharacteristic
103C3×#121—52no—
104C3×#121—52no—
105C3×#121—101no—
106C3×#121—101no—
107C2×C3×C4⋊C4—51no—
108C2×C3×C22⋊C4—101no—
109C2×#217—101no—
110C2×#208—21no—
111C3⋊#95—52no—
112C3⋊#95—101no—
113#830—21no—
114#830C2×D512yescomplemented
115C24×C5#6711yescharacteristic
116C23×D5—21no—
117C22×C4×C5—42no—
118C22×C4×C5C2×Dic311yescharacteristic
119C22×C4×C5C2×Dic311yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C22×C4×C5#6711yescharacteristic
123C22×C4×C5C22×D311yescharacteristic
124C2×C22⋊D5—22no—
125C2×C22⋊D5—22no—
126C2×C22⋊D5—44no—
127C22×Dic5—21no—
128C22×Dic5—62no—
129C2×D20—21no—
130C2×D20—42no—
131C2×D20C2×Dic312yes—
132C5×M16—122no—
133C2×C5×C8—62no—
134C22⋊Dic5—122no—
135#685—22no—
136#685—22no—
137C4⋊Dic5—21no—
138C4⋊Dic5C2×Dic312yes—
139C2×#121—51no—
140#407—31no—
141#381—151no—
142#327—154no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—44no—
151C22×C3×C5#9912yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5AGL(1,ℤ/8)12yes—
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C2×C3×D5—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162Dic15—82no—
163C3×Dic5—42no—
164C24×C3—101no—
165C24×C3D2011yescharacteristic
166C2×C3×D4—52no—
167C2×C3×D4—102no—
168C2×C3×D4—102no—
169C2×C3×D4—101no—
170C2×C3×D4—202no—
171C2×C3×D4—204no—
172C22×C3×C4—42no—
173C22×C3×C4—101no—
174C22×C3×C4C4×D511yescharacteristic
175C22×C3×C4C4×D511yescharacteristic
176C22×C3×C4D2011yescharacteristic
177C22×C3×C4C22⋊D511yescharacteristic
178C22×C3×C4C22⋊D511yescharacteristic
179C22×C3×C4C22×D511yescharacteristic
180C22×Dic3—102no—
181C3×C4⋊C4—52no—
182C3×C4⋊C4—101no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185#217—202no—
186#208—42no—
187C2×C3⋊C8—22no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—41no—
191C23×C5#21711yescharacteristic
192C23×C5#21711yescharacteristic
193C23×C5C2×#6711yescharacteristic
194C22×D5—22no—
195C22×D5—42no—
196C22×D5—42no—
197C22×D5—42no—
198C2×C4×C5—22no—
199C2×C4×C5—22no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5#21711yescharacteristic
205C2×C4×C5#21711yescharacteristic
206C2×C4×C5C22×Dic311yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C22⋊D5—44no—
209C22⋊D5—44no—
210C2×Dic5—22no—
211C2×Dic5—42no—
212C2×Dic5—122no—
213C2×Dic5—122no—
214C2×Dic5—122no—
215D20—42no—
216D20—42no—
217C5×C8—122no—
218C22×D4—51no—
219C22×D4—101no—
220C23×C4D3×D511yescharacteristic
221C2×M16—61no—
222#121—52no—
223#121—52no—
224#121—101no—
225#121—101no—
226C2×C4⋊C4—51no—
227C2×C22⋊C4—101no—
228C2×C22⋊C4—301no—
229C22⋊C8—32no—
230C22⋊C8—61no—
231#95—152no—
232#95—301no—
233C2×C3×C5—22no—
234C2×C3×C5—22no—
235C2×C3×C5—41no—
236C2×C3×C5C2×#9911yescharacteristic
237C2×C3×C5#41811yescharacteristic
238C2×C3×C5#42111yescharacteristic
239C3×D5—82no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3—102no—
244C23×C3—202no—
245C23×C3—202no—
246C23×C3—202no—
247C23×C3#68511yescharacteristic
248C23×C3#68511yescharacteristic
249C23×C3C2×D2011yescharacteristic
250C3×D4—202no—
251C3×D4—202no—
252C3×D4—204no—
253C3×D4—204no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—102no—
261C2×C3×C4—202no—
262C2×C3×C4#68511yescharacteristic
263C2×C3×C4#68511yescharacteristic
264C2×C3×C4C2×C4×D511yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C2×Dic3—202no—
267C2×Dic3—202no—
268C2×Dic3—202no—
269C3⋊C8—42no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—44no—
278C22×C5#83412yes—
279C22×C5#93212yes—
280C22×C5C2×#21711yescharacteristic
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—42no—
284C2×D5—84no—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289Dic5—42no—
290Dic5—242no—
291C24—101no—
292C24#120211yescharacteristic
293C2×D4—52no—
294C2×D4—102no—
295C2×D4—102no—
296C2×D4—101no—
297C2×D4—202no—
298C2×D4—204no—
299C22×C4—42no—
300C22×C4—101no—
301C22×C4—302no—
302C22×C4D5×Dic311yescharacteristic
303C22×C4D5×Dic311yescharacteristic
304C22×C4#120111yescharacteristic
305C22×C4#120111yescharacteristic
306C22×C4#120211yescharacteristic
307C22×C4C2×D3×D511yescharacteristic
308M16—122no—
309C2×C8—62no—
310C4⋊C4—52no—
311C4⋊C4—101no—
312C22⋊C4—102no—
313C22⋊C4—102no—
314C22⋊C4—602no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3—202no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—404no—
328C22×C3#393812yes—
329C22×C3#405412yes—
330C22×C3C2×#68511yescharacteristic
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—202no—
336Dic3—402no—
337C2×C5—22no—
338C2×C5—22no—
339C2×C5—41no—
340C2×C5#521511yescharacteristic
341C2×C5C2×#83411yescharacteristic
342C2×C5#523611yescharacteristic
343D5—82no—
344C23—22no—
345C23—22no—
346C23—41no—
347C23—102no—
348C23—202no—
349C23—202no—
350C23—202no—
351C23#666511yescharacteristic
352C23#666511yescharacteristic
353C23C2×#120211yescharacteristic
354D4—202no—
355D4—202no—
356D4—204no—
357D4—204no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—102no—
365C2×C4—202no—
366C2×C4—602no—
367C2×C4—602no—
368C2×C4—602no—
369C2×C4#666511yescharacteristic
370C2×C4#666511yescharacteristic
371C2×C4C2×D5×Dic311yescharacteristic
372C2×C4C2×#120111yescharacteristic
373C8—122no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3—402no—
378C2×C3C2×#393811yescharacteristic
379C2×C3#6542011yescharacteristic
380C2×C3#6542811yescharacteristic
381C5#7167411yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—44no—
390C22—202no—
391C22—202no—
392C22—202no—
393C22—404no—
394C22#9099512yes—
395C22#9131212yes—
396C22C2×#666511yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—202no—
402C4—1202no—
403C3#1060077111yescharacteristic, complemented, Sylow
404C2—22no—
405C2—22no—
406C2—41no—
407C2—402no—
408C2#1174836711yescharacteristic
409C2#1174842011yescharacteristic
410C2C2×#9099511yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4076C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751312C2semidirect
3. C5×#5207C2semidirect
4. #11745955C2semidirect
8. C22×C3×D20C4semidirect
13. C3×#4076C4semidirect
16. C2×C3×C4⋊Dic5C4semidirect
18. #91115C22semidirect
20. C5×#830C22semidirect
52. #5207D5semidirect
56. C22×D20Dic3semidirect
61. #4076Dic3semidirect
64. C2×C4⋊Dic5Dic3semidirect
114. #830C2×D5semidirect
315. C3×C5#1510semidirect
381. C5#71674semidirect
403. C3#10600771semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40762
#117513122
C5×#52072
#117459552
#106007713
#716745