Finite Group Databasebeta

← #14283239

Subgroups — #14283239

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5624C211yesmaximal, characteristic
2#11748667C211yesmaximal, characteristic, complemented
3#11748337C211yesmaximal, characteristic, complemented
4#11746359C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic
7#11745956C211yesmaximal, characteristic
8#10602548—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C5×#947C411yescharacteristic, complemented
11C5×Q8×Dic3C411yescharacteristic, complemented
12C5×#930C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C5×#898—21no—
15C5×#893C411yescharacteristic, complemented
16C5×#892—21no—
17C5×#890C411yescharacteristic, complemented
18C5×#886—21no—
19C5×#67⋊C4—21no—
20C2×Dic3⋊Dic5—21no—
21C2×Dic3×Dic5—21no—
22#91115C2211yescharacteristic
23#91114C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26Dic3⋊#168—21no—
27#90953—21no—
28#68311—51nomaximal, Hall
29C5×#529—31no—
30C4×C4⋊Dic5—31no—
31#65215—31no—
32#64758—31no—
33#64758D311yescharacteristic, complemented
34#64757—31no—
35#64757—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×C5×#67—21no—
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C5×D12C2×C411yescharacteristic
43C2×C4×C5×D3—21no—
44C22×C3×Dic5—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3C2×C411yescharacteristic
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3C2×C411yescharacteristic
60C4×C5×Dic3D411yescharacteristic
61C4×C5×Dic3D411yescharacteristic
62C2×C3×#168—21no—
63Dic3⋊Dic5—24no—
64Dic3×Dic5—42no—
65#5624D511yescharacteristic
66#4719—51no—
67#4649—51no—
68C3×#328—51no—
69#4538—51no—
70#4470—51no—
71#4451—51no—
72C5×#126—61no—
73C5×#125—31no—
74C5×#124—31no—
75C5×#123—61no—
76C5×C22⋊Q8C2×D311yescharacteristic
77C5×#121—31no—
78C4×C5×Q8—31no—
79C4×C5×D4—31no—
80C4×C5×D4—61no—
81C5×#117—61no—
82C2×C42×C5—31no—
83C2×C4⋊Dic5—61no—
84C2×C4×Dic5—61no—
85#3963—31no—
86#3963C2×D311yescharacteristic
87C22⋊#168—31no—
88C22⋊#168C2×D311yescharacteristic
89C4⋊#168—61no—
90#3935—61no—
91#1509—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C5×D3—21no—
94C3×C5×Q8—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×Dic15—22no—
101C2×Dic15—41no—
102C2×Dic15—41no—
103C5×#67—41no—
104C5×#67—41no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3C22⋊C411yescharacteristic
110C2×C5×Dic3C22⋊C411yescharacteristic
111C2×C5×Dic3C22⋊C411yescharacteristic
112C2×C5×Dic3C22⋊C411yescharacteristic
113C5×D12—41no—
114C4×C5×D3—42no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C3⋊#168—41no—
119C3×#168—41no—
120C3×C22⋊Q8C2×D511yescharacteristic
121#947Dic511yescharacteristic, complemented
122Q8×Dic3Dic511yescharacteristic, complemented
123#930C2×D511yescharacteristic
124C2×Dic3⋊C4—101no—
125C2×C4×Dic3—101no—
126C2×C4×Dic3C2×D511yescharacteristic
127#898—21no—
128#893Dic511yescharacteristic, complemented
129#892—21no—
130#890Dic511yescharacteristic, complemented
131#886—21no—
132#67⋊C4—21no—
133C3×C22⋊C8—51no—
134C3×#95—51no—
135C3⋊#95—51no—
136#830—51no—
137#815—101no—
138Dic3⋊C8—101no—
139C2×C5×Q8C4×D311yescharacteristic
140C2×C5×D4—31no—
141C2×C5×D4—61no—
142C22×C4×C5—31no—
143C22×C4×C5—31no—
144C22×C4×C5—61no—
145C22×C4×C5C22×D311yescharacteristic
146C22×Dic5—21no—
147C22×Dic5—61no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—31no—
150C5×C4⋊C4—61no—
151C5×C4⋊C4—61no—
152C5×C4⋊C4—61no—
153C5×C4⋊C4C4×D311yescharacteristic
154C5×C22⋊C4—21no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C42×C5—31no—
160C42×C5—31no—
161C42×C5—31no—
162C42×C5—31no—
163C42×C5—61no—
164C4⋊Dic5—64no—
165C4×Dic5—122no—
166C2×#168—21no—
167C2×#168—61no—
168#529—31no—
169#432—151no—
170C4×C4⋊C4—151no—
171#328—51no—
172#328—151no—
173#327—151no—
174#327—151no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C5×D3—41no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—41no—
186C3×C4×C5—41no—
187Dic15—42no—
188C3×Dic5—42no—
189C5×Dic3—21no—
190C5×Dic3—21no—
191C5×Dic3—21no—
192C5×Dic3—41no—
193C5×Dic3#10412yes—
194C2×C3×Q8C2×Dic511yescharacteristic
195C22×C3×C4—101no—
196C22×C3×C4C22×D511yescharacteristic
197C2×#67—21no—
198C22×Dic3—101no—
199C22×Dic3C22⋊D511yescharacteristic
200C22×Dic3C22⋊D511yescharacteristic
201C2×D12C2×Dic511yescharacteristic
202C2×C4×D3—21no—
203C2×C3×C8—101no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4C2×Dic511yescharacteristic
206C3×C22⋊C4—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3C2×Dic511yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—104no—
216C4×Dic3—21no—
217C4×Dic3—202no—
218C4×Dic3C2×Dic511yescharacteristic
219C4×Dic3C2×Dic511yescharacteristic
220C4×Dic3C22⋊D511yescharacteristic
221C4×Dic3C22⋊D511yescharacteristic
222C2×C3⋊C8—101no—
223C23×C5—61no—
224C23×C5D3×D411yescharacteristic
225C5×Q8—41no—
226C5×D4—121no—
227C5×D4—121no—
228C5×D4—121no—
229C2×C4×C5—21no—
230C2×C4×C5—21no—
231C2×C4×C5—31no—
232C2×C4×C5—31no—
233C2×C4×C5—31no—
234C2×C4×C5—31no—
235C2×C4×C5—41no—
236C2×C4×C5—62no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—122no—
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243C2×Dic5—22no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246C2×Dic5—62no—
247C2×Dic5—121no—
248C2×Dic5—121no—
249#168—41no—
250#168—121no—
251#126—61no—
252#125—31no—
253#124—31no—
254#123—61no—
255C22⋊Q8D3×D511yescharacteristic
256#121—31no—
257C4×Q8—31no—
258C4×D4—31no—
259C4×D4—61no—
260#117—61no—
261C2×C4⋊C4—301no—
262C2×C42—31no—
263C2×C42—301no—
264C4⋊C8—301no—
265C22⋊C8—51no—
266C22⋊C8—151no—
267#97—301no—
268#95—51no—
269#95—151no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#41011yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5C2×#10411yescharacteristic
275C5×D3—81no—
276C23×C3C2×C22⋊D511yescharacteristic
277C22×D3—21no—
278C3×Q8—41no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—41no—
282C2×C3×C4—102no—
283C2×C3×C4—201no—
284C2×C3×C4—201no—
285C2×C3×C4C22×Dic511yescharacteristic
286C2×C3×C4C2×C22⋊D511yescharacteristic
287#67—41no—
288#67—41no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—22no—
292C2×Dic3—21no—
293C2×Dic3—102no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296C2×Dic3C22⋊Dic511yescharacteristic
297C2×Dic3C22⋊Dic511yescharacteristic
298C2×Dic3C22⋊Dic511yescharacteristic
299C2×Dic3C22⋊Dic511yescharacteristic
300D12—41no—
301C4×D3—42no—
302C3×C8—201no—
303C3⋊C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5—121no—
307C22×C5—121no—
308C22×C5—121no—
309C22×C5D3×C22⋊C411yescharacteristic
310C22×C5#91411yescharacteristic
311C22×C5#91811yescharacteristic
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—32no—
315C4×C5—41no—
316C4×C5—41no—
317C4×C5—61no—
318C4×C5—61no—
319C4×C5—61no—
320C4×C5—121no—
321Dic5—42no—
322Dic5—122no—
323C2×Q8D3×Dic511yescharacteristic
324C2×D4—31no—
325C2×D4—61no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—61no—
329C22×C4—101no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332C2×C8—101no—
333C2×C8—301no—
334C4⋊C4—21no—
335C4⋊C4—31no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—304no—
340C4⋊C4D3×Dic511yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C42—31no—
347C42—31no—
348C42—31no—
349C42—31no—
350C42—61no—
351C42—602no—
352C3×C5#150911yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3#409511yescharacteristic
356C22×C3#409711yescharacteristic
357C22×C3C2×C22⋊Dic511yescharacteristic
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—41no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—202no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—41no—
370Dic3—202no—
371Dic3#396912yes—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—241no—
375C2×C5#474011yescharacteristic
376C2×C5#480311yescharacteristic
377C2×C5D3×#10411yescharacteristic
378C23—61no—
379C23D3×C22⋊D511yescharacteristic
380Q8—41no—
381D4—121no—
382D4—121no—
383D4—121no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—41no—
391C2×C4—62no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—102no—
396C2×C4—122no—
397C2×C4—201no—
398C2×C4—201no—
399C2×C4—302no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C4C2×D3×Dic511yescharacteristic
403C2×C4D3×C22⋊D511yescharacteristic
404C8—201no—
405C8—601no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3#6552111yescharacteristic
409C2×C3C2×#396911yescharacteristic
410C2×C3#6552911yescharacteristic
411D3—81no—
412C5#6831111yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—121no—
416C22—121no—
417C22—121no—
418C22#9150411yescharacteristic
419C22#9151011yescharacteristic
420C22D3×C22⋊Dic511yescharacteristic
421C4—21no—
422C4—21no—
423C4—32no—
424C4—41no—
425C4—41no—
426C4—61no—
427C4—61no—
428C4—61no—
429C4—121no—
430C4—202no—
431C4—602no—
432C3#1060254811yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—241no—
436C2#1174917311yescharacteristic
437C2#1174920111yescharacteristic
438C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#930C22
cosocleC22×C3×C4×C5C23
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11748667C2semidirect
3. #11748337C2semidirect
4. #11746359C2semidirect
5. C3×#64758C2semidirect
10. C5×#947C4semidirect
11. C5×Q8×Dic3C4semidirect
15. C5×#893C4semidirect
17. C5×#890C4semidirect
33. #64758D3semidirect
121. #947Dic5semidirect
122. Q8×Dic3Dic5semidirect
128. #893Dic5semidirect
130. #890Dic5semidirect
352. C3×C5#1509semidirect
412. C5#68311semidirect
432. C3#10602548semidirect

Maximal subgroups

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

subgroupindex
C5×#56242
#117486672
#117483372
#117463592
C3×#647582
#117459572
#117459562
#106025483
#683115