Finite Group Databasebeta

← #14458561

Subgroups — #14458561

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756338C211yesmaximal, characteristic, complemented
2#11752745C211yesmaximal, characteristic
3C4×C5×#215C211yesmaximal, characteristic, complemented
4C3×#65316C211yesmaximal, characteristic, complemented
5#11749399C212yesmaximal, complemented
6#11749277C212yesmaximal, complemented
7#11747478C212yesmaximal, complemented
8#11747332C212yesmaximal, complemented
9#11746994C211yesmaximal, characteristic, complemented
10#11746890C211yesmaximal, characteristic, complemented
11#11746883C211yesmaximal, characteristic, complemented
12#10611407—31nomaximal, Hall
13C2×#6777C2212yes—
14C2×D3×D20—21no—
15C3×C4×C5×Q8C2211yescharacteristic, complemented
16#91835C2212yescomplemented
17#91785—22no—
18C4⋊C4×D15C2212yescomplemented
19C4×D60—21no—
20C4×D60C2211yescharacteristic
21#91759—21no—
22#91758C2211yescharacteristic, complemented
23C2×C5×#215C2211yescharacteristic
24C4×C5×D12C2211yescharacteristic
25C2×C3×#688C2212yescomplemented
26C3×#4020C2211yescharacteristic
27#91474—22no—
28#91465C2212yes—
29#91456—21no—
30C2×#6648C2212yescomplemented
31C5×#835C2211yescharacteristic, complemented
32C5×#809C2211yescharacteristic
33C5×#808C2211yescharacteristic, complemented
34C4×C5×C3⋊C8C2211yescharacteristic, complemented
35C3×#3941C2212yescomplemented
36C3×C4⋊#168C2211yescharacteristic, complemented
37#90985C2212yescomplemented
38#90967C2212yes—
39#90965C2212yescomplemented
40#90965C2212yescomplemented
41#90957C2212yescomplemented
42#80395—51nomaximal, Hall
43#65913—31no—
44D4×D20—31no—
45C4×C5×SD16—31no—
46#65458—32no—
47#65316D311yescharacteristic, complemented
48#65297—31no—
49#65152—32no—
50#65096—32no—
51D5×#102—32no—
52#64983—31no—
53C8×D20—31no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×D60D411yescharacteristic
57C2×C4×D15—22no—
58C2×C4×D15C2312yes—
59C2×Dic30—21no—
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20C2312yes—
65C2×#1202—22no—
66C2×#1201—22no—
67#6777—24no—
68#6777—42no—
69D3×D20—44no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C42×C5—21no—
73C3×C42×C5C2311yescharacteristic
74#6714—22no—
75#6714D412yes—
76C4⋊Dic15—21no—
77C4⋊Dic15D411yescharacteristic
78C4⋊Dic15C2312yes—
79#6712—22no—
80#6712—22no—
81C5×#215—22no—
82C5×(C2×D3)⋊C4—21no—
83C5×C4⋊Dic3C2311yescharacteristic
84C2×C5×C3⋊C8C2311yescharacteristic
85C2×C5×C3⋊C8C2311yescharacteristic
86C3×#688—42no—
87C2×C3×#168C2312yes—
88#6665—22no—
89#6648—42no—
90#5717—51no—
91#5579—51no—
92C3×#460—51no—
93#5171—52no—
94#5169—52no—
95#5070—51no—
96C4×#215D511yescharacteristic, complemented
97#4842—51no—
98#4834—51no—
99#4777—52no—
100D3×#102—52no—
101C2×D4×D5—32no—
102C22×D20—61no—
103C2×C5×SD16—31no—
104C4×C5×Q8C2×D311yescharacteristic, complemented
105C4×C5×D4—31no—
106#4092—32no—
107C2×#688C2×D312yescomplemented
108#4076—61no—
109C2×C8×D5—32no—
110#4042—62no—
111#4041—32no—
112D5×C4⋊C4—32no—
113#4028—62no—
114#4020C2×D311yescharacteristic
115C4×D20—31no—
116C4×D20—61no—
117#4016—61no—
118#4015—31no—
119C5×#106—31no—
120C5×#103—31no—
121C5×#102—31no—
122C4×C5×C8—31no—
123#3964—32no—
124#3953—32no—
125#3953—32no—
126#3952—32no—
127#3941C2×D312yescomplemented
128#3940—32no—
129C4⋊#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C22×D15C2×D412yes—
132C22×C5×D3—21no—
133C22×C3×D5—22no—
134C2×D3×D5—44no—
135C2×D3×D5—44no—
136C2×D3×D5—82no—
137C3×C5×Q8—21no—
138C3×C5×Q8—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—22no—
145C2×Dic15C2×D412yes—
146D60SD1614yescomplemented
147C4×D15—22no—
148C4×D15—22no—
149C4×D15—82no—
150Dic30—81no—
151C2×C5×Dic3—21no—
152C5×D12—21no—
153C5×D12#4112yes—
154C4×C5×D3—42no—
155C3×D20—22no—
156C3×D20—22no—
157C3×D20—42no—
158C3×D20—81no—
159#1202—44no—
160#1201—44no—
161C3×#168—22no—
162C5×C3⋊C8—21no—
163C5×C3⋊C8—21no—
164C2×D3×D4—52no—
165C2×D3×D4—101no—
166C2×C3×SD16—52no—
167C3×#127—51no—
168C3×C4×Q8C2×D511yescharacteristic, complemented
169#946—52no—
170C2×#215C2×D511yescharacteristic
171#938—52no—
172#938—101no—
173#937—102no—
174C2×D3×C8—52no—
175#896—102no—
176D3×C4⋊C4—52no—
177C4×D12—51no—
178C4×D12—101no—
179C4×D12C2×D511yescharacteristic
180#870—101no—
181#869—51no—
182C3×C4⋊C8—51no—
183C3×#102—52no—
184#835C2×D511yescharacteristic, complemented
185#832—52no—
186#832—52no—
187#821—52no—
188(C2×D3)⋊C8—52no—
189#817—52no—
190#809C2×D511yescharacteristic
191#808C2×D511yescharacteristic, complemented
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—62no—
194C2×C5×Q8C22×D311yescharacteristic
195C2×C5×D4—31no—
196C22×C4×C5—61no—
197C2×C22⋊D5—62no—
198D4×D5—64no—
199D4×D5—122no—
200C2×D20—21no—
201C2×D20—21no—
202C2×D20—31no—
203C2×D20—62no—
204C2×D20—124no—
205C2×D20C22×D312yes—
206C2×C4×D5—32no—
207C2×C4×D5—62no—
208C2×Dic10—61no—
209C5×SD16—62no—
210C2×C5×C8—31no—
211C2×C5×C8—31no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—31no—
214C5×C4⋊C4C22×D311yescharacteristic
215C5×C22⋊C4—61no—
216C42×C5—21no—
217C42×C5C22×D311yescharacteristic
218#688—42no—
219#685—32no—
220#685—62no—
221#685—62no—
222C4⋊Dic5—31no—
223C4⋊Dic5—32no—
224C4⋊Dic5—61no—
225#683—62no—
226#683—62no—
227C2×#168C22×D312yes—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—51no—
236#450—152no—
237C4×SD16—31no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5C22×D411yescharacteristic
241C2×D15—22no—
242C2×D15—22no—
243C2×D15C2×SD1614yes—
244C2×C5×D3—22no—
245C2×C5×D3—41no—
246C2×C5×D3—41no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—42no—
250D3×D5—88no—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5—41no—
254C3×C4×C5C2×SD1612yes—
255C3×C4×C5C2×#4111yescharacteristic
256C3×C4×C5H(5,𝔽2)11yescharacteristic
257Dic15—22no—
258Dic15—42no—
259C5×Dic3—41no—
260C23×D3—102no—
261C2×C3×Q8C22×D511yescharacteristic
262C2×C3×D4—52no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×#67—102no—
266C2×#67—102no—
267D3×D4—104no—
268D3×D4—204no—
269D3×D4—202no—
270C2×D12—51no—
271C2×D12C22×D511yescharacteristic
272C2×C4×D3—21no—
273C2×C4×D3—52no—
274C2×C4×D3—102no—
275C2×Dic6—101no—
276C3×SD16—202no—
277C2×C3×C8—52no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4C22×D511yescharacteristic
280C3×C42—21no—
281C3×C42C22×D511yescharacteristic
282#217—102no—
283#215—22no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—52no—
286(C2×D3)⋊C4—102no—
287C4⋊Dic3—51no—
288C4⋊Dic3—52no—
289C4⋊Dic3—101no—
290C4⋊Dic3C22×D511yescharacteristic
291Dic3⋊C4—102no—
292Dic3⋊C4—102no—
293C2×C3⋊C8C22×D511yescharacteristic
294C2×C3⋊C8C22×D511yescharacteristic
295D3×C8—202no—
296C23×C5—61no—
297C22×D5—22no—
298C22×D5—32no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—21no—
303C5×Q8—21no—
304C5×D4—32no—
305C5×D4—61no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—61no—
309C2×C4×C5—122no—
310C2×C4×C5D3×D411yescharacteristic
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C22⋊D5—124no—
314C2×Dic5—32no—
315C2×Dic5—62no—
316D20—22no—
317D20—22no—
318D20—34no—
319D20—42no—
320D20—81no—
321D20—124no—
322C4×D5—62no—
323C4×D5—62no—
324C4×D5—242no—
325Dic10—241no—
326C5×C8—61no—
327C5×C8—61no—
328#168—22no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—31no—
332C2×SD16—52no—
333C22×C8—152no—
334C4⋊Q8—151no—
335#127—51no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8D3×D511yescharacteristic, complemented
343C4×D4—31no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—31no—
348#106—152no—
349C4⋊C8—51no—
350#103—31no—
351#102—31no—
352#102—52no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—31no—
358C2×C3×C5#54611yescharacteristic
359C2×C3×C5C22×SD1611yescharacteristic
360C2×C3×C5#57611yescharacteristic
361D15—24no—
362C3×D5—82no—
363C5×D3—42no—
364C23×C3—102no—
365C22×D3—21no—
366C22×D3—52no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—21no—
371C3×Q8—21no—
372C3×D4—102no—
373C3×D4—102no—
374C3×D4—202no—
375C3×D4—401no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—204no—
382#67—204no—
383C2×Dic3—21no—
384C2×Dic3—52no—
385C2×Dic3—102no—
386D12—21no—
387D12—54no—
388D12#70912yes—
389C4×D3—42no—
390C4×D3—102no—
391C4×D3—102no—
392C4×D3—402no—
393Dic6—401no—
394C3×C8—102no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C22×C5—62no—
398C22×C5—121no—
399C22×C5—121no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—34no—
402C2×D5—42no—
403C2×D5—42no—
404C2×D5—42no—
405C2×D5—62no—
406C2×D5—62no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—41no—
411C4×C5—121no—
412C4×C5D3×SD1612yes—
413C4×C5#100411yescharacteristic
414C4×C5D3×#4111yescharacteristic
415Dic5—62no—
416Dic5—122no—
417C24—302no—
418C2×Q8—301no—
419C2×Q8C2×D3×D511yescharacteristic
420C2×D4—31no—
421C2×D4—52no—
422C2×D4—101no—
423C2×D4—101no—
424C2×D4—151no—
425C2×D4—302no—
426C2×D4—302no—
427C2×D4—304no—
428C2×D4—604no—
429C2×D4—602no—
430C22×C4—61no—
431C22×C4—152no—
432C22×C4—302no—
433SD16—62no—
434SD16—202no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—52no—
438C2×C8—602no—
439C4⋊C4—21no—
440C4⋊C4—31no—
441C4⋊C4—151no—
442C4⋊C4—152no—
443C4⋊C4—302no—
444C4⋊C4—302no—
445C4⋊C4—301no—
446C4⋊C4C2×D3×D511yescharacteristic
447C22⋊C4—61no—
448C22⋊C4—152no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—21no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—202no—
455C22×C3—202no—
456C22×C3—202no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—22no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—54no—
462C2×D3—102no—
463C2×D3—102no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4D5×SD1612yes—
469C3×C4C2×#70911yescharacteristic
470C3×C4#414911yescharacteristic
471Dic3—41no—
472Dic3—102no—
473Dic3—202no—
474C2×C5—122no—
475C2×C5#561211yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#577411yescharacteristic
478D5—64no—
479D5—82no—
480C23—61no—
481C23—102no—
482C23—152no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—21no—
487Q8—21no—
488Q8—1201no—
489D4—32no—
490D4—61no—
491D4—102no—
492D4—102no—
493D4—154no—
494D4—202no—
495D4—401no—
496D4—604no—
497D4—604no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—61no—
501C2×C4—122no—
502C2×C4—152no—
503C2×C4—302no—
504C2×C4—302no—
505C2×C4—302no—
506C2×C4—1202no—
507C2×C4#679011yescharacteristic
508C2×C4#679011yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—102no—
513C2×C3—402no—
514C2×C3#6588411yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610311yescharacteristic
517D3—42no—
518D3—104no—
519C5#8039511yescharacteristic, complemented, Sylow
520C22—62no—
521C22—121no—
522C22—121no—
523C22—154no—
524C22—202no—
525C22—202no—
526C22—202no—
527C22—302no—
528C22—302no—
529C22—1208no—
530C22C2×#679011yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—121no—
535C4—302no—
536C4—602no—
537C4#9150512yes—
538C4D3×#70911yescharacteristic
539C4#9201711yescharacteristic
540C3#1061140711yescharacteristic, complemented, Sylow
541C2—122no—
542C2—304no—
543C2—402no—
544C2#1175466711yescharacteristic
545C2C2×#9150511yescharacteristic
546C2#1175533011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752745C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756338C2semidirect
3. C4×C5×#215C2semidirect
4. C3×#65316C2semidirect
5. #11749399C2semidirect
6. #11749277C2semidirect
7. #11747478C2semidirect
8. #11747332C2semidirect
9. #11746994C2semidirect
10. #11746890C2semidirect
11. #11746883C2semidirect
15. C3×C4×C5×Q8C22semidirect
16. #91835C22semidirect
18. C4⋊C4×D15C22semidirect
22. #91758C22semidirect
25. C2×C3×#688C22semidirect
30. C2×#6648C22semidirect
31. C5×#835C22semidirect
33. C5×#808C22semidirect
34. C4×C5×C3⋊C8C22semidirect
35. C3×#3941C22semidirect
36. C3×C4⋊#168C22semidirect
37. #90985C22semidirect
39. #90965C22semidirect
40. #90965C22semidirect
41. #90957C22semidirect
47. #65316D3semidirect
96. C4×#215D5semidirect
104. C4×C5×Q8C2×D3semidirect
107. C2×#688C2×D3semidirect
127. #3941C2×D3semidirect
129. C4⋊#168C2×D3semidirect
146. D60SD16semidirect
168. C3×C4×Q8C2×D5semidirect
184. #835C2×D5semidirect
191. #808C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
342. C4×Q8D3×D5semidirect
453. C3×C5#3295semidirect
519. C5#80395semidirect
540. C3#10611407semidirect

Maximal subgroups

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

subgroupindex
#117563382
#117527452
C4×C5×#2152
C3×#653162
#117493992
#117492772
#117474782
#117473322
#117469942
#117468902
#117468832
#106114073
#803955