Finite Group Databasebeta

← #14458573

Subgroups — #14458573

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#11756476C211yesmaximal, characteristic
2#11752654C211yesmaximal, characteristic, complemented
3C5×#5070C211yesmaximal, characteristic, complemented
4C3×#65364C211yesmaximal, characteristic, complemented
5#11749064C212yesmaximal, complemented
6#11749053C212yesmaximal, complemented
7#11748960C212yesmaximal, complemented
8#11748957C212yesmaximal, complemented
9C4×#6658C211yesmaximal, characteristic, complemented
10#11746994C211yesmaximal, characteristic, complemented
11#11746885C211yesmaximal, characteristic, complemented
12#10613308—31nomaximal, Hall
13C2×D4×D15—21no—
14C2×D4×D15C2212yes—
15C3×C5×#127C2211yescharacteristic
16#91827—21no—
17#91827C2212yes—
18#91826—22no—
19C4×D60C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C5×#869C2211yescharacteristic, complemented
22C2×C3×#687C2212yescomplemented
23C3×C4×Dic10C2211yescharacteristic, complemented
24#91437C2212yescomplemented
25#91424—22no—
26#91418—21no—
27#91390C2212yescomplemented
28#91388—21no—
29C2×#6658C2211yescharacteristic
30C2×#6648C2212yescomplemented
31C5×#832C2212yescomplemented
32C5×#832C2212yescomplemented
33C4×C5×C3⋊C8C2211yescharacteristic, complemented
34C3×#3964C2212yescomplemented
35C3×C4⋊#168C2211yescharacteristic, complemented
36#90987C2211yescharacteristic, complemented
37#90985C2212yescomplemented
38#90971C2211yescharacteristic, complemented
39#90969C2212yes—
40#90968C2211yescharacteristic
41#90957C2212yescomplemented
42#80395—51nomaximal, Hall
43#66064—31no—
44#66051—31no—
45C5×#486—31no—
46#65373—31no—
47#65364D311yescharacteristic, complemented
48#65067—32no—
49#65066—32no—
50#65065—32no—
51D5×#102—32no—
52C4×#677—31no—
53C8×D20—31no—
54C23×D15—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2312yes—
58C2×#1220—22no—
59C2×#1220—22no—
60D4×D15—24no—
61D4×D15—42no—
62D4×D15—44no—
63C2×D60D411yescharacteristic
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×C4×D15C2312yes—
67C2×C5×Dic6—21no—
68C2×C3×Dic10C2311yescharacteristic
69C2×#1200—22no—
70C3×C42×C5C2311yescharacteristic
71#6719—22no—
72#6714—21no—
73#6714D412yes—
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×#687—42no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—21no—
83C3×C4×Dic5—21no—
84C2×C3×#168C2312yes—
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6667—22no—
88#6658—22no—
89#6648—42no—
90#5717—51no—
91#5579—51no—
92C3×#460—51no—
93#5171—52no—
94#5169—52no—
95#5070D511yescharacteristic, complemented
96C4×#215—51no—
97#4842—51no—
98#4834—51no—
99#4777—52no—
100D3×#102—52no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C5×C4⋊Q8—31no—
104C5×#127C2×D311yescharacteristic
105#4092—62no—
106#4084—32no—
107#4084—61no—
108#4083—62no—
109C2×#687C2×D312yescomplemented
110C2×#677—31no—
111C2×C8×D5—32no—
112#4043—32no—
113#4039—61no—
114D5×C4⋊C4—32no—
115#4036—61no—
116C4×D20—31no—
117C4×D20—31no—
118C4×Dic10C2×D311yescharacteristic, complemented
119C5×#102—32no—
120C5×#102—32no—
121C4×C5×C8—31no—
122#3964C2×D312yescomplemented
123#3953—31no—
124#3952—32no—
125#3949—31no—
126#3948—31no—
127#3941—32no—
128#3940—32no—
129C4⋊#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C23×C3×C5—22no—
132C22×D15—21no—
133C22×D15—44no—
134C22×D15—44no—
135C22×D15—82no—
136C22×D15C2×D412yes—
137C3×C5×D4—22no—
138C3×C5×D4—22no—
139C3×C5×D4—42no—
140C3×C5×D4—81no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144#1220—44no—
145#1220—44no—
146C2×Dic15—21no—
147C2×Dic15C2×D412yes—
148D60—21no—
149D60SD1614yescomplemented
150D60#4112yes—
151C4×D15—22no—
152C4×D15—22no—
153C4×D15—42no—
154C2×C5×Dic3—22no—
155C5×Dic6—81no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C3×Dic10—21no—
159C3×Dic10—21no—
160#1200—82no—
161C3×#168—22no—
162C5×C3⋊C8—21no—
163C5×C3⋊C8—21no—
164C2×D3×D4—52no—
165C2×D3×D4—101no—
166C2×C3×SD16—52no—
167C3×#127C2×D511yescharacteristic
168C3×C4×Q8—51no—
169#946—52no—
170C2×#215—51no—
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—51no—
179C4×D12—101no—
180#870—101no—
181#869C2×D511yescharacteristic, complemented
182C3×C4⋊C8—51no—
183C3×#102—52no—
184#835—51no—
185#832C2×D512yescomplemented
186#832C2×D512yescomplemented
187#821—52no—
188(C2×D3)⋊C8—52no—
189#817—52no—
190#809—51no—
191#808—51no—
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—62no—
194C2×C5×Q8—61no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4C22×D312yes—
198C2×C22⋊D5—62no—
199C2×C22⋊D5—62no—
200D4×D5—64no—
201D4×D5—122no—
202D4×D5—124no—
203C2×D20—31no—
204C2×D20—31no—
205C2×C4×D5—32no—
206C2×C4×D5—61no—
207C2×C4×D5—62no—
208C2×Dic10C22×D311yescharacteristic
209C2×C5×C8—31no—
210C2×C5×C8—31no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—61no—
213C42×C5C22×D311yescharacteristic
214C22⋊Dic5—62no—
215#687—42no—
216#685—32no—
217#685—62no—
218#685—61no—
219C4⋊Dic5—31no—
220C4⋊Dic5—31no—
221C4⋊Dic5—62no—
222C4⋊Dic5C22×D311yescharacteristic
223#683—21no—
224#683—62no—
225C4×Dic5—21no—
226C2×#168C22×D312yes—
227#677—62no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—31no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—51no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5C22×D411yescharacteristic
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C2×D15—88no—
250C2×D15C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5C2×SD1612yes—
253C3×C4×C5C2×#4111yescharacteristic
254C3×C4×C5H(5,𝔽2)11yescharacteristic
255Dic15—22no—
256Dic15—41no—
257C3×Dic5—41no—
258C3×Dic5—41no—
259C5×Dic3—42no—
260C23×D3—102no—
261C2×C3×Q8—51no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4C22×D512yes—
265C2×#67—102no—
266C2×#67—102no—
267D3×D4—104no—
268D3×D4—202no—
269D3×D4—204no—
270C2×D12—51no—
271C2×D12—51no—
272C2×C4×D3—52no—
273C2×C4×D3—101no—
274C2×C4×D3—102no—
275C2×Dic6—21no—
276C3×SD16—202no—
277C2×C3×C8—52no—
278C3×C4⋊C4—51no—
279C3×C4⋊C4—101no—
280C3×C42—101no—
281C3×C42C22×D511yescharacteristic
282#217—102no—
283#215—102no—
284(C2×D3)⋊C4—52no—
285(C2×D3)⋊C4—102no—
286(C2×D3)⋊C4—101no—
287C4⋊Dic3—21no—
288C4⋊Dic3—51no—
289C4⋊Dic3—51no—
290C4⋊Dic3C22×D512yes—
291Dic3⋊C4—102no—
292Dic3⋊C4—102no—
293C2×C3⋊C8C22×D511yescharacteristic
294C2×C3⋊C8C22×D511yescharacteristic
295D3×C8—202no—
296C23×C5—22no—
297C22×D5—32no—
298C22×D5—61no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—241no—
303C5×D4—22no—
304C5×D4—22no—
305C5×D4—42no—
306C5×D4—81no—
307C2×C4×C5—62no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C22⋊D5—124no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—32no—
316C2×Dic5—61no—
317D20—34no—
318D20—32no—
319D20—61no—
320C4×D5—62no—
321C4×D5—62no—
322C4×D5—122no—
323C4×D5—242no—
324Dic10—21no—
325Dic10—21no—
326C5×C8—61no—
327C5×C8—61no—
328#168—22no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—52no—
332C2×SD16—151no—
333C22×C8—152no—
334C4⋊Q8—31no—
335#127D3×D511yescharacteristic
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—51no—
343C4×D4—151no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—152no—
348#106—151no—
349C4⋊C8—51no—
350#103—151no—
351#102—32no—
352#102—32no—
353#102—52no—
354#102—152no—
355#102—151no—
356C22⋊C8—152no—
357C4×C8—31no—
358C2×C3×C5—82no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362D15—24no—
363D15—42no—
364C23×C3—22no—
365C22×D3—52no—
366C22×D3—101no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—101no—
371C3×Q8—101no—
372C3×D4—22no—
373C3×D4—22no—
374C3×D4—42no—
375C3×D4—81no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—204no—
382#67—204no—
383C2×Dic3—22no—
384C2×Dic3—52no—
385C2×Dic3—101no—
386D12—52no—
387D12—54no—
388D12—101no—
389C4×D3—102no—
390C4×D3—102no—
391C4×D3—202no—
392C4×D3—402no—
393Dic6—81no—
394C3×C8—102no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—34no—
402C2×D5—62no—
403C2×D5—62no—
404C2×D5—62no—
405C2×D5—121no—
406C2×D5—121no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—122no—
410C4×C5D3×SD1612yes—
411C4×C5#100411yescharacteristic
412C4×C5D3×#4111yescharacteristic
413Dic5—41no—
414Dic5—41no—
415Dic5—62no—
416Dic5—121no—
417C24—302no—
418C2×Q8—51no—
419C2×Q8—61no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—151no—
423C2×D4—151no—
424C2×D4—302no—
425C2×D4—304no—
426C2×D4—302no—
427C2×D4—602no—
428C2×D4—604no—
429C2×D4C2×D3×D512yes—
430C22×C4—152no—
431C22×C4—302no—
432C22×C4—301no—
433SD16—202no—
434SD16—302no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—52no—
438C2×C8—602no—
439C4⋊C4—32no—
440C4⋊C4—51no—
441C4⋊C4—61no—
442C4⋊C4—101no—
443C4⋊C4—151no—
444C4⋊C4—151no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C22⋊C4—152no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—101no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—54no—
459C2×D3—102no—
460C2×D3—102no—
461C2×D3—102no—
462C2×D3—201no—
463C2×D3—201no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—201no—
467C3×C4—201no—
468C3×C4D5×SD1612yes—
469C3×C4D5×#4111yescharacteristic
470C3×C4#414911yescharacteristic
471Dic3—42no—
472Dic3—102no—
473Dic3—201no—
474C2×C5—82no—
475C2×C5#561211yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#577411yescharacteristic
478D5—64no—
479D5—122no—
480C23—22no—
481C23—152no—
482C23—301no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—101no—
487Q8—101no—
488Q8—241no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—81no—
493D4—154no—
494D4—152no—
495D4—301no—
496D4—604no—
497D4—604no—
498C2×C4—62no—
499C2×C4—101no—
500C2×C4—101no—
501C2×C4—152no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—301no—
505C2×C4—602no—
506C2×C4—1202no—
507C2×C4#679011yescharacteristic
508C2×C4#679011yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—102no—
513C2×C3—82no—
514C2×C3#6601011yescharacteristic
515C2×C3#6609111yescharacteristic
516C2×C3C2×D5×SD1611yescharacteristic
517D3—104no—
518D3—202no—
519C5#8039511yescharacteristic, complemented, Sylow
520C22—42no—
521C22—42no—
522C22—42no—
523C22—154no—
524C22—302no—
525C22—302no—
526C22—302no—
527C22—601no—
528C22—601no—
529C22—1208no—
530C22C2×#679011yescharacteristic
531C4—21no—
532C4—122no—
533C4—201no—
534C4—201no—
535C4—302no—
536C4—601no—
537C4#9148712yes—
538C4#9202411yescharacteristic
539C4#9202611yescharacteristic
540C3#1061330811yescharacteristic, complemented, Sylow
541C2—82no—
542C2—304no—
543C2—602no—
544C2#1175470411yescharacteristic
545C2C2×#9148711yescharacteristic
546C2#1175495811yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radical#11756476C2
hypercenter#127D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11752654C2semidirect
3. C5×#5070C2semidirect
4. C3×#65364C2semidirect
5. #11749064C2semidirect
6. #11749053C2semidirect
7. #11748960C2semidirect
8. #11748957C2semidirect
9. C4×#6658C2semidirect
10. #11746994C2semidirect
11. #11746885C2semidirect
21. C5×#869C22semidirect
22. C2×C3×#687C22semidirect
23. C3×C4×Dic10C22semidirect
24. #91437C22semidirect
27. #91390C22semidirect
30. C2×#6648C22semidirect
31. C5×#832C22semidirect
32. C5×#832C22semidirect
33. C4×C5×C3⋊C8C22semidirect
34. C3×#3964C22semidirect
35. C3×C4⋊#168C22semidirect
36. #90987C22semidirect
37. #90985C22semidirect
38. #90971C22semidirect
41. #90957C22semidirect
47. #65364D3semidirect
95. #5070D5semidirect
109. C2×#687C2×D3semidirect
118. C4×Dic10C2×D3semidirect
122. #3964C2×D3semidirect
129. C4⋊#168C2×D3semidirect
149. D60SD16semidirect
181. #869C2×D5semidirect
185. #832C2×D5semidirect
186. #832C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
453. C3×C5#3295semidirect
519. C5#80395semidirect
540. C3#10613308semidirect

Maximal subgroups

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

subgroupindex
#117564762
#117526542
C5×#50702
C3×#653642
#117490642
#117490532
#117489602
#117489572
C4×#66582
#117469942
#117468852
#106133083
#803955