Finite Group Databasebeta

← #14458576

Subgroups — #14458576

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#11752645C211yesmaximal, characteristic, complemented
3C5×#5075C211yesmaximal, characteristic, complemented
4C3×#65359C211yesmaximal, characteristic, complemented
5#11749121C212yesmaximal, complemented
6#11749062C212yesmaximal, complemented
7#11748960C212yesmaximal, complemented
8#11748957C212yesmaximal, complemented
9C4×#6660C211yesmaximal, characteristic, complemented
10#11746988C211yesmaximal, characteristic, complemented
11#11746942C211yesmaximal, characteristic, complemented
12#10612126—31nomaximal, Hall
13C2×D4×D15—21no—
14C2×D4×D15C2212yes—
15C3×C5×#127C2211yescharacteristic
16#91827—21no—
17#91827C2212yes—
18#91826—22no—
19C4×D60C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C2×C5×#214C2212yescomplemented
22C4×C5×Dic6C2211yescharacteristic, complemented
23C3×#4015C2211yescharacteristic, complemented
24#91437C2212yescomplemented
25#91428—21no—
26#91411—22no—
27#91383C2212yescomplemented
28#91381—21no—
29C2×#6660C2211yescharacteristic
30C2×#6648C2212yescomplemented
31C5×#832C2212yescomplemented
32C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×#3964C2212yescomplemented
34C3×#3964C2212yescomplemented
35C3×C4×#168C2211yescharacteristic, complemented
36#90987C2212yescomplemented
37#90985C2211yescharacteristic, complemented
38#90973C2211yescharacteristic, complemented
39#90969C2211yescharacteristic
40#90968C2212yes—
41#90957C2212yescomplemented
42#81577—51nomaximal, Hall
43#66051—31no—
44#65913—31no—
45C5×#460—31no—
46#65460—32no—
47#65458—32no—
48#65359D311yescharacteristic, complemented
49C4×#688—31no—
50#65131—31no—
51#65123—31no—
52#65066—32no—
53D5×#102—32no—
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×Dic6C2311yescharacteristic
68C2×C3×Dic10—21no—
69C2×#1200—22no—
70C3×C42×C5C2311yescharacteristic
71#6719—22no—
72#6714—21no—
73#6714D412yes—
74C4⋊Dic15D411yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C5×#214—42no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×Dic3⋊C4—21no—
79C4×C5×Dic3—21no—
80C2×C5×C3⋊C8C2312yes—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85#6669—22no—
86#6668—22no—
87#6667—22no—
88#6660—22no—
89#6648—42no—
90#5730—51no—
91#5717—51no—
92C3×#486—51no—
93#5084—51no—
94#5075D511yescharacteristic, complemented
95#4778—52no—
96#4777—52no—
97#4776—52no—
98D3×#102—52no—
99C4×#204—51no—
100C8×D12—51no—
101C2×D4×D5—32no—
102C2×D4×D5—61no—
103C2×C5×SD16—32no—
104C5×#127C2×D311yescharacteristic
105C4×C5×Q8—31no—
106#4092—32no—
107C2×#688—31no—
108#4084—32no—
109#4084—61no—
110#4083—62no—
111C2×C8×D5—32no—
112#4042—62no—
113D5×C4⋊C4—32no—
114C4×D20—31no—
115C4×D20—31no—
116C4×D20—61no—
117#4016—61no—
118#4015C2×D311yescharacteristic, complemented
119C5×C4⋊C8—31no—
120C5×#102—32no—
121#3967—31no—
122#3964C2×D312yescomplemented
123#3964C2×D312yescomplemented
124#3953—32no—
125#3952—32no—
126#3949—32no—
127#3941—31no—
128#3940—31no—
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—21no—
155C2×C5×Dic3—21no—
156C5×Dic6—21no—
157C5×Dic6—21no—
158C2×C3×Dic5—22no—
159C3×Dic10—81no—
160#1200—82no—
161C3×#168—21no—
162C3×#168—21no—
163C5×C3⋊C8—22no—
164C2×D3×D4—52no—
165C2×D3×D4—101no—
166C3×C4⋊Q8—51no—
167C3×#127C2×D511yescharacteristic
168#946—102no—
169#938—52no—
170#938—101no—
171#937—102no—
172C2×#214C2×D512yescomplemented
173C2×#204—51no—
174C2×D3×C8—52no—
175#897—52no—
176#893—101no—
177D3×C4⋊C4—52no—
178#890—101no—
179C4×D12—51no—
180C4×D12—51no—
181C4×Dic6C2×D511yescharacteristic, complemented
182C3×#102—52no—
183C3×#102—52no—
184C3×C4×C8—51no—
185#832C2×D512yescomplemented
186#821—51no—
187(C2×D3)⋊C8—52no—
188#817—51no—
189#816—51no—
190#809—52no—
191#808—52no—
192C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
193C23×D5—62no—
194C2×C5×Q8—31no—
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×Dic10—21no—
209C5×SD16—122no—
210C2×C5×C8—32no—
211C5×C4⋊C4—31no—
212C5×C4⋊C4—61no—
213C42×C5—61no—
214C42×C5C22×D311yescharacteristic
215C22⋊Dic5—62no—
216#688—62no—
217#685—32no—
218#685—62no—
219#685—61no—
220C4⋊Dic5—21no—
221C4⋊Dic5—31no—
222C4⋊Dic5—31no—
223C4⋊Dic5C22×D312yes—
224#683—62no—
225#683—62no—
226C2×#168C22×D311yescharacteristic
227C2×#168C22×D311yescharacteristic
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—51no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—31no—
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—42no—
258C5×Dic3—41no—
259C5×Dic3—41no—
260C23×D3—102no—
261C2×C3×Q8—101no—
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×Dic6C22×D511yescharacteristic
276C2×C3×C8—51no—
277C2×C3×C8—51no—
278C3×C4⋊C4—52no—
279C3×C4⋊C4—101no—
280C3×C42C22×D511yescharacteristic
281#217—102no—
282#214—42no—
283(C2×D3)⋊C4—52no—
284(C2×D3)⋊C4—102no—
285(C2×D3)⋊C4—101no—
286C4⋊Dic3—51no—
287C4⋊Dic3—51no—
288C4⋊Dic3—102no—
289C4⋊Dic3C22×D511yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—102no—
292C4×Dic3—21no—
293C2×C3⋊C8C22×D512yes—
294#204—102no—
295D3×C8—202no—
296C23×C5—22no—
297C22×D5—32no—
298C22×D5—61no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—61no—
303C5×Q8—61no—
304C5×D4—22no—
305C5×D4—22no—
306C5×D4—42no—
307C5×D4—81no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5D3×D411yescharacteristic
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C22⋊D5—124no—
314C22⋊D5—124no—
315C2×Dic5—22no—
316C2×Dic5—32no—
317C2×Dic5—61no—
318D20—34no—
319D20—32no—
320D20—61no—
321C4×D5—62no—
322C4×D5—62no—
323C4×D5—122no—
324C4×D5—242no—
325Dic10—81no—
326C5×C8—62no—
327#168—21no—
328#168—21no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—32no—
332C2×SD16—151no—
333C22×C8—152no—
334C4⋊Q8—51no—
335#127D3×D511yescharacteristic
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—31no—
343C4×D4—151no—
344C4×D4—151no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—151no—
348#106—152no—
349C4⋊C8—31no—
350#103—151no—
351#102—32no—
352#102—52no—
353#102—52no—
354#102—151no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—51no—
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—401no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—42no—
374C3×D4—81no—
375C2×C3×C4—102no—
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379#67—204no—
380#67—204no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—52no—
384C2×Dic3—101no—
385D12—52no—
386D12—54no—
387D12—101no—
388C4×D3—102no—
389C4×D3—102no—
390C4×D3—202no—
391C4×D3—402no—
392Dic6—21no—
393Dic6—21no—
394C3×C8—101no—
395C3×C8—101no—
396C3⋊C8—22no—
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—121no—
410C4×C5—121no—
411C4×C5D3×SD1612yes—
412C4×C5D3×#4111yescharacteristic
413C4×C5#100911yescharacteristic
414Dic5—42no—
415Dic5—62no—
416Dic5—121no—
417C24—302no—
418C2×Q8—31no—
419C2×Q8—101no—
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—122no—
434SD16—302no—
435C2×C8—32no—
436C2×C8—51no—
437C2×C8—51no—
438C2×C8—602no—
439C4⋊C4—31no—
440C4⋊C4—52no—
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—61no—
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—202no—
467C3×C4D5×SD1612yes—
468C3×C4#414411yescharacteristic
469C3×C4D5×#4111yescharacteristic
470Dic3—41no—
471Dic3—41no—
472Dic3—102no—
473Dic3—201no—
474C2×C5—82no—
475C2×C5#567611yescharacteristic
476C2×C5#575711yescharacteristic
477C2×C5C2×D3×SD1611yescharacteristic
478D5—64no—
479D5—122no—
480C23—22no—
481C23—152no—
482C23—301no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—61no—
487Q8—61no—
488Q8—401no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—81no—
493D4—154no—
494D4—152no—
495D4—301no—
496D4—604no—
497D4—604no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—102no—
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—62no—
511C8—101no—
512C8—101no—
513C2×C3—82no—
514C2×C3#6594611yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610811yescharacteristic
517D3—104no—
518D3—202no—
519C5#8157711yescharacteristic, 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—121no—
533C4—121no—
534C4—202no—
535C4—302no—
536C4—601no—
537C4#9148712yes—
538C4#9202411yescharacteristic
539C4#9202711yescharacteristic
540C3#1061212611yescharacteristic, complemented, Sylow
541C2—82no—
542C2—304no—
543C2—602no—
544C2#1175470311yescharacteristic
545C2C2×#9148711yescharacteristic
546C2#1175495911yescharacteristic
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. #11752645C2semidirect
3. C5×#5075C2semidirect
4. C3×#65359C2semidirect
5. #11749121C2semidirect
6. #11749062C2semidirect
7. #11748960C2semidirect
8. #11748957C2semidirect
9. C4×#6660C2semidirect
10. #11746988C2semidirect
11. #11746942C2semidirect
21. C2×C5×#214C22semidirect
22. C4×C5×Dic6C22semidirect
23. C3×#4015C22semidirect
24. #91437C22semidirect
27. #91383C22semidirect
30. C2×#6648C22semidirect
31. C5×#832C22semidirect
32. C5×C4⋊(C3⋊C8)C22semidirect
33. C3×#3964C22semidirect
34. C3×#3964C22semidirect
35. C3×C4×#168C22semidirect
36. #90987C22semidirect
37. #90985C22semidirect
38. #90973C22semidirect
41. #90957C22semidirect
48. #65359D3semidirect
94. #5075D5semidirect
118. #4015C2×D3semidirect
122. #3964C2×D3semidirect
123. #3964C2×D3semidirect
129. C4×#168C2×D3semidirect
149. D60SD16semidirect
172. C2×#214C2×D5semidirect
181. C4×Dic6C2×D5semidirect
185. #832C2×D5semidirect
192. C4⋊(C3⋊C8)C2×D5semidirect
453. C3×C5#3295semidirect
519. C5#81577semidirect
540. C3#10612126semidirect

Maximal subgroups

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

subgroupindex
#117564762
#117526452
C5×#50752
C3×#653592
#117491212
#117490622
#117489602
#117489572
C4×#66602
#117469882
#117469422
#106121263
#815775