Finite Group Databasebeta

← #14437873

Subgroups — #14437873

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752751C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic, complemented
3D15×#97C211yesmaximal, characteristic, complemented
4C5×#4714C211yesmaximal, characteristic, complemented
5C3×#65003C211yesmaximal, characteristic, complemented
6#11748108C212yesmaximal
7#11747976C212yesmaximal, complemented
8#11747975C212yesmaximal, complemented
9#11747609C212yesmaximal, complemented
10#11746904C211yesmaximal, characteristic, complemented
11#11746898C211yesmaximal, characteristic, complemented
12D5×#489—31nomaximal, Hall
13C2×#6777C2211yescharacteristic
14C2×D15⋊Q8—21no—
15C2×D15⋊Q8C2211yescharacteristic
16C2×C8×D15C2212yes—
17C42×D15C2211yescharacteristic
18C5×#875C2211yescharacteristic
19C5×#869C2211yescharacteristic, complemented
20C3×#4021C2211yescharacteristic
21C3×#4015C2211yescharacteristic, complemented
22#91473—21no—
23#91473—21no—
24#91470—21no—
25#91470C2212yescomplemented
26#91464—21no—
27#91464—21no—
28#91437—21no—
29#91437C2212yes—
30#91385—21no—
31#91370C2211yescharacteristic
32#91368C2211yescharacteristic
33C3×C5×#97C2211yescharacteristic, complemented
34#91099C2212yescomplemented
35#91087C2211yescharacteristic, complemented
36C5×#821C2212yes—
37C5×#816C2212yescomplemented
38C3×#3953C2212yes—
39C3×#3948C2212yescomplemented
40#90972C2212yescomplemented
41#90970C2212yescomplemented
42#90966C2212yes—
43#90964C2212yes—
44D3×#489—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46D5×#124—31no—
47C5×#489—31no—
48#65378—31no—
49#65344—31no—
50D5×#103—32no—
51#65084—32no—
52D5×#102—32no—
53#65054—32no—
54#65003D311yescharacteristic, complemented
55D5×#97—31no—
56C22×D3×D5—21no—
57C2×C4×D15D411yescharacteristic
58C2×C4×D15D411yescharacteristic
59C2×C4×D15C2311yescharacteristic
60C2×C5×D12C2311yescharacteristic
61C2×C5×Dic6—21no—
62C2×C5×Dic6C2311yescharacteristic
63C2×C3×D20C2311yescharacteristic
64C2×C3×Dic10—21no—
65C2×C3×Dic10C2311yescharacteristic
66C2×#1204—21no—
67C2×#1204—22no—
68C2×#1201—21no—
69C2×#1200—22no—
70C2×#1200—21no—
71#6777—24no—
72D15⋊Q8—24no—
73D15⋊Q8—44no—
74C2×C3×C5×C8C2312yes—
75C3×C42×C5C2311yescharacteristic
76C4×Dic15D411yescharacteristic
77C4×Dic15D411yescharacteristic
78C4×Dic15C2311yescharacteristic
79C2×C3⋊#168C2312yes—
80C8×D15—24no—
81C5×(C2×D3)⋊C4—21no—
82C5×(C2×D3)⋊C4—21no—
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3C2312yes—
85C3×#685—21no—
86C3×#685—21no—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89#6669—22no—
90#6669—22no—
91(C2×D3)⋊Dic5—21no—
92(C2×D3)⋊Dic5—21no—
93#6665—21no—
94#6665—21no—
95D3×C4⋊Q8—51no—
96D3×#124—51no—
97C3×#489—51no—
98#5089—51no—
99#5055—51no—
100D3×#103—52no—
101#4794—52no—
102D3×#102—52no—
103#4765—52no—
104#4714D511yescharacteristic, complemented
105D3×#97—51no—
106C2×Q8×D5—31no—
107C2×Q8×D5—61no—
108C2×D4×D5—31no—
109C5×C4⋊Q8—31no—
110C5×#124—31no—
111#4093—31no—
112#4090—61no—
113#4082—31no—
114C2×C8×D5—32no—
115D5×C4⋊C4—32no—
116D5×C4⋊C4—61no—
117#4034—32no—
118#4034—61no—
119#4031—61no—
120#4031—61no—
121D5×C22⋊C4—61no—
122D5×C22⋊C4—61no—
123#4021C2×D311yescharacteristic
124C42×D5—31no—
125#4015C2×D311yescharacteristic, complemented
126C5×#103—32no—
127C5×#102—32no—
128C5×#97C2×D311yescharacteristic, complemented
129#3967—32no—
130#3964—32no—
131#3953C2×D312yes—
132#3948C2×D312yescomplemented
133#3947—32no—
134#3942—32no—
135#3941—32no—
136#3935—31no—
137C2×#489—151noSylow
138C22×D15C2×D411yescharacteristic
139C22×C5×D3—21no—
140C22×C3×D5—21no—
141C2×D3×D5—42no—
142C2×D3×D5—42no—
143C2×D3×D5—42no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15C2×D411yescharacteristic
148C2×Dic15C2×D411yescharacteristic
149C2×Dic15C2×D411yescharacteristic
150C4×D15—22no—
151C4×D15—22no—
152C4×D15#4114yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—22no—
155C5×D12—22no—
156C5×Dic6—22no—
157C5×Dic6—42no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C3×D20—22no—
161C3×Dic10—22no—
162C3×Dic10—42no—
163#1204—44no—
164#1204—42no—
165#1201—42no—
166#1200—42no—
167#1200—44no—
168C3×C5×C8—22no—
169C3⋊#168—22no—
170C2×D3×Q8—51no—
171C2×D3×Q8—101no—
172C2×D3×D4—51no—
173C3×C4⋊Q8—51no—
174C3×#124—51no—
175#947—51no—
176#944—101no—
177#936—51no—
178C2×D3×C8—52no—
179D3×C4⋊C4—52no—
180D3×C4⋊C4—101no—
181#888—52no—
182#888—101no—
183#885—101no—
184#885—101no—
185D3×C22⋊C4—101no—
186D3×C22⋊C4—101no—
187#875C2×D511yescharacteristic
188C42×D3—51no—
189#869C2×D511yescharacteristic, complemented
190C3×#103—52no—
191C3×#102—52no—
192C3×#97C2×D511yescharacteristic, complemented
193#835—52no—
194#832—52no—
195#821C2×D512yes—
196#816C2×D512yescomplemented
197#815—52no—
198#810—52no—
199#809—52no—
200#803—51no—
201C23×D5—61no—
202C2×C5×Q8—31no—
203C2×C5×Q8—61no—
204C2×C5×D4—31no—
205C2×C22⋊D5—61no—
206Q8×D5—64no—
207Q8×D5—124no—
208D4×D5—64no—
209C2×D20C22×D311yescharacteristic
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—61no—
214C2×C4×D5—62no—
215C2×Dic10—21no—
216C2×Dic10—61no—
217C2×Dic10—62no—
218C2×Dic10C22×D311yescharacteristic
219C2×C5×C8C22×D312yes—
220C5×C4⋊C4—32no—
221C5×C4⋊C4—61no—
222C5×C22⋊C4—61no—
223C5×C22⋊C4—61no—
224C42×C5C22×D311yescharacteristic
225C22⋊Dic5—61no—
226C22⋊Dic5—61no—
227#685—21no—
228#685—21no—
229#685—61no—
230#685—61no—
231C4⋊Dic5—21no—
232C4⋊Dic5C22×D312yes—
233#683—62no—
234#683—62no—
235C4×Dic5—31no—
236C4×Dic5—31no—
237C4×Dic5—31no—
238C2×#168—32no—
239C8×D5—64no—
240C2×C4⋊Q8—151no—
241C2×#124—151no—
242#489—31no—
243#489—51no—
244#489—152no—
245#489—152no—
246#489—151no—
247#489—151no—
248C2×#103—152no—
249C2×#102—152no—
250C2×#97—151no—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15#12412yes—
253C2×D15AGL(1,ℤ/8)12yes—
254C2×D15#13712yes—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C2×C5×D3—41no—
258C2×C3×D5—41no—
259C2×C3×D5—41no—
260C2×C3×D5—41no—
261D3×D5—84no—
262C3×C4×C5—21no—
263C3×C4×C5—21no—
264C3×C4×C5C2×#4112yes—
265Dic15—21no—
266Dic15—21no—
267Dic15#12412yes—
268C3×Dic5—41no—
269C3×Dic5—42no—
270C5×Dic3—41no—
271C5×Dic3—42no—
272C23×D3—101no—
273C2×C3×Q8—51no—
274C2×C3×Q8—101no—
275C2×C3×D4—51no—
276C2×#67—101no—
277D3×Q8—104no—
278D3×Q8—204no—
279D3×D4—104no—
280C2×D12C22×D511yescharacteristic
281C2×C4×D3—51no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—101no—
285C2×C4×D3—102no—
286C2×Dic6—21no—
287C2×Dic6—101no—
288C2×Dic6—102no—
289C2×Dic6C22×D511yescharacteristic
290C2×C3×C8C22×D512yes—
291C3×C4⋊C4—52no—
292C3×C4⋊C4—101no—
293C3×C22⋊C4—101no—
294C3×C22⋊C4—101no—
295C3×C42C22×D511yescharacteristic
296#217—101no—
297#217—101no—
298(C2×D3)⋊C4—21no—
299(C2×D3)⋊C4—21no—
300(C2×D3)⋊C4—101no—
301(C2×D3)⋊C4—101no—
302C4⋊Dic3—21no—
303C4⋊Dic3C22×D512yes—
304Dic3⋊C4—102no—
305Dic3⋊C4—102no—
306C4×Dic3—51no—
307C4×Dic3—51no—
308C4×Dic3—51no—
309C2×C3⋊C8—52no—
310D3×C8—104no—
311C23×C5—61no—
312C22×D5—21no—
313C22×D5—31no—
314C22×D5—122no—
315C22×D5—122no—
316C22×D5—122no—
317C5×Q8—62no—
318C5×Q8—122no—
319C5×D4—62no—
320C2×C4×C5—62no—
321C2×C4×C5—61no—
322C2×C4×C5D3×D411yescharacteristic
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—122no—
326C2×Dic5—22no—
327C2×Dic5—21no—
328C2×Dic5—31no—
329C2×Dic5—31no—
330C2×Dic5—31no—
331D20—22no—
332C4×D5—34no—
333C4×D5—62no—
334C4×D5—62no—
335C4×D5—122no—
336C4×D5—124no—
337Dic10—22no—
338Dic10—42no—
339Dic10—122no—
340Dic10—124no—
341C5×C8—22no—
342#168—62no—
343C22×Q8—151no—
344C22×Q8—301no—
345C22×D4—151no—
346C22×C8—152no—
347C4⋊Q8—31no—
348C4⋊Q8—51no—
349C4⋊Q8—152no—
350C4⋊Q8—301no—
351C4⋊Q8—301no—
352#124—31no—
353#124—51no—
354#124—151no—
355#124—151no—
356#124—301no—
357#124—301no—
358C2×C4⋊C4—152no—
359C2×C4⋊C4—301no—
360C2×C22⋊C4—301no—
361C2×C22⋊C4—301no—
362C2×C42—151no—
363#103—32no—
364#103—52no—
365#103—152no—
366#103—152no—
367#102—32no—
368#102—52no—
369#102—152no—
370#102—152no—
371#97—152no—
372#97—151no—
373#97D3×D511yescharacteristic, complemented
374C2×C3×C5C2×#12411yescharacteristic
375C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C3×C5C2×#13711yescharacteristic
377D15#48914yescomplemented
378C3×D5—81no—
379C5×D3—81no—
380C23×C3—101no—
381C22×D3—21no—
382C22×D3—51no—
383C22×D3—202no—
384C22×D3—202no—
385C22×D3—202no—
386C3×Q8—102no—
387C3×Q8—202no—
388C3×D4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—101no—
391C2×C3×C4D4×D511yescharacteristic
392C2×C3×C4D4×D511yescharacteristic
393C2×C3×C4C23×D511yescharacteristic
394#67—202no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—51no—
398C2×Dic3—51no—
399C2×Dic3—51no—
400D12—22no—
401C4×D3—54no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—202no—
405C4×D3—204no—
406Dic6—22no—
407Dic6—42no—
408Dic6—202no—
409Dic6—204no—
410C3×C8—22no—
411C3⋊C8—102no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5—121no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—32no—
417C2×D5—32no—
418C2×D5—32no—
419C2×D5—41no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—244no—
423C4×C5—21no—
424C4×C5—21no—
425C4×C5—121no—
426C4×C5—122no—
427C4×C5D3×#4112yes—
428Dic5—32no—
429Dic5—41no—
430Dic5—42no—
431Dic5—61no—
432Dic5—61no—
433C24—301no—
434C2×Q8—31no—
435C2×Q8—51no—
436C2×Q8—61no—
437C2×Q8—101no—
438C2×Q8—301no—
439C2×Q8—302no—
440C2×Q8—304no—
441C2×Q8—604no—
442C2×D4—31no—
443C2×D4—51no—
444C2×D4—304no—
445C2×D4—301no—
446C22×C4—151no—
447C22×C4—151no—
448C22×C4—151no—
449C22×C4—301no—
450C22×C4—302no—
451C2×C8—152no—
452C2×C8—304no—
453C2×C8C2×D3×D512yes—
454C4⋊C4—32no—
455C4⋊C4—52no—
456C4⋊C4—61no—
457C4⋊C4—101no—
458C4⋊C4—302no—
459C4⋊C4—302no—
460C22⋊C4—61no—
461C22⋊C4—61no—
462C22⋊C4—101no—
463C22⋊C4—101no—
464C22⋊C4—301no—
465C22⋊C4—301no—
466C22⋊C4—301no—
467C22⋊C4—301no—
468C42—151no—
469C42—151no—
470C42—151no—
471C42C2×D3×D511yescharacteristic
472C3×C5C2×#48911yescharacteristic, complemented, Hall
473C22×C3—201no—
474C22×C3—201no—
475C22×C3—201no—
476C22×C3C2×D4×D511yescharacteristic
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—52no—
481C2×D3—52no—
482C2×D3—52no—
483C2×D3—404no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—202no—
487C3×C4—201no—
488C3×C4D5×#4112yes—
489Dic3—42no—
490Dic3—41no—
491Dic3—52no—
492Dic3—101no—
493Dic3—101no—
494C2×C5—241no—
495C2×C5D3×#12411yescharacteristic
496C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
497C2×C5D3×#13711yescharacteristic
498D5—34no—
499D5—81no—
500C23—61no—
501C23—101no—
502C23—151no—
503C23—602no—
504C23—602no—
505C23—602no—
506Q8—62no—
507Q8—102no—
508Q8—122no—
509Q8—202no—
510Q8—602no—
511Q8—604no—
512D4—62no—
513D4—102no—
514D4—602no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—101no—
518C2×C4—102no—
519C2×C4—151no—
520C2×C4—154no—
521C2×C4—151no—
522C2×C4—151no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—602no—
526C2×C4—604no—
527C2×C4#677711yescharacteristic
528C2×C4#677711yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—22no—
531C8—302no—
532C2×C3—401no—
533C2×C3D5×#12411yescharacteristic
534C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
535C2×C3D5×#13711yescharacteristic
536D3—54no—
537D3—81no—
538C5D3×#48911yescharacteristic, complemented, Sylow
539C22—121no—
540C22—121no—
541C22—121no—
542C22—152no—
543C22—152no—
544C22—152no—
545C22—201no—
546C22—201no—
547C22—201no—
548C22—1204no—
549C22C2×#677711yescharacteristic
550C4—21no—
551C4—21no—
552C4—121no—
553C4—122no—
554C4—152no—
555C4—201no—
556C4—202no—
557C4—301no—
558C4—301no—
559C4#9201612yes—
560C3D5×#48911yescharacteristic, complemented, Sylow
561C2—154no—
562C2—241no—
563C2—401no—
564C2#1175275111yescharacteristic
565C2#1175403311yescharacteristic
566C2#1175403411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC2×#6777C22
hypercenter#97D3×D5
hypocenterC3×C5C2×#489
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11752562C2semidirect
3. D15×#97C2semidirect
4. C5×#4714C2semidirect
5. C3×#65003C2semidirect
7. #11747976C2semidirect
8. #11747975C2semidirect
9. #11747609C2semidirect
10. #11746904C2semidirect
11. #11746898C2semidirect
19. C5×#869C22semidirect
21. C3×#4015C22semidirect
25. #91470C22semidirect
33. C3×C5×#97C22semidirect
34. #91099C22semidirect
35. #91087C22semidirect
37. C5×#816C22semidirect
39. C3×#3948C22semidirect
40. #90972C22semidirect
41. #90970C22semidirect
54. #65003D3semidirect
104. #4714D5semidirect
125. #4015C2×D3semidirect
128. C5×#97C2×D3semidirect
132. #3948C2×D3semidirect
189. #869C2×D5semidirect
192. C3×#97C2×D5semidirect
196. #816C2×D5semidirect
373. #97D3×D5semidirect
377. D15#489semidirect
472. C3×C5C2×#489semidirect
538. C5D3×#489semidirect
560. C3D5×#489semidirect

Maximal subgroups

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

subgroupindex
#117527512
#117525622
D15×#972
C5×#47142
C3×#650032
#117481082
#117479762
#117479752
#117476092
#117469042
#117468982
D5×#4893
D3×#4895