Finite Group Databasebeta

← #14439481

Subgroups — #14439481

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756589C211yesmaximal, characteristic, complemented
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C2×C3×#4096C211yesmaximal, characteristic, complemented
4#11754251C211yesmaximal, characteristic, complemented
5C22×#6660C211yesmaximal, characteristic, complemented
6C2×#91301C211yesmaximal, characteristic, complemented
7#11749356C212yesmaximal, complemented
8#11749318C212yesmaximal, complemented
9#11749109C212yesmaximal, complemented
10#11749073C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615705—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17#91836C2212yes—
18#91829C2212yes—
19#91826—22no—
20#91819—22no—
21#91815C2211yescharacteristic
22C5×#951—24no—
23C2×C5×#216C2212yescomplemented
24C2×C5×#214C2212yescomplemented
25C2×C5×#208C2211yescharacteristic
26C3×#4096—24no—
27C2×C3×#689C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic, complemented
29C2×C3×#687C2211yescharacteristic, complemented
30C2×C3×#686C2211yescharacteristic, complemented
31C22×C3×#168C2211yescharacteristic
32#91536—22no—
33#91385C2212yescomplemented
34#91368C2212yescomplemented
35#91359—22no—
36C2×#6660—24no—
37C2×#6660C2212yes—
38C2×#6660C2212yes—
39C2×#6658C2212yes—
40#91301—24no—
41C2×#6653C2212yes—
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83905—51nomaximal, Hall
45C2×C5×#137—31no—
46#66164—31no—
47C2×#4096D311yescharacteristic, complemented
48#66150—31no—
49C22×#688—31no—
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65464—32no—
55#65411—31no—
56C23×D15—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—24no—
65C2×D60—22no—
66C2×D60—22no—
67C2×D60—21no—
68C2×D60C2312yes—
69C22×C5×Dic3—21no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6C2312yes—
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80#6719D412yes—
81#6714—24no—
82C4⋊Dic15D412yes—
83C4×Dic15C2312yes—
84C5×#216—24no—
85C5×#214—24no—
86C5×#208D414yescomplemented
87C2×C5×C3⋊C8C2312yes—
88C3×#689—22no—
89C3×#688—22no—
90C3×#687—22no—
91C3×#686—22no—
92C2×C3×#168D414yescomplemented
93C2×C3×#168C2311yescharacteristic
94C2×C3×#168C2311yescharacteristic
95#6669—24no—
96#6665—24no—
97#6660—24no—
98#6660—24no—
99#6658—24no—
100#6653—24no—
101C2×C3×#135—51no—
102#5830—51no—
103#5825—51no—
104C2×#951D511yescharacteristic, complemented
105C2×#949—51no—
106C22×#204—51no—
107#5190—52no—
108#5175—52no—
109#5168—52no—
110#5154—52no—
111#5101—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4096—24no—
121#4093—32no—
122#4093—32no—
123#4092—62no—
124#4090—32no—
125C2×#689C2×D311yescharacteristic, complemented
126C2×#688—32no—
127C2×#688—32no—
128C2×#688—64no—
129C2×#688C2×D311yescharacteristic, complemented
130#4086—32no—
131#4083—62no—
132C2×#687C2×D311yescharacteristic, complemented
133C2×#686C2×D311yescharacteristic, complemented
134#4076—62no—
135#4075—62no—
136#4072—31no—
137C22×#168C2×D311yescharacteristic
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C3×D5—21no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—84no—
162C2×Dic15C2×D414yes—
163D60—22no—
164D60—22no—
165D60—42no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—42no—
168C5×Dic6—22no—
169C5×Dic6—22no—
170C5×Dic6—42no—
171C3×C22⋊D5—42no—
172C2×C3×Dic5—21no—
173C3×D20—21no—
174C3×D20—21no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178C3×#168C2×D412yes—
179C3×#168C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41—51no—
182C2×C3×#41C2×D511yescharacteristic
183C22×D12—51no—
184C22×Dic6C2×D511yescharacteristic
185C3×#135—104no—
186C2×C3×Q16—51no—
187C2×C3×SD16—51no—
188C2×C3×SD16—51no—
189C2×C3×D8—51no—
190C22×C3×C8—51no—
191#951—24no—
192#949—104no—
193#947—52no—
194#944—52no—
195C2×#216C2×D512yescomplemented
196C2×#215—52no—
197#940—52no—
198#937—102no—
199#936—52no—
200#935—102no—
201C2×#214C2×D512yescomplemented
202C2×#213—52no—
203#930—102no—
204#926—51no—
205#924—102no—
206C2×#208C2×D511yescharacteristic
207C2×#204—52no—
208C2×#204—52no—
209C2×#204—104no—
210#815—52no—
211C8×Dic3—52no—
212C23×D5—61no—
213C5×#41—22no—
214C5×#41—22no—
215C2×C5×Q8—32no—
216C2×C5×Q8—61no—
217C2×C5×Q8—62no—
218C2×C5×Q8—62no—
219C2×C5×Q8C22×D311yescharacteristic
220C2×C5×D4—21no—
221C2×C5×D4C22×D311yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C2×C22⋊D5—64no—
227#709—22no—
228#709—22no—
229C2×D20—32no—
230C2×D20—62no—
231C2×D20—62no—
232C2×D20—61no—
233C2×D20C22×D311yescharacteristic
234C2×C4×D5—21no—
235C2×Dic10C22×D311yescharacteristic
236C5×Q16—64no—
237C5×SD16—64no—
238C5×M16—34no—
239C2×C5×C8—32no—
240C22⋊Dic5—32no—
241#689—22no—
242#688—22no—
243#688—64no—
244#688—64no—
245#687—22no—
246#686—22no—
247#685—64no—
248#685—64no—
249C4⋊Dic5—32no—
250#683—64no—
251C4×Dic5—32no—
252C2×#168#6714yescomplemented
253C2×#168C22×D311yescharacteristic
254C2×#168C22×D311yescharacteristic
255D40—64no—
256#677—64no—
257C2×#137—31no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—51no—
260C22×SD16—151no—
261#536—151no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—42no—
274C2×D15—44no—
275C2×D15—84no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5—41no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—24no—
283C3×Dic5—41no—
284C5×Dic3—42no—
285C23×D3—101no—
286C3×#41—22no—
287C3×#41—22no—
288C3×#41—102no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×Q8C22×D511yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—51no—
294C2×C3×D4—101no—
295C2×C3×D4C22×D511yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—104no—
300C22×Dic3—21no—
301C2×D12—52no—
302C2×D12—102no—
303C2×D12—102no—
304C2×D12—101no—
305C2×Dic6—22no—
306C2×Dic6—22no—
307C2×Dic6—21no—
308C2×Dic6C22×D512yes—
309C3×Q16—102no—
310C3×SD16—102no—
311C3×SD16—102no—
312C3×D8—102no—
313C2×C3×C8—54no—
314C2×C3×C8—51no—
315C2×C3×C8—51no—
316#217—52no—
317#217—104no—
318#216—24no—
319#215—104no—
320#214—24no—
321#213—104no—
322(C2×D3)⋊C4—104no—
323C4⋊Dic3—52no—
324Dic3⋊C4—104no—
325C4×Dic3—52no—
326#208C22⋊D514yescomplemented
327C2×C3⋊C8C22×D512yes—
328#204—104no—
329#204—104no—
330C23×C5—21no—
331C23×C5D3×D411yescharacteristic
332C22×D5—21no—
333C22×D5—62no—
334C22×D5—122no—
335C22×D5—242no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×Q8—62no—
339C5×Q8—62no—
340C5×Q8—122no—
341C5×D4—21no—
342C5×D4—21no—
343C5×D4—42no—
344C2×C4×C5—21no—
345C2×C4×C5—42no—
346C2×C4×C5—62no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—42no—
353C22⋊D5—244no—
354C2×Dic5—21no—
355C2×Dic5—34no—
356D20—21no—
357D20—21no—
358D20—62no—
359D20—62no—
360D20—122no—
361C4×D5—42no—
362Dic10—21no—
363Dic10—21no—
364C5×C8—34no—
365#168C2×#6712yes—
366#168C2×#6712yes—
367C2×#41—51no—
368C2×#41D3×D511yescharacteristic
369C22×Q8—31no—
370C22×D4—151no—
371#137—64no—
372AGL(1,ℤ/8)—304no—
373#135—104no—
374C2×Q16—32no—
375C2×Q16—51no—
376C2×SD16—32no—
377C2×SD16—51no—
378C2×SD16—51no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—51no—
384C2×D8—152no—
385C2×M16—31no—
386C22×C8—51no—
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—151no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—82no—
403C3×D5—81no—
404C23×C3—21no—
405C23×C3—101no—
406C23×C3D4×D511yescharacteristic
407C22×D3—102no—
408C22×D3—202no—
409C22×D3—402no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—101no—
413C3×Q8—101no—
414C3×D4—21no—
415C3×D4—21no—
416C3×D4—42no—
417C3×D4—101no—
418C3×D4—101no—
419C3×D4—202no—
420C2×C3×C4—21no—
421C2×C3×C4—42no—
422C2×C3×C4—101no—
423C2×C3×C4—202no—
424C2×C3×C4D4×D512yes—
425C2×C3×C4D4×D511yescharacteristic
426C2×C3×C4C2×C22⋊D512yes—
427C2×C3×C4C23×D511yescharacteristic
428#67—404no—
429C2×Dic3—22no—
430C2×Dic3—42no—
431C2×Dic3—54no—
432D12—102no—
433D12—102no—
434D12—202no—
435Dic6—22no—
436Dic6—22no—
437Dic6—42no—
438C3×C8—52no—
439C3×C8—52no—
440C3⋊C8C2×C22⋊D514yes—
441C22×C5—22no—
442C22×C5—42no—
443C22×C5—41no—
444C22×C5#94012yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—42no—
447C2×D5—41no—
448C2×D5—124no—
449C2×D5—122no—
450C2×D5—244no—
451C4×C5—41no—
452C4×C5—122no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—41no—
457Dic5—64no—
458C24—301no—
459#41—22no—
460#41—22no—
461#41—102no—
462#41—102no—
463C2×Q8—32no—
464C2×Q8—51no—
465C2×Q8—61no—
466C2×Q8—62no—
467C2×Q8—62no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—51no—
471C2×D4—101no—
472C2×D4—152no—
473C2×D4—304no—
474C2×D4—302no—
475C2×D4—302no—
476C2×D4—301no—
477C2×D4C2×D3×D511yescharacteristic
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—64no—
483Q16—102no—
484SD16—64no—
485SD16—102no—
486SD16—102no—
487SD16—304no—
488SD16—304no—
489SD16—304no—
490D8—102no—
491D8—304no—
492M16—34no—
493C2×C8—32no—
494C2×C8—54no—
495C2×C8—51no—
496C2×C8—51no—
497C4⋊C4—152no—
498C4⋊C4—304no—
499C22⋊C4—152no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—152no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3—202no—
508C22×C3—201no—
509C22×C3#408612yes—
510C22×C3C2×D4×D511yescharacteristic
511C2×D3—204no—
512C2×D3—202no—
513C2×D3—404no—
514C3×C4—41no—
515C3×C4—201no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C22×C22⋊D511yescharacteristic
519Dic3—42no—
520Dic3—104no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5#577012yes—
524C2×C5C2×#94011yescharacteristic
525D5—81no—
526D5—242no—
527C23—21no—
528C23—101no—
529C23—302no—
530C23—602no—
531C23—1202no—
532C23#679011yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—62no—
536Q8—62no—
537Q8—101no—
538Q8—101no—
539Q8—122no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—101no—
544D4—101no—
545D4—202no—
546D4—302no—
547D4—302no—
548D4—602no—
549D4—1204no—
550C2×C4—21no—
551C2×C4—42no—
552C2×C4—62no—
553C2×C4—101no—
554C2×C4—122no—
555C2×C4—154no—
556C2×C4—202no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D512yes—
559C2×C4#679011yescharacteristic
560C2×C4C22×D3×D511yescharacteristic
561C8—34no—
562C8—52no—
563C8—52no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3—401no—
567C2×C3#6611212yes—
568C2×C3C2×#408611yescharacteristic
569D3—402no—
570C5#8390511yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—41no—
574C22—202no—
575C22—201no—
576C22—604no—
577C22—602no—
578C22—1204no—
579C22#9156712yes—
580C22C2×#679011yescharacteristic
581C4—41no—
582C4—122no—
583C4—201no—
584C4—304no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061570511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—401no—
592C2—1202no—
593C2#1175535112yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756589C2semidirect
2. C2×C5×#951C2semidirect
3. C2×C3×#4096C2semidirect
4. #11754251C2semidirect
5. C22×#6660C2semidirect
6. C2×#91301C2semidirect
7. #11749356C2semidirect
8. #11749318C2semidirect
9. #11749109C2semidirect
10. #11749073C2semidirect
11. #11748324C2semidirect
23. C2×C5×#216C22semidirect
24. C2×C5×#214C22semidirect
27. C2×C3×#689C22semidirect
28. C2×C3×#688C22semidirect
29. C2×C3×#687C22semidirect
30. C2×C3×#686C22semidirect
33. #91385C22semidirect
34. #91368C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
47. C2×#4096D3semidirect
86. C5×#208D4semidirect
92. C2×C3×#168D4semidirect
104. C2×#951D5semidirect
125. C2×#689C2×D3semidirect
129. C2×#688C2×D3semidirect
132. C2×#687C2×D3semidirect
133. C2×#686C2×D3semidirect
195. C2×#216C2×D5semidirect
201. C2×#214C2×D5semidirect
252. C2×#168#67semidirect
326. #208C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83905semidirect
588. C3#10615705semidirect

Maximal subgroups

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

subgroupindex
#117565892
C2×C5×#9512
C2×C3×#40962
#117542512
C22×#66602
C2×#913012
#117493562
#117493182
#117491092
#117490732
#117483242
#106157053
#839055