Finite Group Databasebeta

← #14439604

Subgroups — #14439604

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756589C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic, complemented
3C2×C3×#4095C211yesmaximal, characteristic, complemented
4#11754600C211yesmaximal, characteristic, complemented
5C2×#91305C211yesmaximal, characteristic, complemented
6C22×#6653C211yesmaximal, characteristic, complemented
7#11749343C212yesmaximal, complemented
8#11749318C212yesmaximal, complemented
9#11749095C212yesmaximal, complemented
10#11749073C212yesmaximal, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10615637—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91836C2212yescomplemented
18#91829C2212yescomplemented
19#91826—22no—
20#91819—22no—
21#91815C2211yescharacteristic
22C5×#950—24no—
23C2×C5×#216C2211yescharacteristic, complemented
24C2×C5×#215C2211yescharacteristic, complemented
25C2×C5×#214C2211yescharacteristic, complemented
26C2×C5×#213C2211yescharacteristic, complemented
27C22×C5×C3⋊C8C2211yescharacteristic
28C3×#4095—24no—
29C2×C3×#688C2212yescomplemented
30C2×C3×#686C2212yescomplemented
31C2×C3×#681C2211yescharacteristic
32#91563—22no—
33#91463C2212yescomplemented
34#91456—22no—
35#91368C2212yescomplemented
36C2×#6660C2212yescomplemented
37#91305—24no—
38C2×#6654C2212yescomplemented
39C2×#6653—24no—
40C2×#6653C2212yes—
41C2×#6653C2212yes—
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83940—51nomaximal, Hall
45C2×C5×#135—31no—
46#66164—31no—
47#66164—31no—
48C2×#4095—31no—
49C2×#4095D311yescharacteristic, complemented
50C22×D40—31no—
51#65480—32no—
52#65465—32no—
53#65465—32no—
54#65440—32no—
55#65390—31no—
56C23×D15—21no—
57C23×C3×D5—21no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×#1220—24no—
66C2×D60—22no—
67C2×D60—22no—
68C2×D60—21no—
69C2×D60C2312yes—
70C2×C5×#67—21no—
71C5×#235—22no—
72C5×#235—22no—
73C2×C5×D12C2311yescharacteristic
74C2×C4×C5×D3—21no—
75C2×C5×Dic6C2311yescharacteristic
76C2×C3×D20—22no—
77C2×C3×D20—22no—
78C2×C3×D20—21no—
79C2×C3×D20C2312yes—
80C2×#1201—24no—
81#6719D412yes—
82#6714—24no—
83C4⋊Dic15D412yes—
84C4×Dic15C2312yes—
85C5×#216—22no—
86C5×#215—22no—
87C5×#214—22no—
88C5×#213—22no—
89C2×C5×C3⋊C8D414yescomplemented
90C2×C5×C3⋊C8C2311yescharacteristic
91C2×C5×C3⋊C8C2311yescharacteristic
92C3×#688—24no—
93C3×#686—24no—
94C3×#681D414yescomplemented
95C2×C3×#168C2312yes—
96#6665—24no—
97#6660—24no—
98#6654—24no—
99#6653—24no—
100#6653—24no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5830—51no—
103C2×#950D511yescharacteristic, complemented
104#5805—51no—
105C22×#213—51no—
106C2×#908—51no—
107#5176—52no—
108#5168—52no—
109#5154—52no—
110#5151—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C2×C5×#41C2×D311yescharacteristic
114C22×D20—31no—
115C22×D20C2×D311yescharacteristic
116C5×#135—64no—
117C2×C5×Q16—31no—
118C2×C5×SD16—31no—
119C2×C5×SD16—31no—
120C2×C5×D8—31no—
121C22×C5×C8—31no—
122#4095—24no—
123#4095—64no—
124#4093—32no—
125#4093—32no—
126C2×#688—32no—
127C2×#688C2×D312yescomplemented
128#4086—32no—
129#4086—32no—
130#4083—62no—
131#4083—62no—
132C2×#686—32no—
133C2×#686C2×D312yescomplemented
134#4076—62no—
135#4076—62no—
136#4072—31no—
137C2×#681C2×D311yescharacteristic
138C2×D40—32no—
139C2×D40—32no—
140C2×D40—64no—
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C5×D3—21no—
150C22×C3×D5—22no—
151C22×C3×D5—42no—
152C22×C3×D5—82no—
153C3×C5×Q8—21no—
154C3×C5×Q8—21no—
155C3×C5×D4—21no—
156C3×C5×D4—21no—
157C3×C5×D4—42no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—42no—
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2411yescharacteristic
164#1220—84no—
165C2×Dic15C2×D414yes—
166D60—22no—
167D60—22no—
168D60—42no—
169C5×#67—42no—
170C2×C5×Dic3—21no—
171C5×D12—21no—
172C5×D12—21no—
173C4×C5×D3—42no—
174C5×Dic6—21no—
175C5×Dic6—21no—
176C3×D20—22no—
177C3×D20—22no—
178C3×D20—42no—
179#1201—84no—
180C3×#168C2×D414yes—
181C5×C3⋊C8C2×D412yes—
182C5×C3⋊C8C2×D412yes—
183C2×C3×#41C2×D511yescharacteristic
184C22×C3×D4—51no—
185C2×#235C2×D511yescharacteristic
186C22×D12—51no—
187C3×AGL(1,ℤ/8)—104no—
188C2×C3×SD16—52no—
189C2×C3×D8—52no—
190C2×C3×M16—51no—
191#953—102no—
192#950—24no—
193#947—52no—
194C2×#216C2×D511yescharacteristic, complemented
195C2×#215C2×D511yescharacteristic, complemented
196#940—52no—
197#940—52no—
198#938—102no—
199#937—102no—
200#936—52no—
201C2×#214C2×D511yescharacteristic, complemented
202C2×#213—52no—
203C2×#213—52no—
204C2×#213—104no—
205C2×#213C2×D511yescharacteristic, complemented
206#930—102no—
207#926—51no—
208C22×C3⋊C8C2×D511yescharacteristic
209#908—104no—
210C2×D24—52no—
211C2×#204—52no—
212#815—52no—
213C8×Dic3—52no—
214C23×D5—21no—
215C23×D5—61no—
216C5×#41—22no—
217C5×#41—22no—
218C5×#41—62no—
219C5×#41—62no—
220C2×C5×Q8—31no—
221C2×C5×Q8C22×D311yescharacteristic
222C2×C5×D4—21no—
223C2×C5×D4—31no—
224C2×C5×D4—61no—
225C2×C5×D4C22×D311yescharacteristic
226C22×C4×C5—21no—
227C22×C4×C5—61no—
228C22×C4×C5C22×D311yescharacteristic
229C2×C22⋊D5—64no—
230C2×C22⋊D5—64no—
231C2×D20—22no—
232C2×D20—22no—
233C2×D20—21no—
234C2×D20—32no—
235C2×D20—62no—
236C2×D20—62no—
237C2×D20—61no—
238C2×D20C22×D312yes—
239C5×Q16—62no—
240C5×SD16—62no—
241C5×SD16—62no—
242C5×D8—62no—
243C2×C5×C8—34no—
244C2×C5×C8—31no—
245C2×C5×C8—31no—
246C22⋊Dic5—32no—
247#688—24no—
248#688—64no—
249#686—24no—
250#686—64no—
251#685—64no—
252#685—64no—
253C4⋊Dic5—32no—
254C4×Dic5—32no—
255#681#6714yescomplemented
256C2×#168C22×D312yes—
257D40—64no—
258D40—64no—
259C2×AGL(1,ℤ/8)—51no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—31no—
262C22×D8—151no—
263#535—151no—
264#535—151no—
265#496—152no—
266#496—152no—
267#495—152no—
268#493—152no—
269#405—151no—
270C22×C3×C5—22no—
271C22×C3×C5—41no—
272C22×C3×C5—42no—
273C22×C3×C5#12712yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×D15—42no—
276C2×D15—44no—
277C2×D15—84no—
278C2×C5×D3—41no—
279C2×C5×D3—42no—
280C2×C3×D5—42no—
281C2×C3×D5—44no—
282C2×C3×D5—84no—
283C3×C4×C5—41no—
284C3×C4×C5#12712yes—
285C3×C4×C5C22×D411yescharacteristic
286C3×C4×C5C22×D411yescharacteristic
287Dic15—24no—
288C5×Dic3—41no—
289C24×C3—101no—
290C23×D3—101no—
291C3×#41—22no—
292C3×#41—22no—
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—52no—
296C2×C3×D4—102no—
297C2×C3×D4—101no—
298C2×C3×D4—102no—
299C2×C3×D4C22×D511yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—21no—
303C2×#67—104no—
304C2×#67—104no—
305#235—22no—
306#235—22no—
307C2×D12—52no—
308C2×D12—102no—
309C2×D12—102no—
310C2×D12—101no—
311C2×D12C22×D511yescharacteristic
312C2×C4×D3—21no—
313C2×Dic6C22×D511yescharacteristic
314C3×SD16—104no—
315C3×D8—104no—
316C3×M16—54no—
317C2×C3×C8—52no—
318#217—52no—
319#217—104no—
320#216—22no—
321#215—22no—
322#214—22no—
323#213—22no—
324#213—104no—
325#213—104no—
326(C2×D3)⋊C4—104no—
327C4⋊Dic3—52no—
328C4×Dic3—52no—
329C2×C3⋊C8C22⋊D514yescomplemented
330C2×C3⋊C8C22×D511yescharacteristic
331C2×C3⋊C8C22×D511yescharacteristic
332D24—104no—
333#204—104no—
334C23×C5—21no—
335C23×C5—61no—
336C23×C5D3×D411yescharacteristic
337C22×D5—22no—
338C22×D5—42no—
339C22×D5—62no—
340C22×D5—82no—
341C22×D5—122no—
342C22×D5—242no—
343C5×Q8—21no—
344C5×Q8—21no—
345C5×Q8—61no—
346C5×Q8—61no—
347C5×D4—21no—
348C5×D4—21no—
349C5×D4—42no—
350C5×D4—61no—
351C5×D4—61no—
352C5×D4—122no—
353C2×C4×C5—21no—
354C2×C4×C5—42no—
355C2×C4×C5—61no—
356C2×C4×C5—122no—
357C2×C4×C5D3×D412yes—
358C2×C4×C5D3×D411yescharacteristic
359C2×C4×C5C2×#6712yes—
360C2×C4×C5C23×D311yescharacteristic
361C22⋊D5—244no—
362C22⋊D5—244no—
363C2×Dic5—34no—
364D20—22no—
365D20—22no—
366D20—42no—
367D20—62no—
368D20—62no—
369D20—122no—
370C5×C8—32no—
371C5×C8—32no—
372#168C2×#6714yes—
373C2×#41—31no—
374C2×#41D3×D511yescharacteristic
375C22×D4—51no—
376C22×D4—151no—
377AGL(1,ℤ/8)—104no—
378AGL(1,ℤ/8)—304no—
379#135—64no—
380C2×Q16—31no—
381C2×SD16—31no—
382C2×SD16—31no—
383C2×SD16—52no—
384C2×SD16—152no—
385C2×D8—31no—
386C2×D8—52no—
387C2×D8—152no—
388C2×D8—152no—
389C2×D8—152no—
390C2×D8—304no—
391C2×M16—51no—
392C22×C8—31no—
393#127—152no—
394#127—152no—
395#124—152no—
396#124—152no—
397#121—302no—
398#121—302no—
399#120—302no—
400#120—302no—
401#117—151no—
402#97—152no—
403C4×C8—152no—
404C2×C3×C5—22no—
405C2×C3×C5—81no—
406C2×C3×C5C2×#12711yescharacteristic
407C2×C3×C5#57612yes—
408D15—82no—
409C3×D5—82no—
410C5×D3—81no—
411C23×C3—21no—
412C23×C3—102no—
413C23×C3—202no—
414C23×C3—402no—
415C23×C3D4×D511yescharacteristic
416C22×D3—21no—
417C22×D3—102no—
418C22×D3—202no—
419C22×D3—402no—
420C3×Q8—21no—
421C3×Q8—21no—
422C3×D4—21no—
423C3×D4—21no—
424C3×D4—42no—
425C3×D4—102no—
426C3×D4—102no—
427C3×D4—202no—
428C2×C3×C4—21no—
429C2×C3×C4—42no—
430C2×C3×C4D4×D512yes—
431C2×C3×C4D4×D511yescharacteristic
432C2×C3×C4C2×C22⋊D512yes—
433C2×C3×C4C23×D511yescharacteristic
434#67—42no—
435#67—404no—
436#67—404no—
437C2×Dic3—21no—
438C2×Dic3—54no—
439D12—21no—
440D12—21no—
441D12—102no—
442D12—102no—
443D12—202no—
444C4×D3—42no—
445Dic6—21no—
446Dic6—21no—
447C3×C8—54no—
448C3⋊C8C2×C22⋊D512yes—
449C3⋊C8C2×C22⋊D512yes—
450C22×C5—22no—
451C22×C5—42no—
452C22×C5—41no—
453C22×C5—122no—
454C22×C5—121no—
455C22×C5#94012yes—
456C22×C5C2×D3×D411yescharacteristic
457C2×D5—44no—
458C2×D5—42no—
459C2×D5—84no—
460C2×D5—124no—
461C2×D5—122no—
462C2×D5—244no—
463C4×C5—41no—
464C4×C5—121no—
465C4×C5#94012yes—
466C4×C5C2×D3×D411yescharacteristic
467C4×C5C22×#6711yescharacteristic
468Dic5—64no—
469C24—101no—
470C24—301no—
471#41—22no—
472#41—22no—
473#41—62no—
474#41—62no—
475C2×Q8—31no—
476C2×Q8C2×D3×D511yescharacteristic
477C2×D4—21no—
478C2×D4—31no—
479C2×D4—52no—
480C2×D4—61no—
481C2×D4—102no—
482C2×D4—102no—
483C2×D4—101no—
484C2×D4—152no—
485C2×D4—304no—
486C2×D4—304no—
487C2×D4—302no—
488C2×D4—302no—
489C2×D4—301no—
490C2×D4C2×D3×D511yescharacteristic
491C22×C4—21no—
492C22×C4—61no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—62no—
495SD16—62no—
496SD16—62no—
497SD16—104no—
498SD16—304no—
499D8—62no—
500D8—104no—
501D8—304no—
502D8—304no—
503D8—304no—
504M16—54no—
505C2×C8—34no—
506C2×C8—31no—
507C2×C8—31no—
508C2×C8—52no—
509C4⋊C4—152no—
510C22⋊C4—152no—
511C22⋊C4—304no—
512C22⋊C4—304no—
513C42—152no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—204no—
519C22×C3—202no—
520C22×C3—404no—
521C22×C3#408612yes—
522C22×C3C2×D4×D511yescharacteristic
523C2×D3—42no—
524C2×D3—41no—
525C2×D3—204no—
526C2×D3—202no—
527C2×D3—404no—
528C3×C4—41no—
529C3×C4#408612yes—
530C3×C4C2×D4×D511yescharacteristic
531C3×C4C22×C22⋊D511yescharacteristic
532Dic3—41no—
533Dic3—104no—
534C2×C5—22no—
535C2×C5—81no—
536C2×C5—241no—
537C2×C5#577412yes—
538C2×C5C2×#94011yescharacteristic
539D5—82no—
540D5—242no—
541C23—21no—
542C23—61no—
543C23—102no—
544C23—202no—
545C23—302no—
546C23—402no—
547C23—602no—
548C23—1202no—
549C23#679011yescharacteristic
550Q8—21no—
551Q8—21no—
552Q8—61no—
553Q8—61no—
554D4—21no—
555D4—21no—
556D4—42no—
557D4—61no—
558D4—61no—
559D4—102no—
560D4—102no—
561D4—122no—
562D4—202no—
563D4—302no—
564D4—302no—
565D4—602no—
566D4—1204no—
567D4—1204no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—61no—
571C2×C4—122no—
572C2×C4—154no—
573C2×C4D5×#6712yes—
574C2×C4D3×C22⋊D512yes—
575C2×C4#679011yescharacteristic
576C2×C4C22×D3×D511yescharacteristic
577C8—32no—
578C8—32no—
579C8—54no—
580C2×C3—22no—
581C2×C3—81no—
582C2×C3—402no—
583C2×C3#6610312yes—
584C2×C3C2×#408611yescharacteristic
585D3—81no—
586D3—402no—
587C5#8394011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—41no—
591C22—122no—
592C22—121no—
593C22—204no—
594C22—202no—
595C22—404no—
596C22—604no—
597C22—602no—
598C22—1204no—
599C22#9156712yes—
600C22C2×#679011yescharacteristic
601C4—41no—
602C4—121no—
603C4—304no—
604C4#9156712yes—
605C4C2×D5×#6711yescharacteristic
606C4C2×D3×C22⋊D511yescharacteristic
607C3#1061563711yescharacteristic, complemented, Sylow
608C2—22no—
609C2—81no—
610C2—241no—
611C2—402no—
612C2—1202no—
613C2#1175533012yes—
614C2C2×#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#3155
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×#950C2semidirect
3. C2×C3×#4095C2semidirect
4. #11754600C2semidirect
5. C2×#91305C2semidirect
6. C22×#6653C2semidirect
7. #11749343C2semidirect
8. #11749318C2semidirect
9. #11749095C2semidirect
10. #11749073C2semidirect
11. #11748326C2semidirect
17. #91836C22semidirect
18. #91829C22semidirect
23. C2×C5×#216C22semidirect
24. C2×C5×#215C22semidirect
25. C2×C5×#214C22semidirect
26. C2×C5×#213C22semidirect
29. C2×C3×#688C22semidirect
30. C2×C3×#686C22semidirect
33. #91463C22semidirect
35. #91368C22semidirect
36. C2×#6660C22semidirect
38. C2×#6654C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
49. C2×#4095D3semidirect
89. C2×C5×C3⋊C8D4semidirect
94. C3×#681D4semidirect
103. C2×#950D5semidirect
127. C2×#688C2×D3semidirect
133. C2×#686C2×D3semidirect
194. C2×#216C2×D5semidirect
195. C2×#215C2×D5semidirect
201. C2×#214C2×D5semidirect
205. C2×#213C2×D5semidirect
255. #681#67semidirect
329. C2×C3⋊C8C22⋊D5semidirect
514. C3×C5#3155semidirect
587. C5#83940semidirect
607. C3#10615637semidirect

Maximal subgroups

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

subgroupindex
#117565892
C2×C5×#9502
C2×C3×#40952
#117546002
C2×#913052
C22×#66532
#117493432
#117493182
#117490952
#117490732
#117483262
#106156373
#839405