Finite Group Databasebeta

← #14307991

Subgroups — #14307991

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756592C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3C2×#91797C211yesmaximal, characteristic, complemented
4C2×C3×C5×#104C211yesmaximal, characteristic, complemented
5#11751040C211yesmaximal, characteristic, complemented
6C2×#91089C211yesmaximal, characteristic, complemented
7#11746375C211yesmaximal, characteristic, complemented
8#10601185—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C22×D60C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14#91838—22no—
15#91838—22no—
16#91835—21no—
17C2×#6717—21no—
18#91828—22no—
19#91827—21no—
20C2×#6715—21no—
21#91819—21no—
22C2×#6714—22no—
23C2×C4⋊Dic15C2211yescharacteristic
24#91813—21no—
25C2×#6710C2211yescharacteristic
26#91797—22no—
27#91797—22no—
28C2×D120—21no—
29C2×#6706—21no—
30C3×C5×#104—22no—
31#91089—22no—
32#70392—51nomaximal, Hall
33#66167—31no—
34C2×#4095—31no—
35C2×#4054—31no—
36C2×C5×#104D311yescharacteristic, complemented
37#65228—31no—
38C2×#3937—31no—
39#64774—31no—
40C23×D15—21no—
41C3×C5×#41—21no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41—21no—
45C2×C3×C5×Q8D411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4D411yescharacteristic
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—21no—
52C2×#1220—22no—
53C22×Dic15D412yes—
54#6817—21no—
55#6817—21no—
56#6817—21no—
57#6817—21no—
58C2×D60—21no—
59C2×D60—21no—
60C2×D60—21no—
61C2×D60—21no—
62C2×D60—21no—
63C2×D60D411yescharacteristic
64C2×D60D412yescomplemented
65C2×C4×D15—21no—
66C2×Dic30D411yescharacteristic
67C3×C5×M16—21no—
68C3×C5×M16D412yescomplemented
69C2×C3×C5×C8—21no—
70C3×C42×C5—21no—
71C3×C42×C5—21no—
72#6719—22no—
73#6717—24no—
74#6715—24no—
75#6714—22no—
76#6714—44no—
77C4⋊Dic15—21no—
78C4⋊Dic15—21no—
79#6712—22no—
80#6710—21no—
81#6710D412yescomplemented
82C2×C3⋊#168—21no—
83D120—24no—
84#6706—24no—
85#5833—51no—
86C2×#949—51no—
87C2×#908—51no—
88C2×C3×#104D511yescharacteristic, complemented
89#4939—51no—
90C2×#805—51no—
91#4554—51no—
92C2×C5×#41C2×D311yescharacteristic
93C2×#709—31no—
94C22×D20—31no—
95C2×C5×M16C2×D311yescharacteristic
96C2×C42×C5C2×D311yescharacteristic
97#4095—62no—
98#4095—62no—
99#4092—61no—
100C2×#688—61no—
101#4085—62no—
102#4084—61no—
103C2×#686—61no—
104#4076—61no—
105C2×#685—62no—
106C2×C4⋊Dic5—31no—
107#4070—61no—
108C2×#681—31no—
109#4054—62no—
110#4054—62no—
111C2×D40—61no—
112C2×#677—61no—
113C5×#104—22no—
114#3937—62no—
115#2006—151noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—21no—
119C22×D15—22no—
120C22×D15—42no—
121C22×D15—42no—
122C22×D15—41no—
123C22×D15—41no—
124C3×C5×Q8—21no—
125C3×C5×Q8—21no—
126C3×C5×D4—21no—
127C3×C5×D4—21no—
128C3×C5×D4—41no—
129C3×C5×D4—41no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4111yescharacteristic
142#1220—41no—
143#1220—41no—
144#1220—82no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15—42no—
148D60—22no—
149D60—21no—
150D60—22no—
151D60—21no—
152D60—41no—
153D60—41no—
154C4×D15—41no—
155C4×D15—41no—
156Dic30—21no—
157Dic30—21no—
158C3×C5×C8—22no—
159C3⋊#168—22no—
160C2×C3×#41C2×D511yescharacteristic
161C2×#235—51no—
162C22×D12—51no—
163C2×C3×M16C2×D511yescharacteristic
164C2×C3×C42C2×D511yescharacteristic
165#949—102no—
166#949—102no—
167#946—101no—
168C2×#215—101no—
169#939—102no—
170#938—101no—
171C2×#213—101no—
172#930—101no—
173C2×(C2×D3)⋊C4—102no—
174C2×C4⋊Dic3—51no—
175#924—101no—
176C2×#208—51no—
177#908—102no—
178#908—102no—
179C2×D24—101no—
180C2×#204—101no—
181C3×#104—22no—
182#805—102no—
183C23×D5—61no—
184C5×#41—21no—
185C5×#41—21no—
186C5×#41—21no—
187C5×#41—21no—
188C2×C5×Q8D1211yescharacteristic
189C2×C5×D4—21no—
190C2×C5×D4D1211yescharacteristic
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—61no—
195C2×C22⋊D5—62no—
196C22×Dic5—32no—
197#709—61no—
198#709—61no—
199#709—61no—
200#709—61no—
201C2×D20—32no—
202C2×D20—31no—
203C2×D20—61no—
204C2×D20—61no—
205C2×D20—61no—
206C2×D20—61no—
207C2×D20—61no—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×M16—21no—
211C5×M16#6712yescomplemented
212C2×C5×C8—21no—
213C42×C5—21no—
214C42×C5—21no—
215C22⋊Dic5—62no—
216#688—64no—
217#686—64no—
218#685—62no—
219#685—124no—
220C4⋊Dic5—61no—
221C4⋊Dic5—61no—
222#683—62no—
223#681—32no—
224#681—61no—
225C2×#168—61no—
226D40—64no—
227#677—64no—
228C2×AGL(1,ℤ/8)—151no—
229C2×AGL(1,ℤ/8)—151no—
230#537—151no—
231C2×#104—151no—
232C2×#104D1511yescharacteristic, complemented
233#390—151no—
234#343—151no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5#12011yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5#12711yescharacteristic
243C2×D15—44no—
244C2×D15—41no—
245C2×D15—42no—
246C2×D15—41no—
247C2×D15—41no—
248C2×D15—82no—
249C2×D15—81no—
250C2×D15—81no—
251C3×C4×C5—42no—
252C3×C4×C5—41no—
253C3×C4×C5#12011yescharacteristic
254C3×C4×C5#12011yescharacteristic
255C3×C4×C5#12111yescharacteristic
256C3×C4×C5#12111yescharacteristic
257Dic15—41no—
258Dic15—42no—
259C23×D3—101no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C2×C3×Q8D2011yescharacteristic
265C2×C3×D4—21no—
266C2×C3×D4D2011yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C2×#67—102no—
272C22×Dic3—52no—
273#235—101no—
274#235—101no—
275#235—101no—
276#235—101no—
277C2×D12—51no—
278C2×D12—52no—
279C2×D12—101no—
280C2×D12—101no—
281C2×D12—101no—
282C2×D12—101no—
283C2×D12—101no—
284C2×C4×D3—101no—
285C2×Dic6—51no—
286C3×M16—21no—
287C3×M16C22⋊D512yescomplemented
288C2×C3×C8—21no—
289C3×C42—21no—
290C3×C42—21no—
291#217—102no—
292#215—104no—
293#213—104no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—204no—
296C4⋊Dic3—101no—
297C4⋊Dic3—101no—
298Dic3⋊C4—102no—
299#208—52no—
300#208—101no—
301C2×C3⋊C8—101no—
302D24—104no—
303#204—104no—
304C23×C5—21no—
305C23×C5D3×D411yescharacteristic
306C22×D5—61no—
307C22×D5—62no—
308C22×D5—122no—
309C22×D5—122no—
310C22×D5—121no—
311C22×D5—121no—
312C5×Q8—21no—
313C5×Q8—21no—
314C5×D4—21no—
315C5×D4—21no—
316C5×D4—41no—
317C5×D4—41no—
318C2×C4×C5—22no—
319C2×C4×C5—21no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5C2×D1211yescharacteristic
325C2×C4×C5#23511yescharacteristic
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5D3×D411yescharacteristic
329C2×C4×C5C2×#6711yescharacteristic
330C22⋊D5—121no—
331C22⋊D5—121no—
332C22⋊D5—242no—
333C2×Dic5—61no—
334C2×Dic5—62no—
335C2×Dic5—122no—
336D20—62no—
337D20—61no—
338D20—62no—
339D20—61no—
340D20—121no—
341D20—121no—
342C4×D5—121no—
343C4×D5—121no—
344Dic10—61no—
345Dic10—61no—
346C5×C8—22no—
347#168—62no—
348C2×#41—151no—
349C2×#41C2×D1511yescharacteristic
350C22×D4—151no—
351AGL(1,ℤ/8)—302no—
352AGL(1,ℤ/8)—302no—
353AGL(1,ℤ/8)—302no—
354AGL(1,ℤ/8)—302no—
355C2×SD16—301no—
356C2×SD16—301no—
357C2×D8—301no—
358C2×D8—301no—
359C2×M16—151no—
360C2×M16C2×D1511yescharacteristic
361C22⋊Q8—301no—
362C22⋊Q8—301no—
363#121—301no—
364#121—302no—
365#121—301no—
366C2×C4⋊C4—151no—
367C2×C22⋊C4—302no—
368C2×C42C2×D1511yescharacteristic
369#104—22no—
370#104—302no—
371C2×C3×C5—21no—
372C2×C3×C5—21no—
373C2×C3×C5—81no—
374C2×C3×C5#39211yescharacteristic
375C2×C3×C5#45311yescharacteristic
376C2×C3×C5#45411yescharacteristic
377D15—81no—
378D15—82no—
379C23×C3—21no—
380C23×C3D4×D511yescharacteristic
381C22×D3—101no—
382C22×D3—102no—
383C22×D3—202no—
384C22×D3—202no—
385C22×D3—201no—
386C22×D3—201no—
387C3×Q8—21no—
388C3×Q8—21no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—41no—
392C3×D4—41no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4C2×D2011yescharacteristic
400C2×C3×C4#70911yescharacteristic
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4D4×D511yescharacteristic
404C2×C3×C4C2×C22⋊D511yescharacteristic
405#67—201no—
406#67—201no—
407#67—402no—
408C2×Dic3—101no—
409C2×Dic3—102no—
410C2×Dic3—202no—
411D12—102no—
412D12—101no—
413D12—102no—
414D12—101no—
415D12—201no—
416D12—201no—
417C4×D3—201no—
418C4×D3—201no—
419Dic6—101no—
420Dic6—101no—
421C3×C8—22no—
422C3⋊C8—102no—
423C22×C5—21no—
424C22×C5—21no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5#88211yescharacteristic
429C22×C5#88411yescharacteristic
430C22×C5#94011yescharacteristic
431C2×D5—124no—
432C2×D5—121no—
433C2×D5—122no—
434C2×D5—121no—
435C2×D5—121no—
436C2×D5—242no—
437C2×D5—241no—
438C2×D5—241no—
439C4×C5—42no—
440C4×C5—41no—
441C4×C5#88211yescharacteristic
442C4×C5#88411yescharacteristic
443C4×C5#93011yescharacteristic
444C4×C5#93711yescharacteristic
445Dic5—121no—
446Dic5—122no—
447C24—301no—
448#41—21no—
449#41—21no—
450#41—21no—
451#41—21no—
452#41—301no—
453#41—301no—
454#41—301no—
455#41—301no—
456C2×Q8—151no—
457C2×Q8D6011yescharacteristic
458C2×D4—21no—
459C2×D4—151no—
460C2×D4—152no—
461C2×D4—301no—
462C2×D4—302no—
463C2×D4—301no—
464C2×D4—301no—
465C2×D4—301no—
466C2×D4—301no—
467C2×D4—301no—
468C2×D4D6011yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—152no—
472C22×C4—301no—
473C22×C4C22×D1511yescharacteristic
474SD16—304no—
475SD16—304no—
476D8—304no—
477D8—304no—
478M16—21no—
479M16—152no—
480M16—301no—
481M16#122012yescomplemented
482C2×C8—21no—
483C2×C8—301no—
484C4⋊C4—302no—
485C4⋊C4—301no—
486C4⋊C4—301no—
487C22⋊C4—302no—
488C22⋊C4—302no—
489C22⋊C4—604no—
490C42—21no—
491C42—21no—
492C3×C5#200611yescharacteristic, complemented, Hall
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3#402811yescharacteristic
499C22×C3#403011yescharacteristic
500C22×C3#408611yescharacteristic
501C2×D3—204no—
502C2×D3—201no—
503C2×D3—201no—
504C2×D3—201no—
505C2×D3—202no—
506C2×D3—402no—
507C2×D3—401no—
508C2×D3—401no—
509C3×C4—42no—
510C3×C4—41no—
511C3×C4#402811yescharacteristic
512C3×C4#403011yescharacteristic
513C3×C4#407611yescharacteristic
514C3×C4#408311yescharacteristic
515Dic3—202no—
516Dic3—201no—
517C2×C5—21no—
518C2×C5—21no—
519C2×C5—81no—
520C2×C5#482211yescharacteristic
521C2×C5#482711yescharacteristic
522C2×C5#496011yescharacteristic
523D5—242no—
524D5—241no—
525C23—21no—
526C23—301no—
527C23—302no—
528C23—602no—
529C23—602no—
530C23—601no—
531C23—601no—
532C23D4×D1511yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—301no—
536Q8—301no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—302no—
542D4—301no—
543D4—301no—
544D4—302no—
545D4—601no—
546D4—601no—
547D4—601no—
548D4—601no—
549D4—1202no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—302no—
557C2×C4—301no—
558C2×C4—601no—
559C2×C4—601no—
560C2×C4—602no—
561C2×C4C2×D6011yescharacteristic
562C2×C4#681711yescharacteristic
563C2×C4D4×D1511yescharacteristic
564C2×C4D4×D1511yescharacteristic
565C2×C4D4×D1511yescharacteristic
566C2×C4C2×#122011yescharacteristic
567C8—22no—
568C8—302no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—81no—
572C2×C3#6511111yescharacteristic
573C2×C3#6511611yescharacteristic
574C2×C3#6524911yescharacteristic
575D3—402no—
576D3—401no—
577C5#7039211yescharacteristic, complemented, Sylow
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—604no—
584C22—601no—
585C22—601no—
586C22—601no—
587C22—602no—
588C22—1202no—
589C22—1201no—
590C22—1201no—
591C22#9177111yescharacteristic
592C22#9177311yescharacteristic
593C22#9182911yescharacteristic
594C4—42no—
595C4—41no—
596C4—602no—
597C4—601no—
598C4#9177111yescharacteristic
599C4#9177311yescharacteristic
600C4#9181911yescharacteristic
601C4#9182611yescharacteristic
602C3#1060118511yescharacteristic, complemented, Sylow
603C2—21no—
604C2—21no—
605C2—81no—
606C2—1202no—
607C2—1201no—
608C2#1175092311yescharacteristic
609C2#1175092811yescharacteristic
610C2#1175106111yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
hypercenterC2×#104D15
hypocenterC3×C5#2006
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #11756592C2semidirect
2. C2×#91838C2semidirect
3. C2×#91797C2semidirect
4. C2×C3×C5×#104C2semidirect
5. #11751040C2semidirect
6. C2×#91089C2semidirect
7. #11746375C2semidirect
36. C2×C5×#104D3semidirect
64. C2×D60D4semidirect
68. C3×C5×M16D4semidirect
81. #6710D4semidirect
88. C2×C3×#104D5semidirect
211. C5×M16#67semidirect
232. C2×#104D15semidirect
287. C3×M16C22⋊D5semidirect
481. M16#1220semidirect
492. C3×C5#2006semidirect
577. C5#70392semidirect
602. C3#10601185semidirect

Maximal subgroups

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

subgroupindex
#117565922
C2×#918382
C2×#917972
C2×C3×C5×#1042
#117510402
C2×#910892
#117463752
#106011853
#703925