Finite Group Databasebeta

← #14308001

Subgroups — #14308001

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
1C2×#91838C211yesmaximal, characteristic, complemented
2C5×#5833C211yesmaximal, characteristic, complemented
3C2×#91305C211yesmaximal, characteristic, complemented
4C2×C3×#3969C211yesmaximal, characteristic, complemented
5#11748768C211yesmaximal, characteristic, complemented
6C2×#90979C211yesmaximal, characteristic, complemented
7#11745986C211yesmaximal, characteristic, complemented
8#10602672—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C2×C5×#235C2211yescharacteristic
12#91838—22no—
13#91838—22no—
14C2×#6717—21no—
15C2×#6715—21no—
16C2×#6710C2211yescharacteristic
17C5×#946—21no—
18C5×#939—22no—
19C5×#938—21no—
20C5×#930—21no—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C5×#924—21no—
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25C2×#6667—22no—
26C2×#6660—21no—
27#91305—22no—
28#91305—22no—
29C2×#6654—21no—
30C3×#3969—22no—
31#90979—22no—
32#70392—51nomaximal, Hall
33C5×#537—31no—
34C2×#4095—31no—
35C2×#4095—31no—
36C2×#3969—31no—
37C2×#3969D311yescharacteristic, complemented
38#65277—31no—
39#64750—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×C5C2311yescharacteristic
50C2×D60—21no—
51C2×D60—21no—
52C2×D60—21no—
53C2×D60—21no—
54C2×D60—21no—
55C2×D60D412yescomplemented
56C2×C5×#67—21no—
57C2×C5×#67—22no—
58C22×C5×Dic3D412yes—
59C5×#235—21no—
60C5×#235—21no—
61C5×#235—21no—
62C5×#235—21no—
63C2×C5×D12D411yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C5×Dic6D411yescharacteristic
66C22×C3×Dic5—21no—
67#6717—24no—
68#6715—24no—
69#6710—21no—
70#6710D412yescomplemented
71C2×C3⋊#168—21no—
72C5×#217—22no—
73C5×(C2×D3)⋊C4—22no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3—21no—
76C5×Dic3⋊C4—22no—
77C3×C4×Dic5—21no—
78C3×C4×Dic5—21no—
79C3×#681—21no—
80C3×#681D412yescomplemented
81C2×C3×#168—21no—
82#6667—44no—
83#6660—24no—
84#6654—24no—
85#5833D511yescharacteristic, complemented
86C2×#949—51no—
87C2×#908—51no—
88C2×C3×#104—51no—
89#4939—51no—
90C2×#805—51no—
91#4554—51no—
92C2×C5×#41—31no—
93C2×C5×#41C2×D311yescharacteristic
94C22×D20—31no—
95C5×C22⋊Q8—61no—
96C5×C22⋊Q8—61no—
97C5×#121—61no—
98C5×#121—62no—
99C5×#121—61no—
100C2×C5×C4⋊C4—31no—
101#4095—62no—
102#4095—62no—
103#4095—62no—
104#4095—62no—
105C2×#688—61no—
106C2×#688—61no—
107C2×#686—61no—
108C2×#686—61no—
109C2×#685—62no—
110C2×C4×Dic5C2×D311yescharacteristic
111C2×#681—31no—
112C2×#681C2×D311yescharacteristic
113#3969—22no—
114#3969—62no—
115#2006—151noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—22no—
119C22×D15—42no—
120C22×D15—42no—
121C22×D15—41no—
122C22×D15—41no—
123C22×C5×D3—21no—
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—21no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5#4111yescharacteristic
139D60—22no—
140D60—22no—
141D60—41no—
142D60—41no—
143C5×#67—41no—
144C5×#67—41no—
145C5×#67—82no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—42no—
149C5×D12—21no—
150C5×D12—21no—
151C4×C5×D3—41no—
152C4×C5×D3—41no—
153C5×Dic6—21no—
154C5×Dic6—21no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—41no—
157C2×C3×Dic5—41no—
158C3⋊#168—22no—
159C3×#168—22no—
160C2×C3×#41C2×D511yescharacteristic
161C2×#235C2×D511yescharacteristic
162C22×D12—51no—
163C2×C3×M16—51no—
164C2×C3×C42—51no—
165#949—102no—
166#949—102no—
167#946—21no—
168C2×#215—101no—
169#939—22no—
170#938—21no—
171C2×#213—101no—
172#930—21no—
173C2×(C2×D3)⋊C4—102no—
174C2×C4⋊Dic3C2×D511yescharacteristic
175#924—21no—
176C2×#208—51no—
177#908—102no—
178#908—102no—
179C2×D24—101no—
180C2×#204—101no—
181C3×#104—102no—
182#805—102no—
183C23×D5—61no—
184C5×#41—21no—
185C5×#41—21no—
186C5×#41—21no—
187C5×#41—21no—
188C5×#41—61no—
189C5×#41—61no—
190C5×#41—61no—
191C5×#41—61no—
192C2×C5×Q8—31no—
193C2×C5×Q8D1211yescharacteristic
194C2×C5×D4—21no—
195C2×C5×D4—31no—
196C2×C5×D4—61no—
197C2×C5×D4—62no—
198C2×C5×D4D1211yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—32no—
201C22×C4×C5—61no—
202C22×C4×C5C22×D311yescharacteristic
203C22×Dic5—21no—
204C2×D20—32no—
205C2×D20—61no—
206C2×D20—61no—
207C2×D20—61no—
208C2×D20—61no—
209C2×D20—61no—
210C5×C4⋊C4—62no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4—61no—
213C5×C22⋊C4—62no—
214C5×C22⋊C4—62no—
215#688—64no—
216#688—64no—
217#686—64no—
218#686—64no—
219#685—124no—
220C4×Dic5—21no—
221C4×Dic5—21no—
222#681—21no—
223#681—32no—
224#681—61no—
225#681#6712yescomplemented
226C2×#168—21no—
227C2×#168—61no—
228C2×AGL(1,ℤ/8)—151no—
229C2×AGL(1,ℤ/8)—151no—
230#537—31no—
231C2×#104—51no—
232C2×#104—151no—
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—42no—
245C2×D15—82no—
246C2×D15—81no—
247C2×D15—81no—
248C2×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C3×C4×C5—41no—
252C3×C4×C5#12011yescharacteristic
253C3×C4×C5#12011yescharacteristic
254C3×C4×C5#12111yescharacteristic
255C3×C4×C5#12111yescharacteristic
256C3×Dic5—42no—
257C5×Dic3—41no—
258C5×Dic3—42no—
259C23×D3—101no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C2×C3×Q8C22⋊D511yescharacteristic
265C2×C3×D4—21no—
266C2×C3×D4C22⋊D511yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—21no—
271C2×#67—22no—
272C22×Dic3C22⋊D512yes—
273#235—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277C2×D12—52no—
278C2×D12—101no—
279C2×D12—101no—
280C2×D12—101no—
281C2×D12—101no—
282C2×D12—101no—
283C2×D12C22⋊D511yescharacteristic
284C2×C4×D3—21no—
285C2×Dic6C22⋊D511yescharacteristic
286C3×M16—52no—
287C3×M16—101no—
288C2×C3×C8—101no—
289C3×C42—101no—
290C3×C42—101no—
291#217—22no—
292#215—104no—
293#213—104no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—204no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298Dic3⋊C4—22no—
299#208—52no—
300#208—101no—
301C2×C3⋊C8—101no—
302D24—104no—
303#204—104no—
304C23×C5—21no—
305C23×C5—61no—
306C23×C5D3×D411yescharacteristic
307C22×D5—62no—
308C22×D5—122no—
309C22×D5—122no—
310C22×D5—121no—
311C22×D5—121no—
312C5×Q8—21no—
313C5×Q8—21no—
314C5×Q8—61no—
315C5×Q8—61no—
316C5×D4—21no—
317C5×D4—21no—
318C5×D4—41no—
319C5×D4—41no—
320C5×D4—61no—
321C5×D4—61no—
322C5×D4—121no—
323C5×D4—121no—
324C5×D4—242no—
325C2×C4×C5—21no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—62no—
329C2×C4×C5—61no—
330C2×C4×C5—121no—
331C2×C4×C5—121no—
332C2×C4×C5—122no—
333C2×C4×C5C2×D1211yescharacteristic
334C2×C4×C5#23511yescharacteristic
335C2×C4×C5D3×D411yescharacteristic
336C2×C4×C5D3×D411yescharacteristic
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5C2×#6711yescharacteristic
339C2×Dic5—22no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342D20—62no—
343D20—62no—
344D20—121no—
345D20—121no—
346#168—22no—
347#168—62no—
348C2×#41—31no—
349C2×#41D3×D511yescharacteristic
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—51no—
360C2×M16—151no—
361C22⋊Q8—61no—
362C22⋊Q8—61no—
363#121—61no—
364#121—62no—
365#121—61no—
366C2×C4⋊C4—31no—
367C2×C22⋊C4—302no—
368C2×C42—51no—
369#104—102no—
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—82no—
378C5×D3—81no—
379C23×C3—21no—
380C23×C3C2×C22⋊D511yescharacteristic
381C22×D3—21no—
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—21no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—102no—
397C2×C3×C4—201no—
398C2×C3×C4—201no—
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4#71111yescharacteristic
403C2×C3×C4C2×C22⋊D511yescharacteristic
404C2×C3×C4C2×C22⋊D511yescharacteristic
405#67—41no—
406#67—41no—
407#67—82no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—42no—
411D12—21no—
412D12—21no—
413D12—102no—
414D12—102no—
415D12—201no—
416D12—201no—
417C4×D3—41no—
418C4×D3—41no—
419Dic6—21no—
420Dic6—21no—
421C3×C8—102no—
422C3⋊C8—102no—
423C22×C5—21no—
424C22×C5—21no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—121no—
429C22×C5—121no—
430C22×C5—121no—
431C22×C5#88211yescharacteristic
432C22×C5#88411yescharacteristic
433C22×C5#94011yescharacteristic
434C2×D5—124no—
435C2×D5—122no—
436C2×D5—242no—
437C2×D5—241no—
438C2×D5—241no—
439C4×C5—41no—
440C4×C5—121no—
441C4×C5—122no—
442C4×C5#88211yescharacteristic
443C4×C5#88411yescharacteristic
444C4×C5#93011yescharacteristic
445C4×C5#93711yescharacteristic
446Dic5—42no—
447C24—301no—
448#41—21no—
449#41—21no—
450#41—21no—
451#41—21no—
452#41—61no—
453#41—61no—
454#41—61no—
455#41—61no—
456C2×Q8—31no—
457C2×Q8#120311yescharacteristic
458C2×D4—21no—
459C2×D4—31no—
460C2×D4—61no—
461C2×D4—62no—
462C2×D4—152no—
463C2×D4—301no—
464C2×D4—301no—
465C2×D4—301no—
466C2×D4—301no—
467C2×D4—301no—
468C2×D4#120311yescharacteristic
469C22×C4—21no—
470C22×C4—32no—
471C22×C4—61no—
472C22×C4—101no—
473C22×C4C2×D3×D511yescharacteristic
474SD16—304no—
475SD16—304no—
476D8—304no—
477D8—304no—
478M16—52no—
479M16—101no—
480M16—152no—
481M16—301no—
482C2×C8—101no—
483C2×C8—301no—
484C4⋊C4—62no—
485C4⋊C4—61no—
486C4⋊C4—61no—
487C22⋊C4—62no—
488C22⋊C4—62no—
489C22⋊C4—604no—
490C42—101no—
491C42—101no—
492C3×C5#200611yescharacteristic, complemented, Hall
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3#408411yescharacteristic
499C22×C3#408611yescharacteristic
500C22×C3#409911yescharacteristic
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—41no—
504C2×D3—204no—
505C2×D3—202no—
506C2×D3—402no—
507C2×D3—401no—
508C2×D3—401no—
509C3×C4—41no—
510C3×C4—202no—
511C3×C4#408311yescharacteristic
512C3×C4#408311yescharacteristic
513C3×C4#408511yescharacteristic
514C3×C4#408511yescharacteristic
515Dic3—41no—
516Dic3—42no—
517C2×C5—21no—
518C2×C5—21no—
519C2×C5—81no—
520C2×C5—241no—
521C2×C5#482211yescharacteristic
522C2×C5#482711yescharacteristic
523C2×C5#496011yescharacteristic
524D5—242no—
525C23—21no—
526C23—61no—
527C23—302no—
528C23—602no—
529C23—602no—
530C23—601no—
531C23—601no—
532C23D3×C22⋊D511yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—61no—
536Q8—61no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—61no—
542D4—61no—
543D4—121no—
544D4—121no—
545D4—242no—
546D4—302no—
547D4—302no—
548D4—601no—
549D4—601no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—102no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—122no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4#678211yescharacteristic
562C2×C4C2×#120311yescharacteristic
563C2×C4D5×#6711yescharacteristic
564C2×C4D3×C22⋊D511yescharacteristic
565C2×C4#679011yescharacteristic
566C2×C4#679011yescharacteristic
567C8—102no—
568C8—302no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—81no—
572C2×C3#6551211yescharacteristic
573C2×C3#6553011yescharacteristic
574C2×C3#6553411yescharacteristic
575D3—81no—
576D3—402no—
577C5#7039211yescharacteristic, complemented, Sylow
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—121no—
584C22—121no—
585C22—121no—
586C22—604no—
587C22—602no—
588C22—1202no—
589C22—1201no—
590C22—1201no—
591C22#9155711yescharacteristic
592C22#9156711yescharacteristic
593C22#9157011yescharacteristic
594C4—41no—
595C4—122no—
596C4—121no—
597C4—202no—
598C4#9155811yescharacteristic
599C4#9156611yescharacteristic
600C4#9157311yescharacteristic
601C4#9157711yescharacteristic
602C3#1060267211yescharacteristic, complemented, Sylow
603C2—21no—
604C2—21no—
605C2—81no—
606C2—241no—
607C2—1202no—
608C2#1174942011yescharacteristic
609C2#1174945911yescharacteristic
610C2#1174952311yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#2006
LCSG ▷ C22×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. C2×#91838C2semidirect
2. C5×#5833C2semidirect
3. C2×#91305C2semidirect
4. C2×C3×#3969C2semidirect
5. #11748768C2semidirect
6. C2×#90979C2semidirect
7. #11745986C2semidirect
37. C2×#3969D3semidirect
55. C2×D60D4semidirect
70. #6710D4semidirect
80. C3×#681D4semidirect
85. #5833D5semidirect
225. #681#67semidirect
492. C3×C5#2006semidirect
577. C5#70392semidirect
602. C3#10602672semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C5×#58332
C2×#913052
C2×C3×#39692
#117487682
C2×#909792
#117459862
#106026723
#703925