Finite Group Databasebeta

← #14424387

Subgroups — #14424387

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92019C211yesmaximal, characteristic
2C5×#5526C211yesmaximal, characteristic, complemented
3C22×#6660C211yesmaximal, characteristic, complemented
4C2×#91307C211yesmaximal, characteristic, complemented
5#11751102C211yesmaximal, characteristic, complemented
6C3×#65291C211yesmaximal, characteristic, complemented
7#11748345C211yesmaximal, characteristic, complemented
8#11747516C214yesmaximal, complemented
9#11747483C214yesmaximal, complemented
10#10615135—31nomaximal, Hall
11C22×D60C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C5×Dic6C2211yescharacteristic, complemented
14C2×C3×#709C2211yescharacteristic
15C2×#6790—22no—
16#92019—24no—
17#92019—24no—
18C2×D3×D20C2212yes—
19C2×D5×D12—21no—
20C2×#6773—21no—
21C2×#6769C2212yes—
22C3×C5×#117C2211yescharacteristic, complemented
23C2×#6710C2211yescharacteristic, complemented
24C5×#897C2214yescomplemented
25C5×#886—22no—
26C5×#875—21no—
27C5×#869—21no—
28C22×C3×#168C2211yescharacteristic, complemented
29C2×#6661C2212yescomplemented
30C2×#6660—24no—
31C2×#6660C2214yescomplemented
32#91307—24no—
33C2×#6655C2212yescomplemented
34#91093C2214yescomplemented
35C3×#3942C2212yescomplemented
36C3×#3941C2212yescomplemented
37(C2×D3)⋊#168C2214yescomplemented
38#78835—51nomaximal, Hall
39C2×#4149—31no—
40C5×#536—31no—
41C2×#4088—31no—
42C22×#688—31no—
43#65523—31no—
44#65336—34no—
45#65335—34no—
46#65291D311yescharacteristic, complemented
47#65290—31no—
48C23×D15—21no—
49C22×D3×D5—22no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×D60—21no—
52C2×D60—22no—
53C2×D60D414yes—
54C2×D60C2312yes—
55C2×C5×#67D412yes—
56C22×C5×Dic3—21no—
57C5×#235—22no—
58C5×#235—22no—
59C2×C5×D12D411yescharacteristic
60C2×C4×C5×D3C2312yes—
61C2×C5×Dic6—22no—
62C2×C5×Dic6—22no—
63C2×C5×Dic6—21no—
64C2×C5×Dic6D411yescharacteristic
65C2×C5×Dic6C2312yes—
66C2×C3×C22⋊D5—21no—
67C3×#709—22no—
68C3×#709D414yes—
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×Dic10C2311yescharacteristic
72#6790—216no—
73C2×#1203—22no—
74C2×#1202—22no—
75C2×#1200—22no—
76D3×D20—24no—
77D3×D20—24no—
78D5×D12—28no—
79#6773—28no—
80#6769—24no—
81#6769—24no—
82C3×C5×C4⋊C4C2312yes—
83C3×C5×C22⋊C4—21no—
84C3×C42×C5—21no—
85#6710—22no—
86C2×C3⋊#168C2312yes—
87C5×(C2×D3)⋊C4—24no—
88C5×C4⋊Dic3—24no—
89C2×C3×#168—22no—
90C2×C3×#168C2312yes—
91#6661—24no—
92#6660—28no—
93#6655—24no—
94C2×#1009—51no—
95C2×#951—51no—
96C22×#204—51no—
97#5526D511yescharacteristic, complemented
98C3×#416—51no—
99#5110—51no—
100#5001—51no—
101#4808—54no—
102#4776—54no—
103C2×C5×#41—31no—
104C22×C5×Q8—31no—
105#4149—64no—
106#4149—64no—
107C2×#713—61no—
108C2×D4×D5—61no—
109C2×D4×D5—62no—
110C2×#709—32no—
111C2×#709C2×D311yescharacteristic
112C22×D20—31no—
113C22×D20—32no—
114C5×C4⋊Q8—61no—
115C5×#124—61no—
116C5×#123—62no—
117C5×C22⋊Q8—34no—
118C5×#117C2×D311yescharacteristic, complemented
119C2×#689—32no—
120#4088—64no—
121C2×#688—32no—
122C2×#688—34no—
123C2×#688—64no—
124C2×#681—31no—
125C22×#168C2×D311yescharacteristic, complemented
126C22⋊#168—34no—
127#3942C2×D312yescomplemented
128#3941—34no—
129#3941C2×D312yescomplemented
130#3009—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—22no—
133C22×D15—24no—
134C22×D15—82no—
135C22×C5×D3C2×D412yes—
136C22×C3×D5—21no—
137C2×D3×D5—28no—
138C2×D3×D5—84no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144D60—24no—
145D60—22no—
146D60C2×D414yes—
147C5×#67—24no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—42no—
150C2×C5×Dic3C2×D412yes—
151C5×D12—22no—
152C4×C5×D3—22no—
153C4×C5×D3—22no—
154C5×Dic6—22no—
155C5×Dic6—22no—
156C5×Dic6—22no—
157C5×Dic6—42no—
158C3×C22⋊D5—24no—
159C2×C3×Dic5—21no—
160C3×D20—21no—
161C3×D20C2×D412yes—
162C3×C4×D5—24no—
163C3×Dic10—21no—
164C3×Dic10C2×D412yes—
165#1203—28no—
166#1202—28no—
167#1200—28no—
168C3⋊#168—22no—
169C3×#168—22no—
170C2×C3×#41—51no—
171#1009—104no—
172#1009—104no—
173C2×#239—52no—
174C2×D3×D4—52no—
175C2×D3×D4—102no—
176C2×#235—101no—
177C2×#235C2×D511yescharacteristic
178C22×D12—51no—
179C22×D12—101no—
180C22×Dic6C2×D511yescharacteristic, complemented
181C22×C3×C8—51no—
182C3×#117C2×D511yescharacteristic, complemented
183#951—104no—
184C2×#216—52no—
185C2×#214—52no—
186C2×#208—51no—
187C2×#204—54no—
188C2×#204—104no—
189#897C2×D514yescomplemented
190#886—22no—
191#875—21no—
192#869—21no—
193C3×#103—52no—
194C3×#102—52no—
195(C2×D3)⋊C8—54no—
196#809—54no—
197C23×D5—62no—
198C23×D5—61no—
199C5×#41—62no—
200C5×#41—62no—
201C2×C5×Q8—31no—
202C2×C5×Q8—32no—
203C2×C5×Q8—61no—
204C2×C5×Q8—62no—
205C2×C5×Q8—62no—
206C2×C5×D4—32no—
207C2×C5×D4—31no—
208C22×C4×C5—32no—
209C22×C4×C5—61no—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—21no—
212C2×C22⋊D5—62no—
213#713—68no—
214D4×D5—68no—
215D4×D5—616no—
216#709—22no—
217#709—64no—
218#709—64no—
219#709D1214yes—
220C2×D20—34no—
221C2×D20—32no—
222C2×D20—64no—
223C2×D20—62no—
224C2×D20—62no—
225C2×D20—61no—
226C2×D20—64no—
227C2×D20C22×D311yescharacteristic
228C2×C4×D5—21no—
229C2×C4×D5—62no—
230C2×Dic10C22×D311yescharacteristic
231C5×C4⋊C4—64no—
232C5×C4⋊C4C22×D312yes—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—64no—
235C42×C5—21no—
236#689—64no—
237#688—68no—
238#688—64no—
239#681—62no—
240C2×#168—22no—
241C2×#168—32no—
242C2×#168C22×D312yes—
243C2×H(5,𝔽2)—151no—
244C2×#137—151no—
245C22×SD16—151no—
246#536—31no—
247#452—154no—
248#450—154no—
249#418—151no—
250#416—51no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—24no—
256C2×D15—44no—
257C2×D15—84no—
258C2×C5×D3—22no—
259C2×C5×D3—24no—
260C2×C3×D5—22no—
261C2×C3×D5—42no—
262D3×D5—88no—
263C3×C4×C5—42no—
264C3×C4×C5#12012yes—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C22×D411yescharacteristic
267C3×Dic5—22no—
268C5×Dic3—22no—
269C5×Dic3—42no—
270C23×D3—101no—
271C23×D3—102no—
272C3×#41—54no—
273C3×#41—102no—
274C2×C3×Q8—51no—
275C2×C3×D4—51no—
276C2×C3×D4—101no—
277C22×C3×C4—101no—
278C22×C3×C4C22×D511yescharacteristic
279C2×#67—102no—
280C2×#67C22⋊D512yes—
281C22×Dic3—21no—
282#239—104no—
283#239—104no—
284D3×D4—104no—
285D3×D4—104no—
286D3×D4—1016no—
287#235—22no—
288#235—22no—
289#235—108no—
290C2×D12—54no—
291C2×D12—52no—
292C2×D12—108no—
293C2×D12—102no—
294C2×D12—102no—
295C2×D12—101no—
296C2×D12C22⋊D511yescharacteristic
297C2×C4×D3—102no—
298C2×C4×D3C22×D512yes—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6C22⋊D511yescharacteristic
303C2×Dic6C22×D512yes—
304C2×C3×C8—52no—
305C2×C3×C8—102no—
306C3×C4⋊C4C22×D512yes—
307C3×C22⋊C4—21no—
308C3×C42—21no—
309#216—104no—
310#214—104no—
311(C2×D3)⋊C4—24no—
312C4⋊Dic3—24no—
313#208—102no—
314C2×C3⋊C8—52no—
315#204—108no—
316C23×C5—32no—
317C23×C5D3×D411yescharacteristic
318C22×D5—21no—
319C22×D5—68no—
320C22×D5—62no—
321C22×D5—64no—
322C22×D5—244no—
323C22×D5—242no—
324C5×Q8—62no—
325C5×Q8—62no—
326C5×Q8—62no—
327C5×Q8—122no—
328C5×D4—64no—
329C5×D4—62no—
330C2×C4×C5—22no—
331C2×C4×C5—32no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5—62no—
335C2×C4×C5—122no—
336C2×C4×C5C2×D1212yes—
337C2×C4×C5D3×D412yes—
338C2×C4×C5D3×D411yescharacteristic
339C2×C4×C5C23×D311yescharacteristic
340C22⋊D5—24no—
341C22⋊D5—68no—
342C2×Dic5—21no—
343D20—21no—
344D20—34no—
345D20—68no—
346D20—64no—
347D20—62no—
348D20C2×D1212yes—
349C4×D5—24no—
350C4×D5—68no—
351Dic10—21no—
352Dic10C2×D1212yes—
353#168—22no—
354#168—62no—
355H(5,𝔽2)—304no—
356H(5,𝔽2)—304no—
357C2×#41—31no—
358C2×#41—51no—
359C2×#41—152no—
360C2×#41—301no—
361C22×Q8—31no—
362C22×D4—152no—
363C22×D4—151no—
364C22×D4—301no—
365C22×D4—302no—
366#137—304no—
367C2×Q16—152no—
368C2×SD16—154no—
369C2×SD16—152no—
370C2×SD16—304no—
371C2×M16—151no—
372C22×C8—51no—
373C4⋊Q8—61no—
374#124—61no—
375#123—62no—
376C22⋊Q8—34no—
377#117D3×D511yescharacteristic, complemented
378#103—52no—
379#102—52no—
380#102—154no—
381C22⋊C8—154no—
382C2×C3×C5—22no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—44no—
386C3×D5—42no—
387C5×D3—42no—
388C23×C3—101no—
389C23×C3C2×C22⋊D511yescharacteristic
390C22×D3—108no—
391C22×D3—102no—
392C22×D3—104no—
393C22×D3—404no—
394C22×D3—402no—
395C22×D3C2×C22⋊D512yes—
396C3×Q8—52no—
397C3×Q8—101no—
398C3×D4—52no—
399C3×D4—104no—
400C3×D4—101no—
401C2×C3×C4—22no—
402C2×C3×C4—101no—
403C2×C3×C4—104no—
404C2×C3×C4D4×D512yes—
405C2×C3×C4D4×D512yes—
406C2×C3×C4C2×C22⋊D511yescharacteristic
407C2×C3×C4C23×D511yescharacteristic
408#67—24no—
409#67—108no—
410C2×Dic3—22no—
411C2×Dic3—42no—
412C2×Dic3C2×C22⋊D512yes—
413D12—22no—
414D12—54no—
415D12—108no—
416D12—102no—
417D12—104no—
418C4×D3—22no—
419C4×D3—22no—
420C4×D3—108no—
421Dic6—22no—
422Dic6—22no—
423Dic6—22no—
424Dic6—42no—
425C3×C8—102no—
426C3⋊C8—102no—
427C22×C5—22no—
428C22×C5—62no—
429C22×C5—64no—
430C22×C5#88212yes—
431C22×C5C2×D3×D411yescharacteristic
432C2×D5—22no—
433C2×D5—42no—
434C2×D5—64no—
435C2×D5—124no—
436C2×D5—248no—
437C2×D5—244no—
438C4×C5—42no—
439C4×C5—62no—
440C4×C5—122no—
441C4×C5#88212yes—
442C4×C5C22×D1211yescharacteristic
443C4×C5C2×D3×D411yescharacteristic
444Dic5—22no—
445C24—302no—
446C24—301no—
447#41—54no—
448#41—62no—
449#41—62no—
450#41—102no—
451#41—304no—
452#41—304no—
453#41—308no—
454C2×Q8—31no—
455C2×Q8—32no—
456C2×Q8—51no—
457C2×Q8—61no—
458C2×Q8—62no—
459C2×Q8—62no—
460C2×D4—32no—
461C2×D4—31no—
462C2×D4—51no—
463C2×D4—101no—
464C2×D4—154no—
465C2×D4—152no—
466C2×D4—302no—
467C2×D4—304no—
468C2×D4—304no—
469C2×D4—308no—
470C2×D4—302no—
471C2×D4—3016no—
472C2×D4—302no—
473C2×D4—301no—
474C22×C4—32no—
475C22×C4—61no—
476C22×C4—101no—
477C22×C4—302no—
478C22×C4C2×D3×D511yescharacteristic
479Q16—304no—
480SD16—308no—
481SD16—304no—
482M16—302no—
483C2×C8—52no—
484C2×C8—102no—
485C2×C8—152no—
486C4⋊C4—64no—
487C4⋊C4C2×D3×D512yes—
488C22⋊C4—21no—
489C22⋊C4—64no—
490C42—21no—
491C3×C5#300911yescharacteristic, complemented, Hall
492C22×C3—22no—
493C22×C3—102no—
494C22×C3—202no—
495C22×C3#408312yes—
496C22×C3C22×C22⋊D511yescharacteristic
497C2×D3—22no—
498C2×D3—24no—
499C2×D3—104no—
500C2×D3—204no—
501C2×D3—408no—
502C2×D3—404no—
503C3×C4—42no—
504C3×C4—102no—
505C3×C4#408312yes—
506C3×C4C2×D4×D511yescharacteristic
507C3×C4C2×D4×D511yescharacteristic
508Dic3—22no—
509Dic3—42no—
510C2×C5—22no—
511C2×C5—122no—
512C2×C5C2×#88211yescharacteristic
513C2×C5#577012yes—
514D5—42no—
515D5—124no—
516C23—32no—
517C23—101no—
518C23—308no—
519C23—302no—
520C23—304no—
521C23—1202no—
522C23—1204no—
523C23D3×C22⋊D511yescharacteristic
524Q8—52no—
525Q8—62no—
526Q8—62no—
527Q8—62no—
528Q8—101no—
529Q8—122no—
530D4—52no—
531D4—64no—
532D4—62no—
533D4—104no—
534D4—101no—
535D4—154no—
536D4—308no—
537D4—308no—
538D4—304no—
539D4—302no—
540C2×C4—22no—
541C2×C4—32no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—101no—
546C2×C4—104no—
547C2×C4—122no—
548C2×C4—308no—
549C2×C4D5×D1212yes—
550C2×C4#677712yes—
551C2×C4D3×C22⋊D511yescharacteristic
552C2×C4C22×D3×D511yescharacteristic
553C8—102no—
554C8—302no—
555C2×C3—22no—
556C2×C3—202no—
557C2×C3C2×#408311yescharacteristic
558C2×C3#6617112yes—
559D3—42no—
560D3—204no—
561C5#7883511yescharacteristic, complemented, Sylow
562C22—22no—
563C22—64no—
564C22—62no—
565C22—102no—
566C22—202no—
567C22—304no—
568C22—604no—
569C22—1204no—
570C22—1208no—
571C22#9147512yes—
572C22C2×D3×C22⋊D511yescharacteristic
573C4—42no—
574C4—62no—
575C4—102no—
576C4—122no—
577C4#9147512yes—
578C4C2×D5×D1211yescharacteristic
579C4C2×#677711yescharacteristic
580C3#1061513511yescharacteristic, complemented, Sylow
581C2—22no—
582C2—122no—
583C2—202no—
584C2—604no—
585C2C2×#9147511yescharacteristic
586C2#1175532612yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#92019C2
hypercenter#117D3×D5
hypocenterC3×C5#3009
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C5×#5526C2semidirect
3. C22×#6660C2semidirect
4. C2×#91307C2semidirect
5. #11751102C2semidirect
6. C3×#65291C2semidirect
7. #11748345C2semidirect
8. #11747516C2semidirect
9. #11747483C2semidirect
13. C22×C5×Dic6C22semidirect
22. C3×C5×#117C22semidirect
23. C2×#6710C22semidirect
24. C5×#897C22semidirect
28. C22×C3×#168C22semidirect
29. C2×#6661C22semidirect
31. C2×#6660C22semidirect
33. C2×#6655C22semidirect
34. #91093C22semidirect
35. C3×#3942C22semidirect
36. C3×#3941C22semidirect
37. (C2×D3)⋊#168C22semidirect
46. #65291D3semidirect
97. #5526D5semidirect
118. C5×#117C2×D3semidirect
125. C22×#168C2×D3semidirect
127. #3942C2×D3semidirect
129. #3941C2×D3semidirect
180. C22×Dic6C2×D5semidirect
182. C3×#117C2×D5semidirect
189. #897C2×D5semidirect
377. #117D3×D5semidirect
491. C3×C5#3009semidirect
561. C5#78835semidirect
580. C3#10615135semidirect

Maximal subgroups

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

subgroupindex
C2×#920192
C5×#55262
C22×#66602
C2×#913072
#117511022
C3×#652912
#117483452
#117475162
#117474832
#106151353
#788355