Finite Group Databasebeta

← #14424379

Subgroups — #14424379

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×#92018C211yesmaximal, characteristic
2C22×C5×#204C211yesmaximal, characteristic, complemented
3#11754270C211yesmaximal, characteristic, complemented
4C2×#91307C211yesmaximal, characteristic, complemented
5#11751211C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748386C211yesmaximal, characteristic, complemented
8#11748158C214yesmaximal, complemented
9#11748118C214yesmaximal, complemented
10#10615590—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13C22×C5×Dic6C2211yescharacteristic, complemented
14C2×C3×#709C2211yescharacteristic
15C2×D3×C22⋊D5—22no—
16#92018—24no—
17#92018—24no—
18C2×#6777C2212yes—
19C2×D5×D12—21no—
20C2×#6772—21no—
21C2×#6768C2212yes—
22C22×C3×C5×C8C2211yescharacteristic, complemented
23C2×#6710C2211yescharacteristic, complemented
24C2×C5×#204—24no—
25C2×C5×#204C2214yescomplemented
26C3×#4072C2211yescharacteristic, complemented
27#91542—22no—
28#91383C2214yescomplemented
29#91376—21no—
30#91375—21no—
31C2×#6661C2212yescomplemented
32#91307—24no—
33C2×#6655C2212yescomplemented
34#91104C2214yescomplemented
35C3×#3953C2212yescomplemented
36C3×#3948C2212yescomplemented
37#90966C2214yescomplemented
38#78835—51nomaximal, Hall
39C2×#4144—31no—
40C22×C5×SD16—31no—
41#66150—31no—
42C2×#4088—31no—
43#65504—31no—
44#65462—34no—
45#65458—34no—
46#65402D311yescharacteristic, complemented
47#65399—31no—
48C23×C5×D3—21no—
49C22×D3×D5—22no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220D412yes—
52#6817—22no—
53#6817—22no—
54C2×D60D411yescharacteristic
55C2×C4×D15C2312yes—
56C2×Dic30D411yescharacteristic
57C22×C5×Dic3—21no—
58C2×C5×D12—21no—
59C2×C5×D12—22no—
60C2×C5×D12D414yes—
61C2×C5×D12C2312yes—
62C2×C5×Dic6—22no—
63C2×C5×Dic6—22no—
64C2×C5×Dic6—21no—
65C2×C5×Dic6C2312yes—
66C2×C3×C22⋊D5—21no—
67C3×#709—22no—
68C3×#709D414yes—
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×Dic10C2311yescharacteristic
72D3×C22⋊D5—216no—
73C2×#1203—22no—
74C2×#1201—22no—
75C2×D3×Dic5—22no—
76#6777—24no—
77#6777—24no—
78D5×D12—28no—
79#6772—28no—
80#6768—24no—
81#6768—24no—
82C2×C3×C5×C8—22no—
83C2×C3×C5×C8C2312yes—
84#6710—22no—
85C2×C3⋊#168C2312yes—
86C5×#204—28no—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90#6668—24no—
91#6667—24no—
92#6661—24no—
93#6655—24no—
94C2×#1009—51no—
95C2×#951—51no—
96C22×#204D511yescharacteristic, complemented
97#5526—51no—
98C3×#416—51no—
99#5110—51no—
100#5001—51no—
101#4808—54no—
102#4776—54no—
103C22×C5×Q8—31no—
104C22×C5×D4—31no—
105C22×C22⋊D5—62no—
106#4144—64no—
107#4144—64no—
108C2×#711—32no—
109C2×#711—61no—
110C2×D4×D5—32no—
111C2×D4×D5—61no—
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C2×C5×SD16—34no—
115C2×C5×SD16—64no—
116C22×C5×C8C2×D311yescharacteristic, complemented
117#4093—61no—
118#4092—34no—
119#4090—61no—
120C2×#689—32no—
121#4088—64no—
122C2×#688—32no—
123#4075—62no—
124#4072C2×D311yescharacteristic, complemented
125C2×#681—31no—
126#3964—34no—
127#3953C2×D312yescomplemented
128#3952—34no—
129#3948C2×D312yescomplemented
130#3009—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15C2×D412yes—
133C22×C5×D3—22no—
134C22×C5×D3—24no—
135C22×C5×D3—82no—
136C22×C3×D5—21no—
137C2×D3×D5—28no—
138C2×D3×D5—84no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2411yescharacteristic
143#1220—24no—
144C2×Dic15C2×D412yes—
145D60—22no—
146C4×D15—22no—
147C4×D15—22no—
148Dic30—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—42no—
151C5×D12—24no—
152C5×D12—22no—
153C5×D12C2×D414yes—
154C5×Dic6—22no—
155C5×Dic6—22no—
156C5×Dic6—42no—
157C3×C22⋊D5—24no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C3×D20—21no—
161C3×D20C2×D412yes—
162C3×C4×D5—24no—
163C3×Dic10—21no—
164C3×Dic10C2×D412yes—
165#1203—28no—
166#1201—28no—
167D3×Dic5—28no—
168C3×C5×C8—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—51no—
177C2×#235—101no—
178C22×D12—101no—
179C22×D12C2×D511yescharacteristic
180C22×Dic6C2×D511yescharacteristic, complemented
181C22×C3×C8C2×D511yescharacteristic, complemented
182C3×#117—51no—
183#951—104no—
184C2×#216—52no—
185C2×#214—52no—
186C2×#208—51no—
187C2×#204—24no—
188C2×#204C2×D514yescomplemented
189#897—54no—
190#886—102no—
191#875—101no—
192#869—101no—
193C3×#103—52no—
194C3×#102—52no—
195(C2×D3)⋊C8—54no—
196#809—54no—
197C24×C5—61no—
198C23×D5—62no—
199C2×C5×Q8—32no—
200C2×C5×Q8—61no—
201C2×C5×Q8—62no—
202C2×C5×Q8—62no—
203C2×C5×D4—34no—
204C2×C5×D4—32no—
205C2×C5×D4—62no—
206C2×C5×D4—61no—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—21no—
210C2×C22⋊D5—32no—
211C2×C22⋊D5—62no—
212C2×C22⋊D5—62no—
213C2×C22⋊D5—616no—
214C22×Dic5—62no—
215#711—64no—
216#711—68no—
217#711—64no—
218D4×D5—68no—
219D4×D5—64no—
220D4×D5—64no—
221#709—22no—
222#709—62no—
223#709—62no—
224#709D1214yes—
225C2×D20—31no—
226C2×D20C22×D311yescharacteristic
227C2×C4×D5—21no—
228C2×C4×D5—32no—
229C2×Dic10—31no—
230C2×Dic10C22×D311yescharacteristic
231C5×SD16—68no—
232C2×C5×C8—22no—
233C2×C5×C8C22×D312yes—
234C22⋊Dic5—21no—
235#689—64no—
236#688—64no—
237#685—64no—
238C4⋊Dic5C22×D312yes—
239#683—64no—
240C4×Dic5—21no—
241#681—62no—
242C2×#168—32no—
243C2×H(5,𝔽2)—151no—
244C2×#137—151no—
245C22×SD16—31no—
246#536—151no—
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—22no—
256C2×D15—24no—
257C2×C5×D3—24no—
258C2×C5×D3—44no—
259C2×C5×D3—84no—
260C2×C3×D5—22no—
261C2×C3×D5—42no—
262D3×D5—88no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267C3×Dic5—22no—
268C3×Dic5—42no—
269C5×Dic3—42no—
270C23×D3—21no—
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—52no—
280C2×#67—102no—
281C22×Dic3—21no—
282#239—104no—
283#239—104no—
284D3×D4—104no—
285D3×D4—1016no—
286D3×D4—104no—
287#235—108no—
288#235—102no—
289#235—102no—
290C2×D12—21no—
291C2×D12—22no—
292C2×D12—51no—
293C2×D12—108no—
294C2×D12—102no—
295C2×D12C22⋊D514yes—
296C2×D12C22×D512yes—
297C2×C4×D3—52no—
298C2×C4×D3—102no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6—51no—
303C2×Dic6C22×D512yes—
304C2×C3×C8—22no—
305C2×C3×C8C22×D512yes—
306C3×C4⋊C4—52no—
307C3×C22⋊C4—101no—
308C3×C42—101no—
309#216—104no—
310#214—104no—
311(C2×D3)⋊C4—104no—
312C4⋊Dic3—104no—
313#208—102no—
314C2×C3⋊C8—52no—
315#204—28no—
316C23×C5—62no—
317C23×C5—64no—
318C23×C5—242no—
319C23×C5D3×D411yescharacteristic
320C22×D5—21no—
321C22×D5—32no—
322C22×D5—68no—
323C22×D5—244no—
324C5×Q8—62no—
325C5×Q8—62no—
326C5×Q8—122no—
327C5×D4—34no—
328C5×D4—64no—
329C5×D4—62no—
330C2×C4×C5—62no—
331C2×C4×C5—122no—
332C2×C4×C5C2×D1212yes—
333C2×C4×C5D3×D411yescharacteristic
334C2×C4×C5D3×D412yes—
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—24no—
337C22⋊D5—68no—
338C22⋊D5—68no—
339C22⋊D5—64no—
340C2×Dic5—21no—
341C2×Dic5—22no—
342C2×Dic5—32no—
343C2×Dic5—68no—
344D20—21no—
345D20—62no—
346D20C2×D1212yes—
347C4×D5—24no—
348C4×D5—62no—
349C4×D5—62no—
350Dic10—21no—
351Dic10—62no—
352Dic10C2×D1212yes—
353C5×C8—22no—
354#168—62no—
355H(5,𝔽2)—304no—
356H(5,𝔽2)—304no—
357C2×#41—51no—
358C2×#41—151no—
359C2×#41—152no—
360C2×#41—301no—
361C22×Q8—31no—
362C22×D4—31no—
363C22×D4—152no—
364C22×D4—301no—
365C22×D4—302no—
366#137—304no—
367C2×Q16—152no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—152no—
371C2×M16—151no—
372C22×C8D3×D511yescharacteristic, complemented
373C4⋊Q8—301no—
374#124—301no—
375#123—302no—
376C22⋊Q8—154no—
377#117—51no—
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—42no—
386C3×D5—42no—
387C5×D3—44no—
388C23×C3—101no—
389C23×C3D4×D511yescharacteristic
390C22×D3—22no—
391C22×D3—24no—
392C22×D3—52no—
393C22×D3—82no—
394C22×D3—108no—
395C22×D3—404no—
396C3×Q8—52no—
397C3×Q8—101no—
398C3×D4—52no—
399C3×D4—104no—
400C3×D4—101no—
401C2×C3×C4—101no—
402C2×C3×C4—104no—
403C2×C3×C4—102no—
404C2×C3×C4D4×D512yes—
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4C2×C22⋊D512yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—108no—
409#67—104no—
410C2×Dic3—22no—
411C2×Dic3—42no—
412C2×Dic3—52no—
413D12—22no—
414D12—24no—
415D12—108no—
416D12—102no—
417D12C2×C22⋊D514yes—
418C4×D3—108no—
419C4×D3—102no—
420C4×D3—102no—
421Dic6—22no—
422Dic6—22no—
423Dic6—42no—
424Dic6—102no—
425C3×C8—22no—
426C3⋊C8—102no—
427C22×C5—22no—
428C22×C5—64no—
429C22×C5—124no—
430C22×C5—244no—
431C22×C5#88212yes—
432C22×C5C2×D3×D411yescharacteristic
433C2×D5—22no—
434C2×D5—42no—
435C2×D5—62no—
436C2×D5—64no—
437C2×D5—248no—
438C4×C5—122no—
439C4×C5#88212yes—
440C4×C5C22×D1211yescharacteristic
441C4×C5C2×D3×D411yescharacteristic
442Dic5—22no—
443Dic5—42no—
444Dic5—62no—
445C24—61no—
446C24—302no—
447#41—54no—
448#41—102no—
449#41—308no—
450#41—304no—
451#41—304no—
452#41—302no—
453#41—302no—
454C2×Q8—32no—
455C2×Q8—51no—
456C2×Q8—61no—
457C2×Q8—62no—
458C2×Q8—62no—
459C2×Q8—151no—
460C2×D4—34no—
461C2×D4—32no—
462C2×D4—51no—
463C2×D4—62no—
464C2×D4—61no—
465C2×D4—101no—
466C2×D4—152no—
467C2×D4—151no—
468C2×D4—308no—
469C2×D4—302no—
470C2×D4—302no—
471C2×D4—304no—
472C2×D4—304no—
473C2×D4—3016no—
474C22×C4—61no—
475C22×C4—101no—
476C22×C4—152no—
477C22×C4—302no—
478C22×C4C2×D3×D511yescharacteristic
479Q16—304no—
480SD16—68no—
481SD16—304no—
482M16—302no—
483C2×C8—22no—
484C2×C8—152no—
485C2×C8C2×D3×D512yes—
486C4⋊C4—52no—
487C4⋊C4—304no—
488C22⋊C4—101no—
489C22⋊C4—304no—
490C42—101no—
491C3×C5#300911yescharacteristic, complemented, Hall
492C22×C3—22no—
493C22×C3—102no—
494C22×C3—202no—
495C22×C3#408312yes—
496C22×C3C2×D4×D511yescharacteristic
497C2×D3—24no—
498C2×D3—44no—
499C2×D3—84no—
500C2×D3—104no—
501C2×D3—102no—
502C2×D3—408no—
503C3×C4—102no—
504C3×C4—202no—
505C3×C4#408312yes—
506C3×C4C2×D4×D511yescharacteristic
507C3×C4C22×C22⋊D511yescharacteristic
508Dic3—42no—
509Dic3—102no—
510C2×C5—22no—
511C2×C5—124no—
512C2×C5C2×#88211yescharacteristic
513C2×C5#577012yes—
514D5—42no—
515D5—122no—
516C23—62no—
517C23—64no—
518C23—101no—
519C23—152no—
520C23—242no—
521C23—308no—
522C23—1204no—
523C23#677711yescharacteristic
524Q8—52no—
525Q8—62no—
526Q8—62no—
527Q8—101no—
528Q8—122no—
529Q8—302no—
530D4—34no—
531D4—52no—
532D4—64no—
533D4—62no—
534D4—104no—
535D4—101no—
536D4—308no—
537D4—308no—
538D4—304no—
539D4—302no—
540C2×C4—62no—
541C2×C4—101no—
542C2×C4—104no—
543C2×C4—102no—
544C2×C4—122no—
545C2×C4—152no—
546C2×C4—308no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4D5×D1212yes—
550C2×C4#677711yescharacteristic
551C2×C4D3×C22⋊D512yes—
552C2×C4C22×D3×D511yescharacteristic
553C8—22no—
554C8—302no—
555C2×C3—22no—
556C2×C3—202no—
557C2×C3#6609612yes—
558C2×C3C2×#408311yescharacteristic
559D3—44no—
560D3—202no—
561C5#7883511yescharacteristic, complemented, Sylow
562C22—22no—
563C22—64no—
564C22—102no—
565C22—124no—
566C22—202no—
567C22—244no—
568C22—302no—
569C22—304no—
570C22—1208no—
571C22#9147512yes—
572C22C2×#677711yescharacteristic
573C4—102no—
574C4—122no—
575C4—202no—
576C4—302no—
577C4#9147512yes—
578C4C2×D5×D1211yescharacteristic
579C4C2×D3×C22⋊D511yescharacteristic
580C3#1061559011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—124no—
583C2—202no—
584C2—602no—
585C2#1175398212yes—
586C2C2×#9147511yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92018C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3009
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C5×#204C2semidirect
3. #11754270C2semidirect
4. C2×#91307C2semidirect
5. #11751211C2semidirect
6. C3×#65402C2semidirect
7. #11748386C2semidirect
8. #11748158C2semidirect
9. #11748118C2semidirect
13. C22×C5×Dic6C22semidirect
22. C22×C3×C5×C8C22semidirect
23. C2×#6710C22semidirect
25. C2×C5×#204C22semidirect
26. C3×#4072C22semidirect
28. #91383C22semidirect
31. C2×#6661C22semidirect
33. C2×#6655C22semidirect
34. #91104C22semidirect
35. C3×#3953C22semidirect
36. C3×#3948C22semidirect
37. #90966C22semidirect
46. #65402D3semidirect
96. C22×#204D5semidirect
116. C22×C5×C8C2×D3semidirect
124. #4072C2×D3semidirect
127. #3953C2×D3semidirect
129. #3948C2×D3semidirect
180. C22×Dic6C2×D5semidirect
181. C22×C3×C8C2×D5semidirect
188. C2×#204C2×D5semidirect
372. C22×C8D3×D5semidirect
491. C3×C5#3009semidirect
561. C5#78835semidirect
580. C3#10615590semidirect

Maximal subgroups

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

subgroupindex
C2×#920182
C22×C5×#2042
#117542702
C2×#913072
#117512112
C3×#654022
#117483862
#117481582
#117481182
#106155903
#788355