Finite Group Databasebeta

← #14424371

Subgroups — #14424371

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×C3×#4144C211yesmaximal, characteristic
2C22×#6716C211yesmaximal, characteristic, complemented
3#11754252C211yesmaximal, characteristic, complemented
4C2×#91313C211yesmaximal, characteristic, complemented
5C5×#5215C211yesmaximal, characteristic, complemented
6#11749049C214yesmaximal, complemented
7#11749045C214yesmaximal, complemented
8#11748364C211yesmaximal, characteristic, complemented
9#11748343C211yesmaximal, characteristic, complemented
10#10610660—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×Dic30C2211yescharacteristic, complemented
13C22×C3×C22⋊D5—22no—
14C3×#4144—24no—
15C3×#4144—24no—
16C2×C3×#711—21no—
17C2×C3×#711C2212yes—
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C2212yes—
20C2×C3×#709C2211yescharacteristic
21C2×C3×#709C2211yescharacteristic
22C2×#6716—24no—
23C2×#6716C2214yescomplemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C5×#926C2211yescharacteristic, complemented
26C2×C5×#208C2211yescharacteristic, complemented
27#91537—22no—
28#91389—21no—
29#91364—21no—
30#91360C2214yescomplemented
31C2×#6662C2212yescomplemented
32#91313—24no—
33C2×#6657C2212yescomplemented
34C5×#832C2214yescomplemented
35#90970C2212yescomplemented
36#90964C2212yescomplemented
37#90955C2214yescomplemented
38#84105—51nomaximal, Hall
39C2×#4144D311yescharacteristic
40C22×#687—31no—
41C2×#4055—31no—
42#65860—31no—
43C5×#418—31no—
44#65418—31no—
45#65291—31no—
46#65072—34no—
47#65065—34no—
48C24×C3×C5—21no—
49C23×C3×D5—22no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4D414yes—
53C2×C3×C5×D4C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—21no—
56C2×Dic30—22no—
57C2×Dic30—22no—
58C2×Dic30—21no—
59C2×Dic30C2312yes—
60C2×C3×C22⋊D5—216no—
61C2×C3×C22⋊D5—21no—
62C2×C3×C22⋊D5—22no—
63C2×C3×C22⋊D5—22no—
64C2×C3×C22⋊D5D412yes—
65C22×C3×Dic5—22no—
66C3×#711—28no—
67C3×#711—24no—
68C3×#711—24no—
69C3×D4×D5—28no—
70C3×D4×D5—24no—
71C3×D4×D5—24no—
72C3×#709—22no—
73C3×#709—22no—
74C3×#709—22no—
75C3×#709D414yes—
76C2×C3×D20D411yescharacteristic
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×C4×D5C2312yes—
80C2×C3×Dic10D411yescharacteristic
81C2×C3×Dic10C2311yescharacteristic
82#6716—28no—
83C2×C3⋊#168—22no—
84C2×C3⋊#168C2312yes—
85C5×#217—21no—
86C5×C4⋊Dic3C2312yes—
87C4×C5×Dic3—21no—
88C5×#208—22no—
89C2×C5×C3⋊C8C2312yes—
90Dic3⋊Dic5—24no—
91#6665—24no—
92#6662—24no—
93#6657—24no—
94C2×C3×H(5,𝔽2)—51no—
95#5825—51no—
96C2×#951—51no—
97C22×#214—51no—
98#5239—54no—
99#5234—51no—
100#5233—51no—
101#5218—54no—
102#5215D511yescharacteristic, complemented
103C22×C5×D4C2×D311yescharacteristic
104C22×C22⋊D5—22no—
105#4144—24no—
106#4144—24no—
107C2×#711—21no—
108C2×#711C2×D312yes—
109C2×D4×D5—21no—
110C2×D4×D5C2×D312yes—
111C2×#709C2×D311yescharacteristic
112C2×#709C2×D311yescharacteristic
113C22×Dic10—31no—
114C2×C5×M16—31no—
115C5×#117—31no—
116C2×#687—34no—
117C2×#687—64no—
118C22×#168—31no—
119#4055—64no—
120C2×Dic20—32no—
121C2×#677—32no—
122#4043—34no—
123#4032—62no—
124#4021—61no—
125#4015—61no—
126C5×#102—34no—
127#3952—34no—
128#3942—32no—
129#3941—32no—
130#3009—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—24no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D411yescharacteristic
135C22×C3×D5—21no—
136C22×C3×D5—28no—
137C22×C3×D5—84no—
138C22×C3×D5C2×D412yes—
139C3×C5×D4—24no—
140C3×C5×D4—22no—
141C3×C5×D4C2×D414yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15—42no—
148Dic30—22no—
149Dic30—22no—
150Dic30—42no—
151C2×C5×Dic3—22no—
152C3×C22⋊D5—28no—
153C3×C22⋊D5—28no—
154C3×C22⋊D5—24no—
155C3×C22⋊D5—24no—
156C2×C3×Dic5—28no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5C2×D412yes—
159C3×D20—22no—
160C3×D20—21no—
161C3×D20C2×D412yes—
162C3×C4×D5—24no—
163C3×C4×D5—22no—
164C3×C4×D5—22no—
165C3×Dic10—22no—
166C3×Dic10—21no—
167C3×Dic10C2×D412yes—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C3×H(5,𝔽2)—104no—
171C3×H(5,𝔽2)—104no—
172C2×C3×#41—51no—
173C2×C3×#41—52no—
174C2×C3×#41—51no—
175C2×C3×#41—101no—
176C22×C3×D4—52no—
177C22×C3×D4—101no—
178C22×C3×D4—102no—
179C22×C3×D4C2×D511yescharacteristic
180C22×Dic6—51no—
181#951—104no—
182#944—101no—
183C2×#216—52no—
184#936—101no—
185#935—102no—
186C2×#214—54no—
187C2×#214—52no—
188C2×#214—104no—
189#926C2×D511yescharacteristic, complemented
190#924—54no—
191C2×#208C2×D511yescharacteristic, complemented
192C22×C3⋊C8—51no—
193#835—52no—
194#832—52no—
195#832C2×D514yescomplemented
196#830—54no—
197C24×C5—21no—
198C23×D5—22no—
199C2×C5×D4—21no—
200C2×C5×D4—22no—
201C2×C5×D4#6714yes—
202C2×C5×D4C22×D312yes—
203C22×C4×C5C22×D311yescharacteristic
204C2×C22⋊D5—216no—
205C2×C22⋊D5—21no—
206C2×C22⋊D5—22no—
207C2×C22⋊D5—22no—
208C2×C22⋊D5#6712yes—
209C22×Dic5—22no—
210C22×Dic5—61no—
211#711—28no—
212#711—24no—
213#711—24no—
214D4×D5—28no—
215D4×D5—24no—
216D4×D5—24no—
217#709—22no—
218#709—22no—
219#709—22no—
220#709#6714yes—
221C2×D20#6711yescharacteristic
222C2×D20C22×D311yescharacteristic
223C2×C4×D5—21no—
224C2×C4×D5C22×D312yes—
225C2×Dic10—32no—
226C2×Dic10—62no—
227C2×Dic10—62no—
228C2×Dic10—61no—
229C2×Dic10#6711yescharacteristic
230C2×Dic10C22×D311yescharacteristic
231C5×M16—62no—
232C2×C5×C8—32no—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236#687—68no—
237#685—64no—
238C4⋊Dic5—64no—
239C2×#168—32no—
240C2×#168—62no—
241Dic20—64no—
242#677—64no—
243C2×H(5,𝔽2)—51no—
244C2×#137—151no—
245C22×SD16—151no—
246#536—151no—
247#452—154no—
248#450—154no—
249#418—31no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—24no—
254C22×C3×C5—44no—
255C22×C3×C5—84no—
256C22×C3×C5#12012yes—
257C22×C3×C5C22×D411yescharacteristic
258C2×C3×D5—22no—
259C2×C3×D5—22no—
260C2×C3×D5—24no—
261C2×C3×D5—42no—
262C2×C3×D5—88no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—42no—
267C3×Dic5—22no—
268C3×Dic5—22no—
269C5×Dic3—42no—
270C24×C3—21no—
271C24×C3—102no—
272C3×#41—54no—
273C3×#41—104no—
274C3×#41—108no—
275C3×#41—104no—
276C3×#41—102no—
277C3×#41—102no—
278C3×#41—102no—
279C2×C3×Q8—51no—
280C2×C3×Q8—51no—
281C2×C3×D4—21no—
282C2×C3×D4—22no—
283C2×C3×D4—52no—
284C2×C3×D4—51no—
285C2×C3×D4—51no—
286C2×C3×D4—102no—
287C2×C3×D4—104no—
288C2×C3×D4—108no—
289C2×C3×D4—102no—
290C2×C3×D4—1016no—
291C2×C3×D4—101no—
292C2×C3×D4—104no—
293C2×C3×D4D2014yes—
294C2×C3×D4C22×D512yes—
295C22×C3×C4—52no—
296C22×C3×C4—102no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—101no—
300C2×Dic6—52no—
301C2×Dic6—102no—
302C2×Dic6—102no—
303C2×Dic6—101no—
304#217—21no—
305#217—104no—
306#216—104no—
307#214—104no—
308#214—108no—
309C4⋊Dic3C22×D512yes—
310Dic3⋊C4—104no—
311C4×Dic3—21no—
312#208—22no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8—102no—
315C2×C3⋊C8C22×D512yes—
316C23×C5—22no—
317C23×C5—24no—
318C23×C5—82no—
319C23×C5C2×#6711yescharacteristic
320C22×D5—21no—
321C22×D5—28no—
322C22×D5—84no—
323C22×D5C2×#6712yes—
324C5×D4—24no—
325C5×D4—22no—
326C5×D4C2×#6714yes—
327C2×C4×C5—62no—
328C2×C4×C5C2×#6712yes—
329C2×C4×C5C2×#6711yescharacteristic
330C2×C4×C5C2×#6712yes—
331C2×C4×C5C23×D311yescharacteristic
332C22⋊D5—28no—
333C22⋊D5—28no—
334C22⋊D5—24no—
335C22⋊D5—24no—
336C2×Dic5—28no—
337C2×Dic5—21no—
338C2×Dic5—62no—
339C2×Dic5—122no—
340C2×Dic5C2×#6712yes—
341D20—22no—
342D20—21no—
343D20C2×#6712yes—
344C4×D5—24no—
345C4×D5—22no—
346C4×D5—22no—
347Dic10—22no—
348Dic10—21no—
349Dic10—62no—
350Dic10—62no—
351Dic10—122no—
352Dic10C2×#6712yes—
353C5×C8—62no—
354#168—62no—
355H(5,𝔽2)—104no—
356H(5,𝔽2)—104no—
357C2×#41—51no—
358C2×#41—52no—
359C2×#41—51no—
360C2×#41—101no—
361C22×Q8—151no—
362C22×D4—52no—
363C22×D4—101no—
364C22×D4—102no—
365C22×D4D3×D511yescharacteristic
366#137—304no—
367C2×Q16—152no—
368C2×SD16—152no—
369C2×SD16—154no—
370C2×SD16—304no—
371C2×M16—31no—
372C22×C8—151no—
373C4⋊Q8—301no—
374#124—301no—
375#123—302no—
376C22⋊Q8—154no—
377#117—31no—
378#103—152no—
379#102—34no—
380#102—152no—
381C22⋊C8—154no—
382C2×C3×C5—22no—
383C2×C3×C5—44no—
384C2×C3×C5C2×#12011yescharacteristic
385C2×C3×C5#57712yes—
386C3×D5—42no—
387C3×D5—42no—
388C23×C3—22no—
389C23×C3—24no—
390C23×C3—52no—
391C23×C3—82no—
392C23×C3—108no—
393C23×C3—101no—
394C23×C3—404no—
395C23×C3D4×D511yescharacteristic
396C3×Q8—52no—
397C3×Q8—101no—
398C3×Q8—102no—
399C3×D4—22no—
400C3×D4—24no—
401C3×D4—52no—
402C3×D4—108no—
403C3×D4—108no—
404C3×D4—104no—
405C3×D4—104no—
406C3×D4—101no—
407C3×D4—102no—
408C3×D4C2×D2014yes—
409C2×C3×C4—52no—
410C2×C3×C4—108no—
411C2×C3×C4—101no—
412C2×C3×C4—102no—
413C2×C3×C4—102no—
414C2×C3×C4—104no—
415C2×C3×C4C2×D2012yes—
416C2×C3×C4D4×D512yes—
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4C23×D511yescharacteristic
419C2×Dic3—22no—
420C2×Dic3—102no—
421C2×Dic3—202no—
422Dic6—102no—
423Dic6—102no—
424Dic6—202no—
425C3⋊C8—22no—
426C3⋊C8—102no—
427C22×C5—22no—
428C22×C5—24no—
429C22×C5—44no—
430C22×C5—84no—
431C22×C5#95312yes—
432C22×C5C22×#6711yescharacteristic
433C2×D5—24no—
434C2×D5—22no—
435C2×D5—22no—
436C2×D5—42no—
437C2×D5—88no—
438C4×C5—122no—
439C4×C5#95312yes—
440C4×C5C22×#6711yescharacteristic
441C4×C5C22×#6711yescharacteristic
442Dic5—22no—
443Dic5—22no—
444Dic5—122no—
445C24—21no—
446C24—102no—
447#41—54no—
448#41—104no—
449#41—108no—
450#41—104no—
451#41—102no—
452#41—102no—
453#41—102no—
454C2×Q8—51no—
455C2×Q8—51no—
456C2×Q8—152no—
457C2×Q8—301no—
458C2×Q8—302no—
459C2×Q8—302no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—52no—
463C2×D4—51no—
464C2×D4—51no—
465C2×D4—102no—
466C2×D4—104no—
467C2×D4—108no—
468C2×D4—102no—
469C2×D4—1016no—
470C2×D4—101no—
471C2×D4—104no—
472C2×D4#120214yes—
473C2×D4C2×D3×D512yes—
474C22×C4—52no—
475C22×C4—102no—
476C22×C4—101no—
477C22×C4—301no—
478C22×C4C2×D3×D511yescharacteristic
479Q16—304no—
480SD16—304no—
481SD16—308no—
482M16—62no—
483C2×C8—32no—
484C2×C8—152no—
485C2×C8—302no—
486C4⋊C4—32no—
487C4⋊C4—304no—
488C22⋊C4—61no—
489C22⋊C4—304no—
490C42—61no—
491C3×C5#300911yescharacteristic, complemented, Hall
492C22×C3—22no—
493C22×C3—24no—
494C22×C3—44no—
495C22×C3—84no—
496C22×C3—102no—
497C22×C3—102no—
498C22×C3—104no—
499C22×C3—202no—
500C22×C3—408no—
501C22×C3#402812yes—
502C22×C3C2×D4×D511yescharacteristic
503C3×C4—102no—
504C3×C4—102no—
505C3×C4#402812yes—
506C3×C4C22×D2011yescharacteristic
507C3×C4C2×D4×D511yescharacteristic
508Dic3—42no—
509Dic3—202no—
510C2×C5—22no—
511C2×C5—44no—
512C2×C5#583612yes—
513C2×C5C2×#95311yescharacteristic
514D5—42no—
515D5—42no—
516C23—22no—
517C23—24no—
518C23—52no—
519C23—82no—
520C23—108no—
521C23—101no—
522C23—404no—
523C23D5×#6711yescharacteristic
524Q8—52no—
525Q8—101no—
526Q8—102no—
527Q8—302no—
528Q8—302no—
529Q8—602no—
530D4—22no—
531D4—24no—
532D4—52no—
533D4—108no—
534D4—108no—
535D4—104no—
536D4—104no—
537D4—101no—
538D4—102no—
539D4C2×#120214yes—
540C2×C4—52no—
541C2×C4—62no—
542C2×C4—108no—
543C2×C4—101no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—104no—
547C2×C4—302no—
548C2×C4—602no—
549C2×C4C2×#120212yes—
550C2×C4D5×#6712yes—
551C2×C4D5×#6711yescharacteristic
552C2×C4C22×D3×D511yescharacteristic
553C8—62no—
554C8—302no—
555C2×C3—22no—
556C2×C3—44no—
557C2×C3—202no—
558C2×C3—202no—
559C2×C3C2×#402811yescharacteristic
560C2×C3#6610912yes—
561C5#8410511yescharacteristic, complemented, Sylow
562C22—22no—
563C22—24no—
564C22—44no—
565C22—84no—
566C22—102no—
567C22—102no—
568C22—104no—
569C22—202no—
570C22—408no—
571C22#9156412yes—
572C22C2×D5×#6711yescharacteristic
573C4—102no—
574C4—102no—
575C4—122no—
576C4—602no—
577C4#9156412yes—
578C4C22×#120211yescharacteristic
579C4C2×D5×#6711yescharacteristic
580C3#1061066011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—44no—
583C2—202no—
584C2—202no—
585C2#1175470812yes—
586C2C2×#9156411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4144C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#3009
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#6716C2semidirect
3. #11754252C2semidirect
4. C2×#91313C2semidirect
5. C5×#5215C2semidirect
6. #11749049C2semidirect
7. #11749045C2semidirect
8. #11748364C2semidirect
9. #11748343C2semidirect
12. C22×Dic30C22semidirect
23. C2×#6716C22semidirect
24. C22×C3⋊#168C22semidirect
25. C5×#926C22semidirect
26. C2×C5×#208C22semidirect
30. #91360C22semidirect
31. C2×#6662C22semidirect
33. C2×#6657C22semidirect
34. C5×#832C22semidirect
35. #90970C22semidirect
36. #90964C22semidirect
37. #90955C22semidirect
102. #5215D5semidirect
189. #926C2×D5semidirect
191. C2×#208C2×D5semidirect
195. #832C2×D5semidirect
491. C3×C5#3009semidirect
561. C5#84105semidirect
580. C3#10610660semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41442
C22×#67162
#117542522
C2×#913132
C5×#52152
#117490492
#117490452
#117483642
#117483432
#106106603
#841055