Finite Group Databasebeta

← #14424249

Subgroups — #14424249

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92018C211yesmaximal, characteristic, complemented
2C2×#91821C211yesmaximal, characteristic, complemented
3C22×C5×#213C211yesmaximal, characteristic, complemented
4C3×#66139C211yesmaximal, characteristic, complemented
5#11749159C214yesmaximal, complemented
6#11749151C214yesmaximal, complemented
7#11748411C211yesmaximal, characteristic, complemented
8#11748386C211yesmaximal, characteristic, complemented
9#11748342C211yesmaximal, characteristic, complemented
10#10615564—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic, complemented
12C2×#6817C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×D3×C22⋊D5—22no—
16#92018—24no—
17#92018—24no—
18C2×#6777—21no—
19C2×D5×D12C2212yescomplemented
20C2×#6772C2212yescomplemented
21C2×#6768—21no—
22C2×#6716C2212yescomplemented
23#91821—24no—
24C2×#6715C2212yescomplemented
25C2×#6710C2211yescharacteristic, complemented
26C2×C5×#213—24no—
27C2×C5×#213C2214yescomplemented
28C22×C5×C3⋊C8C2211yescharacteristic, complemented
29C3×#4099—22no—
30C3×#4086—21no—
31C3×#4084C2214yescomplemented
32C3×#4082—21no—
33C3×#4072C2211yescharacteristic, complemented
34#90974C2212yescomplemented
35#90968C2212yescomplemented
36#90966C2214yescomplemented
37#90955C2214yescomplemented
38#83383—51nomaximal, Hall
39C2×#4144—31no—
40C22×C5×D8—31no—
41#66139D311yescharacteristic, complemented
42C2×#4078—31no—
43#65504—31no—
44#65447—34no—
45#65445—34no—
46#65402—31no—
47#65399—31no—
48C24×C3×C5—21no—
49C23×C5×D3—21no—
50C22×D3×D5—22no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—21no—
54C2×C3×C5×D4C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—21no—
57#6817—22no—
58#6817D414yescomplemented
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2311yescharacteristic
62C2×C5×D12—21no—
63C2×C5×D12—22no—
64C2×C5×D12D414yescomplemented
65C2×C5×D12C2312yes—
66C2×C3×C22⋊D5—24no—
67C2×C3×C22⋊D5D412yes—
68C3×#709—22no—
69C3×#709—22no—
70C2×C3×D20D411yescharacteristic
71C2×C3×C4×D5C2312yes—
72C2×C3×Dic10D411yescharacteristic
73D3×C22⋊D5—216no—
74C2×#1203—22no—
75C2×#1201—22no—
76C2×D3×Dic5—22no—
77#6777—28no—
78D5×D12—24no—
79D5×D12—24no—
80#6772—24no—
81#6772—24no—
82#6768—28no—
83#6716—24no—
84#6715—24no—
85#6710—22no—
86C2×C3⋊#168C2312yes—
87C5×#213—28no—
88C2×C5×C3⋊C8—22no—
89C2×C5×C3⋊C8C2312yes—
90C3×C22⋊Dic5—21no—
91C3×C22⋊Dic5—24no—
92C3×C4⋊Dic5C2312yes—
93C3×C4×Dic5—21no—
94C2×#1009—51no—
95C3×#535—51no—
96C2×#932—51no—
97C22×#213D511yescharacteristic, complemented
98#5234—51no—
99#5037—54no—
100#5036—54no—
101#5002—51no—
102#5001—51no—
103C22×C5×D4—31no—
104C22×C5×D4C2×D311yescharacteristic, complemented
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×D8—34no—
115C2×C5×D8—64no—
116C22×C5×C8—31no—
117#4099—22no—
118#4086—21no—
119#4084C2×D314yescomplemented
120#4082—21no—
121C2×#687—32no—
122#4078—64no—
123C2×#686—32no—
124#4072C2×D311yescharacteristic, complemented
125C2×#681—31no—
126#3964—34no—
127#3953—32no—
128#3952—34no—
129#3948—32no—
130#3008—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—42no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D411yescharacteristic
135C22×D15—21no—
136C22×C5×D3—22no—
137C22×C5×D3—24no—
138C22×C5×D3—82no—
139C22×C3×D5C2×D412yes—
140C2×D3×D5—28no—
141C2×D3×D5—84no—
142C3×C5×D4—22no—
143C3×C5×D4—22no—
144C3×C5×D4—42no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—24no—
150C2×Dic15—21no—
151D60—21no—
152D60C2×D412yes—
153C4×D15—24no—
154Dic30—21no—
155Dic30C2×D412yes—
156C5×D12—24no—
157C5×D12—22no—
158C5×D12C2×D414yes—
159C3×C22⋊D5—24no—
160C3×C22⋊D5—84no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5C2×D412yes—
163C3×D20—22no—
164C3×C4×D5—22no—
165C3×C4×D5—22no—
166C3×Dic10—22no—
167#1203—28no—
168#1201—28no—
169D3×Dic5—28no—
170C3⋊#168—22no—
171C5×C3⋊C8—22no—
172C2×C3×#41—51no—
173C22×C3×D4C2×D511yescharacteristic, complemented
174#1009—104no—
175#1009—104no—
176C2×#239—101no—
177C2×D3×D4—101no—
178C2×D3×D4—102no—
179C2×#235—51no—
180C2×#235—52no—
181C22×D12—52no—
182C22×D12C2×D511yescharacteristic
183C3×#127—101no—
184C3×#124—101no—
185C3×#121—54no—
186C3×#120—102no—
187C3×#117—51no—
188C2×#214—52no—
189#932—104no—
190C2×#213—24no—
191C2×#213—52no—
192C2×#213C2×D514yescomplemented
193C2×#208—51no—
194C22×C3⋊C8C2×D511yescharacteristic, complemented
195#830—54no—
196#810—52no—
197#809—54no—
198#809—52no—
199C24×C5—21no—
200C24×C5—61no—
201C23×D5—62no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—21no—
205C2×C5×D4—34no—
206C2×C5×D4—32no—
207C2×C5×D4—62no—
208C2×C5×D4—61no—
209C2×C5×D4C22×D312yes—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—24no—
212C2×C22⋊D5—616no—
213C2×C22⋊D5—61no—
214C2×C22⋊D5—62no—
215C2×C22⋊D5—62no—
216C2×C22⋊D5#6712yes—
217C22×Dic5—62no—
218#711—68no—
219#711—64no—
220#711—64no—
221D4×D5—64no—
222D4×D5—64no—
223D4×D5—68no—
224#709—22no—
225#709—22no—
226#709—34no—
227#709—62no—
228C2×D20—31no—
229C2×D20#6711yescharacteristic
230C2×C4×D5—61no—
231C2×C4×D5C22×D312yes—
232C2×Dic10—31no—
233C2×Dic10#6711yescharacteristic
234C5×D8—68no—
235C2×C5×C8—32no—
236C2×C5×C8—62no—
237C22⋊Dic5—21no—
238C22⋊Dic5—24no—
239#687—64no—
240#686—64no—
241C4⋊Dic5C22×D312yes—
242C4×Dic5—21no—
243#681—62no—
244C2×#168—32no—
245C2×H(5,𝔽2)—151no—
246C2×AGL(1,ℤ/8)—151no—
247C22×D8—31no—
248#535—51no—
249#449—154no—
250#447—154no—
251#418—151no—
252#416—151no—
253#408—151no—
254C22×C3×C5—22no—
255C22×C3×C5—42no—
256C22×C3×C5—44no—
257C22×C3×C5—84no—
258C22×C3×C5#12012yes—
259C22×C3×C5C22×D411yescharacteristic
260C2×D15—22no—
261C2×D15—42no—
262C2×C5×D3—24no—
263C2×C5×D3—44no—
264C2×C5×D3—84no—
265C2×C3×D5—22no—
266C2×C3×D5—24no—
267D3×D5—88no—
268C3×C4×C5#12012yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272C3×Dic5—22no—
273C3×Dic5—42no—
274C24×C3—21no—
275C23×D3—21no—
276C23×D3—102no—
277C3×#41—102no—
278C3×#41—102no—
279C2×C3×Q8—51no—
280C2×C3×D4—22no—
281C2×C3×D4—21no—
282C2×C3×D4—22no—
283C2×C3×D4—52no—
284C2×C3×D4—51no—
285C2×C3×D4—104no—
286C2×C3×D4C22×D512yes—
287C22×C3×C4—52no—
288C22×C3×C4C22×D511yescharacteristic
289C2×#67—102no—
290C2×#67—101no—
291#239—108no—
292D3×D4—108no—
293D3×D4—1016no—
294#235—54no—
295#235—104no—
296#235—102no—
297#235—104no—
298C2×D12—21no—
299C2×D12—22no—
300C2×D12—51no—
301C2×D12—104no—
302C2×D12—102no—
303C2×D12—104no—
304C2×D12C22⋊D514yescomplemented
305C2×D12C22×D512yes—
306C2×C4×D3—102no—
307C2×C4×D3—101no—
308C2×Dic6—51no—
309C3×C4⋊C4—52no—
310C3×C22⋊C4—104no—
311C3×C22⋊C4—101no—
312C3×C42—101no—
313#214—104no—
314#213—28no—
315#213—104no—
316#208—102no—
317C2×C3⋊C8—22no—
318C2×C3⋊C8—52no—
319C2×C3⋊C8C22×D512yes—
320C23×C5—22no—
321C23×C5—42no—
322C23×C5—62no—
323C23×C5—64no—
324C23×C5—82no—
325C23×C5—242no—
326C23×C5C2×#6711yescharacteristic
327C22×D5—68no—
328C22×D5—61no—
329C22×D5—244no—
330C22×D5C2×#6712yes—
331C5×D4—22no—
332C5×D4—22no—
333C5×D4—34no—
334C5×D4—42no—
335C5×D4—64no—
336C5×D4—62no—
337C2×C4×C5D3×D412yes—
338C2×C4×C5D3×D412yes—
339C2×C4×C5C2×#6711yescharacteristic
340C2×C4×C5C23×D311yescharacteristic
341C22⋊D5—24no—
342C22⋊D5—68no—
343C22⋊D5—68no—
344C22⋊D5—64no—
345C22⋊D5—84no—
346C2×Dic5—22no—
347C2×Dic5—68no—
348C2×Dic5—61no—
349C2×Dic5C2×#6712yes—
350D20—22no—
351D20—32no—
352D20—61no—
353C4×D5—22no—
354C4×D5—22no—
355C4×D5—64no—
356Dic10—22no—
357Dic10—32no—
358Dic10—61no—
359C5×C8—62no—
360#168—62no—
361H(5,𝔽2)—304no—
362H(5,𝔽2)—304no—
363C2×#41—51no—
364C2×#41—152no—
365C2×#41—151no—
366C2×#41—301no—
367C22×D4—31no—
368C22×D4—152no—
369C22×D4—301no—
370C22×D4—302no—
371C22×D4D3×D511yescharacteristic, complemented
372AGL(1,ℤ/8)—304no—
373C2×SD16—152no—
374C2×D8—34no—
375C2×D8—64no—
376C2×D8—152no—
377C2×M16—151no—
378C22×C8—31no—
379#127—101no—
380#124—101no—
381#121—54no—
382#120—102no—
383#117—51no—
384#103—152no—
385#102—152no—
386#102—154no—
387C22⋊C8—154no—
388C2×C3×C5—22no—
389C2×C3×C5—82no—
390C2×C3×C5C2×#12011yescharacteristic
391C2×C3×C5#57612yes—
392D15—42no—
393C3×D5—42no—
394C5×D3—44no—
395C23×C3—22no—
396C23×C3—42no—
397C23×C3—52no—
398C23×C3—82no—
399C23×C3D4×D511yescharacteristic
400C22×D3—22no—
401C22×D3—24no—
402C22×D3—82no—
403C22×D3—108no—
404C22×D3—101no—
405C22×D3—404no—
406C3×Q8—102no—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—42no—
410C3×D4—104no—
411C3×D4—102no—
412C3×D4—404no—
413C2×C3×C4—52no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4D4×D512yes—
419C2×C3×C4C2×C22⋊D512yes—
420C2×C3×C4C23×D511yescharacteristic
421#67—108no—
422#67—104no—
423C2×Dic3—101no—
424D12—22no—
425D12—24no—
426D12—52no—
427D12—108no—
428D12—101no—
429D12C2×C22⋊D514yes—
430C4×D3—108no—
431C4×D3—104no—
432Dic6—52no—
433Dic6—101no—
434C3⋊C8—22no—
435C3⋊C8—102no—
436C22×C5—22no—
437C22×C5—42no—
438C22×C5—44no—
439C22×C5—64no—
440C22×C5—84no—
441C22×C5—124no—
442C22×C5—244no—
443C22×C5#93712yes—
444C22×C5C22×#6711yescharacteristic
445C2×D5—22no—
446C2×D5—24no—
447C2×D5—62no—
448C2×D5—122no—
449C2×D5—248no—
450C4×C5#93712yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C2×D3×D411yescharacteristic
453Dic5—22no—
454Dic5—42no—
455Dic5—62no—
456C24—21no—
457C24—61no—
458C24—302no—
459#41—102no—
460#41—102no—
461#41—154no—
462#41—304no—
463#41—304no—
464#41—308no—
465#41—302no—
466C2×Q8—51no—
467C2×Q8—151no—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—34no—
472C2×D4—32no—
473C2×D4—52no—
474C2×D4—51no—
475C2×D4—61no—
476C2×D4—62no—
477C2×D4—104no—
478C2×D4—151no—
479C2×D4—302no—
480C2×D4—304no—
481C2×D4—304no—
482C2×D4—308no—
483C2×D4—3016no—
484C2×D4—302no—
485C2×D4—301no—
486C2×D4C2×D3×D512yes—
487C22×C4—52no—
488C22×C4—302no—
489C22×C4—301no—
490C22×C4C2×D3×D511yescharacteristic
491SD16—304no—
492D8—68no—
493D8—304no—
494M16—302no—
495C2×C8—32no—
496C2×C8—62no—
497C2×C8—152no—
498C4⋊C4—52no—
499C22⋊C4—104no—
500C22⋊C4—101no—
501C42—101no—
502C3×C5#300811yescharacteristic, complemented, Hall
503C22×C3—22no—
504C22×C3—44no—
505C22×C3—42no—
506C22×C3—84no—
507C22×C3—104no—
508C22×C3—102no—
509C22×C3#408312yes—
510C22×C3C2×D4×D511yescharacteristic
511C2×D3—24no—
512C2×D3—44no—
513C2×D3—84no—
514C2×D3—102no—
515C2×D3—202no—
516C2×D3—408no—
517C3×C4—102no—
518C3×C4—202no—
519C3×C4#408312yes—
520C3×C4C2×D4×D511yescharacteristic
521C3×C4C22×C22⋊D511yescharacteristic
522Dic3—102no—
523C2×C5—22no—
524C2×C5—82no—
525C2×C5—124no—
526C2×C5C2×#93711yescharacteristic
527C2×C5#583512yes—
528D5—42no—
529D5—122no—
530C23—22no—
531C23—42no—
532C23—52no—
533C23—62no—
534C23—64no—
535C23—82no—
536C23—242no—
537C23—308no—
538C23—301no—
539C23—1204no—
540C23D5×#6711yescharacteristic
541Q8—102no—
542Q8—152no—
543Q8—301no—
544D4—22no—
545D4—22no—
546D4—34no—
547D4—42no—
548D4—62no—
549D4—64no—
550D4—104no—
551D4—102no—
552D4—152no—
553D4—308no—
554D4—308no—
555D4—304no—
556D4—301no—
557D4—404no—
558C2×C4—52no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—308no—
563C2×C4—301no—
564C2×C4—304no—
565C2×C4D5×#6711yescharacteristic
566C2×C4D3×C22⋊D512yes—
567C2×C4#679012yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—62no—
570C8—302no—
571C2×C3—22no—
572C2×C3—82no—
573C2×C3—202no—
574C2×C3#6609112yes—
575C2×C3C2×#408311yescharacteristic
576D3—44no—
577D3—202no—
578C5#8338311yescharacteristic, complemented, Sylow
579C22—22no—
580C22—42no—
581C22—44no—
582C22—64no—
583C22—84no—
584C22—102no—
585C22—104no—
586C22—124no—
587C22—244no—
588C22—302no—
589C22—602no—
590C22—1208no—
591C22#9157712yes—
592C22C2×D5×#6711yescharacteristic
593C4—102no—
594C4—202no—
595C4—302no—
596C4#9157712yes—
597C4C2×D3×C22⋊D511yescharacteristic
598C4C2×#679011yescharacteristic
599C3#1061556411yescharacteristic, complemented, Sylow
600C2—22no—
601C2—82no—
602C2—124no—
603C2—202no—
604C2—602no—
605C2#1175469112yes—
606C2C2×#9157711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3008
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
1. C2×#92018C2semidirect
2. C2×#91821C2semidirect
3. C22×C5×#213C2semidirect
4. C3×#66139C2semidirect
5. #11749159C2semidirect
6. #11749151C2semidirect
7. #11748411C2semidirect
8. #11748386C2semidirect
9. #11748342C2semidirect
11. C22×C3×C5×D4C22semidirect
19. C2×D5×D12C22semidirect
20. C2×#6772C22semidirect
22. C2×#6716C22semidirect
24. C2×#6715C22semidirect
25. C2×#6710C22semidirect
27. C2×C5×#213C22semidirect
28. C22×C5×C3⋊C8C22semidirect
31. C3×#4084C22semidirect
33. C3×#4072C22semidirect
34. #90974C22semidirect
35. #90968C22semidirect
36. #90966C22semidirect
37. #90955C22semidirect
41. #66139D3semidirect
58. #6817D4semidirect
64. C2×C5×D12D4semidirect
97. C22×#213D5semidirect
104. C22×C5×D4C2×D3semidirect
119. #4084C2×D3semidirect
124. #4072C2×D3semidirect
173. C22×C3×D4C2×D5semidirect
192. C2×#213C2×D5semidirect
194. C22×C3⋊C8C2×D5semidirect
304. C2×D12C22⋊D5semidirect
371. C22×D4D3×D5semidirect
502. C3×C5#3008semidirect
578. C5#83383semidirect
599. C3#10615564semidirect

Maximal subgroups

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

subgroupindex
C2×#920182
C2×#918212
C22×C5×#2132
C3×#661392
#117491592
#117491512
#117484112
#117483862
#117483422
#106155643
#833835