Finite Group Databasebeta

← #14424271

Subgroups — #14424271

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×#92017C211yesmaximal, characteristic, complemented
2C22×C3×D40C211yesmaximal, characteristic, complemented
3#11754602C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751211C211yesmaximal, characteristic, complemented
6C5×#5113C211yesmaximal, characteristic, complemented
7#11748366C211yesmaximal, characteristic, complemented
8#11748150C214yesmaximal, complemented
9#11748113C214yesmaximal, complemented
10#10610565—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic, complemented
15C2×D5×#67—22no—
16#92017—24no—
17#92017—24no—
18C2×#6777C2212yescomplemented
19C2×D3×D20—21no—
20C2×#6766C2212yescomplemented
21C2×#6765—21no—
22C22×C3×C5×C8C2211yescharacteristic, complemented
23C2×#6710C2211yescharacteristic, complemented
24C5×#926C2211yescharacteristic, complemented
25C2×C3×D40—24no—
26C2×C3×D40C2214yescomplemented
27#91564—22no—
28#91465C2214yescomplemented
29#91458—21no—
30#91364—21no—
31C2×#6655C2212yescomplemented
32#91298—24no—
33C2×#6652C2212yescomplemented
34#91104C2214yescomplemented
35C5×#821C2212yescomplemented
36C5×#816C2212yescomplemented
37#90964C2214yescomplemented
38#83833—51nomaximal, Hall
39C2×#4149—31no—
40C2×#4095—31no—
41C22×D40D311yescharacteristic, complemented
42#65859—31no—
43C5×#416—31no—
44#65399—31no—
45#65290—31no—
46#65100—34no—
47#65062—34no—
48C23×C3×D5—21no—
49C23×C3×D5—21no—
50C22×D3×D5—22no—
51C22×C3×C4×C5C2311yescharacteristic
52C2×#1220D412yes—
53#6817—22no—
54#6817—22no—
55C2×D60D411yescharacteristic
56C2×C4×D15C2312yes—
57C2×Dic30D411yescharacteristic
58C2×C5×#67—21no—
59C5×#235—22no—
60C5×#235D414yescomplemented
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2311yescharacteristic
64C2×C3×D20—21no—
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20—22no—
68C2×C3×D20—21no—
69C2×C3×D20D414yescomplemented
70C2×C3×D20C2312yes—
71C2×C3×D20C2312yes—
72D5×#67—216no—
73C2×#1202—22no—
74C2×#1202—24no—
75C2×#1201—22no—
76C2×D5×Dic3—22no—
77#6777—24no—
78#6777—24no—
79D3×D20—28no—
80#6766—24no—
81#6766—24no—
82#6765—28no—
83C2×C3×C5×C8—22no—
84C2×C3×C5×C8C2312yes—
85#6710—22no—
86C2×C3⋊#168C2312yes—
87C5×#217—21no—
88C5×C4⋊Dic3C2312yes—
89C4×C5×Dic3—21no—
90C3×D40—28no—
91#6665—24no—
92#6655—24no—
93#6652—24no—
94C2×#1004—51no—
95C22×C3×D8—51no—
96#5805—51no—
97C2×#932—51no—
98#5215—51no—
99#5158—54no—
100#5156—54no—
101#5113D511yescharacteristic, complemented
102#5110—51no—
103C2×C5×#41—31no—
104#4149—64no—
105#4149—64no—
106C2×#713—32no—
107C2×D4×D5—32no—
108C2×D4×D5—62no—
109C2×#709—31no—
110C2×#709—61no—
111C22×D20—61no—
112C22×D20C2×D311yescharacteristic
113C22×D20C2×D311yescharacteristic, complemented
114C22×C5×C8C2×D311yescharacteristic, complemented
115C5×#117—31no—
116#4095—64no—
117C2×#688—32no—
118C2×#686—32no—
119C2×#681—31no—
120C2×D40—24no—
121C2×D40C2×D314yescomplemented
122#4041—34no—
123#4028—62no—
124#4021—61no—
125#4020—61no—
126C5×#103—32no—
127C5×#102—32no—
128#3952—34no—
129#3941—34no—
130#3008—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15C2×D412yes—
133C22×C5×D3—21no—
134C22×C3×D5—22no—
135C22×C3×D5—24no—
136C22×C3×D5—22no—
137C22×C3×D5—42no—
138C22×C3×D5—82no—
139C22×C3×D5—82no—
140C2×D3×D5—28no—
141C2×D3×D5—84no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15C2×D412yes—
148D60—22no—
149C4×D15—22no—
150C4×D15—22no—
151Dic30—22no—
152C5×#67—24no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—22no—
155C5×D12—21no—
156C5×D12C2×D412yes—
157C4×C5×D3—24no—
158C5×Dic6—21no—
159C5×Dic6C2×D412yes—
160C3×D20—24no—
161C3×D20—22no—
162C3×D20—22no—
163C3×D20—22no—
164C3×D20—42no—
165C3×D20C2×D414yes—
166#1202—28no—
167#1202—84no—
168#1201—28no—
169D5×Dic3—28no—
170C3×C5×C8—22no—
171C3⋊#168—22no—
172C22×C3×D4—51no—
173C22×C3×D4—51no—
174C22×#67—102no—
175#1004—104no—
176#1004—104no—
177C2×#237—52no—
178C2×#237—101no—
179C2×D3×D4—52no—
180C2×D3×D4—101no—
181C2×#235—51no—
182C2×#235C2×D511yescharacteristic
183C2×C3×D8—54no—
184C2×C3×D8—104no—
185C22×C3×C8C2×D511yescharacteristic, complemented
186#953—102no—
187#940—101no—
188#938—54no—
189#936—101no—
190C2×#214—52no—
191#932—104no—
192C2×#213—52no—
193#926C2×D511yescharacteristic, complemented
194C2×#208—51no—
195#832—54no—
196#821C2×D512yescomplemented
197(C2×D3)⋊C8—54no—
198#816C2×D512yescomplemented
199C23×D5—21no—
200C23×D5—21no—
201C23×D5—62no—
202C5×#41—34no—
203C5×#41—62no—
204C2×C5×Q8—31no—
205C2×C5×D4—31no—
206C2×C5×D4—61no—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—32no—
210C2×C22⋊D5—62no—
211#713—64no—
212#713—64no—
213D4×D5—64no—
214D4×D5—616no—
215D4×D5—64no—
216#709—68no—
217#709—62no—
218#709—62no—
219C2×D20—21no—
220C2×D20—22no—
221C2×D20—22no—
222C2×D20—22no—
223C2×D20—21no—
224C2×D20—31no—
225C2×D20—68no—
226C2×D20—62no—
227C2×D20—64no—
228C2×D20#6714yescomplemented
229C2×D20C22×D312yes—
230C2×D20C22×D312yes—
231C2×C4×D5—32no—
232C2×C4×D5—62no—
233C2×Dic10—31no—
234C2×C5×C8—22no—
235C2×C5×C8C22×D312yes—
236C5×C4⋊C4—32no—
237C5×C22⋊C4—61no—
238C42×C5—61no—
239#688—64no—
240#686—64no—
241#685—64no—
242#681—62no—
243C2×#168—32no—
244D40—28no—
245C2×H(5,𝔽2)—151no—
246C2×AGL(1,ℤ/8)—151no—
247C22×D8—51no—
248#535—151no—
249#449—154no—
250#447—154no—
251#418—151no—
252#416—31no—
253#408—151no—
254C22×C3×C5—22no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—22no—
258C2×D15—24no—
259C2×C5×D3—22no—
260C2×C5×D3—42no—
261C2×C3×D5—24no—
262C2×C3×D5—44no—
263C2×C3×D5—42no—
264C2×C3×D5—44no—
265C2×C3×D5—84no—
266C2×C3×D5—84no—
267D3×D5—88no—
268C3×C4×C5#12012yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272C5×Dic3—22no—
273C5×Dic3—42no—
274C24×C3—101no—
275C24×C3—101no—
276C23×D3—102no—
277C2×C3×D4—54no—
278C2×C3×D4—52no—
279C2×C3×D4—52no—
280C2×C3×D4—102no—
281C2×C3×D4—102no—
282C2×C3×D4—101no—
283C2×C3×D4—102no—
284C2×C3×D4—101no—
285C22×C3×C4C22×D511yescharacteristic
286C2×#67—21no—
287C2×#67—52no—
288C2×#67—102no—
289C2×#67—104no—
290C2×#67—102no—
291C2×#67—1016no—
292C22×Dic3—102no—
293#237—104no—
294#237—108no—
295#237—104no—
296D3×D4—108no—
297D3×D4—104no—
298D3×D4—104no—
299#235—22no—
300#235—102no—
301#235—102no—
302#235D2014yescomplemented
303C2×D12—51no—
304C2×D12C22×D511yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—52no—
307C2×Dic6—51no—
308C2×Dic6C22×D511yescharacteristic
309C3×D8—108no—
310C2×C3×C8—22no—
311C2×C3×C8C22×D512yes—
312#217—21no—
313#217—104no—
314#214—104no—
315#213—104no—
316C4⋊Dic3C22×D512yes—
317C4×Dic3—21no—
318#208—102no—
319C2×C3⋊C8—52no—
320C23×C5—61no—
321C23×C5D3×D411yescharacteristic
322C22×D5—22no—
323C22×D5—24no—
324C22×D5—22no—
325C22×D5—32no—
326C22×D5—42no—
327C22×D5—68no—
328C22×D5—82no—
329C22×D5—82no—
330C22×D5—244no—
331C5×Q8—32no—
332C5×Q8—61no—
333C5×D4—32no—
334C5×D4—64no—
335C5×D4—61no—
336C2×C4×C5—61no—
337C2×C4×C5—64no—
338C2×C4×C5—62no—
339C2×C4×C5D3×D412yes—
340C2×C4×C5D3×D411yescharacteristic
341C2×C4×C5C2×#6712yes—
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—68no—
344C22⋊D5—64no—
345C2×Dic5—32no—
346D20—24no—
347D20—22no—
348D20—22no—
349D20—22no—
350D20—42no—
351D20—68no—
352D20—62no—
353D20—244no—
354D20C2×#6714yes—
355C4×D5—68no—
356C4×D5—62no—
357C4×D5—62no—
358Dic10—62no—
359C5×C8—22no—
360#168—62no—
361H(5,𝔽2)—304no—
362H(5,𝔽2)—304no—
363C2×#41—31no—
364C2×#41—151no—
365C2×#41—152no—
366C2×#41—301no—
367C22×D4—51no—
368C22×D4—51no—
369C22×D4—152no—
370C22×D4—301no—
371C22×D4—302no—
372AGL(1,ℤ/8)—304no—
373C2×SD16—152no—
374C2×D8—54no—
375C2×D8—104no—
376C2×D8—152no—
377C2×M16—151no—
378C22×C8D3×D511yescharacteristic, complemented
379#127—301no—
380#124—301no—
381#121—154no—
382#120—302no—
383#117—31no—
384#103—32no—
385#102—32no—
386#102—154no—
387C22⋊C8—154no—
388C2×C3×C5—22no—
389C2×C3×C5C2×#12011yescharacteristic
390C2×C3×C5#57612yes—
391D15—42no—
392C3×D5—44no—
393C3×D5—82no—
394C5×D3—42no—
395C23×C3—102no—
396C23×C3—104no—
397C23×C3—102no—
398C23×C3—202no—
399C23×C3—402no—
400C23×C3—402no—
401C23×C3D4×D511yescharacteristic
402C22×D3—21no—
403C22×D3—52no—
404C22×D3—108no—
405C22×D3—404no—
406C3×D4—54no—
407C3×D4—102no—
408C3×D4—102no—
409C3×D4—102no—
410C3×D4—104no—
411C3×D4—202no—
412C2×C3×C4C2×D2012yes—
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4D4×D512yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—24no—
417#67—108no—
418#67—108no—
419#67—104no—
420#67—404no—
421C2×Dic3—21no—
422C2×Dic3—22no—
423C2×Dic3—52no—
424C2×Dic3—108no—
425D12—21no—
426D12—102no—
427D12C2×D2012yes—
428C4×D3—24no—
429C4×D3—102no—
430C4×D3—102no—
431Dic6—21no—
432Dic6—102no—
433Dic6C2×D2012yes—
434C3×C8—22no—
435C3⋊C8—102no—
436C22×C5—22no—
437C22×C5—62no—
438C22×C5—122no—
439C22×C5#93712yes—
440C22×C5C2×D3×D411yescharacteristic
441C2×D5—24no—
442C2×D5—44no—
443C2×D5—44no—
444C2×D5—42no—
445C2×D5—64no—
446C2×D5—62no—
447C2×D5—84no—
448C2×D5—84no—
449C2×D5—248no—
450C4×C5—62no—
451C4×C5—122no—
452C4×C5#93712yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—62no—
456C24—101no—
457C24—101no—
458C24—302no—
459#41—34no—
460#41—62no—
461#41—308no—
462#41—304no—
463#41—304no—
464#41—302no—
465#41—302no—
466C2×Q8—31no—
467C2×Q8—151no—
468C2×D4—31no—
469C2×D4—54no—
470C2×D4—52no—
471C2×D4—52no—
472C2×D4—61no—
473C2×D4—102no—
474C2×D4—102no—
475C2×D4—101no—
476C2×D4—101no—
477C2×D4—102no—
478C2×D4—152no—
479C2×D4—151no—
480C2×D4—308no—
481C2×D4—302no—
482C2×D4—304no—
483C2×D4—302no—
484C2×D4—304no—
485C2×D4—304no—
486C2×D4—3016no—
487C22×C4—61no—
488C22×C4—152no—
489C22×C4—302no—
490C22×C4C2×D3×D511yescharacteristic
491SD16—304no—
492D8—108no—
493D8—304no—
494M16—302no—
495C2×C8—22no—
496C2×C8—152no—
497C2×C8C2×D3×D512yes—
498C4⋊C4—32no—
499C22⋊C4—61no—
500C22⋊C4—304no—
501C42—61no—
502C3×C5#300811yescharacteristic, complemented, Hall
503C22×C3—22no—
504C22×C3—104no—
505C22×C3—204no—
506C22×C3—202no—
507C22×C3—204no—
508C22×C3—404no—
509C22×C3—404no—
510C22×C3#402812yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—22no—
513C2×D3—42no—
514C2×D3—102no—
515C2×D3—104no—
516C2×D3—408no—
517C3×C4#402812yes—
518C3×C4C22×D2011yescharacteristic
519C3×C4C2×D4×D511yescharacteristic
520Dic3—22no—
521Dic3—42no—
522Dic3—102no—
523C2×C5—22no—
524C2×C5—122no—
525C2×C5#575712yes—
526C2×C5C2×#93711yescharacteristic
527D5—44no—
528D5—82no—
529D5—122no—
530C23—61no—
531C23—102no—
532C23—104no—
533C23—102no—
534C23—152no—
535C23—202no—
536C23—308no—
537C23—402no—
538C23—402no—
539C23—1204no—
540C23#677711yescharacteristic
541Q8—32no—
542Q8—61no—
543Q8—302no—
544D4—32no—
545D4—54no—
546D4—64no—
547D4—61no—
548D4—104no—
549D4—102no—
550D4—102no—
551D4—102no—
552D4—202no—
553D4—308no—
554D4—308no—
555D4—304no—
556D4—302no—
557D4—1204no—
558C2×C4—61no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—152no—
562C2×C4—308no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4D3×D2012yes—
566C2×C4#677711yescharacteristic
567C2×C4D5×#6712yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—22no—
570C8—302no—
571C2×C3—22no—
572C2×C3—204no—
573C2×C3—402no—
574C2×C3C2×#402811yescharacteristic
575C2×C3#6610312yes—
576D3—42no—
577D3—202no—
578C5#8383311yescharacteristic, complemented, Sylow
579C22—22no—
580C22—62no—
581C22—104no—
582C22—122no—
583C22—204no—
584C22—202no—
585C22—204no—
586C22—302no—
587C22—304no—
588C22—404no—
589C22—404no—
590C22—1208no—
591C22#9147412yes—
592C22C2×#677711yescharacteristic
593C4—62no—
594C4—122no—
595C4—302no—
596C4#9147412yes—
597C4C2×D3×D2011yescharacteristic
598C4C2×D5×#6711yescharacteristic
599C3#1061056511yescharacteristic, complemented, Sylow
600C2—22no—
601C2—122no—
602C2—204no—
603C2—402no—
604C2—602no—
605C2#1175398112yes—
606C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3008
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
1. C2×#92017C2semidirect
2. C22×C3×D40C2semidirect
3. #11754602C2semidirect
4. C2×#91298C2semidirect
5. #11751211C2semidirect
6. C5×#5113C2semidirect
7. #11748366C2semidirect
8. #11748150C2semidirect
9. #11748113C2semidirect
14. C22×C3×D20C22semidirect
18. C2×#6777C22semidirect
20. C2×#6766C22semidirect
22. C22×C3×C5×C8C22semidirect
23. C2×#6710C22semidirect
24. C5×#926C22semidirect
26. C2×C3×D40C22semidirect
28. #91465C22semidirect
31. C2×#6655C22semidirect
33. C2×#6652C22semidirect
34. #91104C22semidirect
35. C5×#821C22semidirect
36. C5×#816C22semidirect
37. #90964C22semidirect
41. C22×D40D3semidirect
60. C5×#235D4semidirect
69. C2×C3×D20D4semidirect
101. #5113D5semidirect
113. C22×D20C2×D3semidirect
114. C22×C5×C8C2×D3semidirect
121. C2×D40C2×D3semidirect
185. C22×C3×C8C2×D5semidirect
193. #926C2×D5semidirect
196. #821C2×D5semidirect
198. #816C2×D5semidirect
228. C2×D20#67semidirect
302. #235D20semidirect
378. C22×C8D3×D5semidirect
502. C3×C5#3008semidirect
578. C5#83833semidirect
599. C3#10610565semidirect

Maximal subgroups

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

subgroupindex
C2×#920172
C22×C3×D402
#117546022
C2×#912982
#117512112
C5×#51132
#117483662
#117481502
#117481132
#106105653
#838335