Finite Group Databasebeta

← #14427853

Subgroups — #14427853

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756283C211yesmaximal, characteristic, complemented
2#11754590C211yesmaximal, characteristic, complemented
3C2×#91311C211yesmaximal, characteristic, complemented
4C22×#6648C211yesmaximal, characteristic, complemented
5C5×#4998C211yesmaximal, characteristic, complemented
6C3×#65291C211yesmaximal, characteristic, complemented
7#11748393C211yesmaximal, characteristic, complemented
8#11747359C212yesmaximal, complemented
9#11747357C212yesmaximal, complemented
10#11747329C212yesmaximal, complemented
11#11747327C212yesmaximal, complemented
12#10610911—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17#91786C2212yes—
18#91784C2212yes—
19#91775—21no—
20#91771—21no—
21C4×D60—22no—
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91572—21no—
26#91537—21no—
27#91465C2212yes—
28C4×#1202—22no—
29#91390C2212yes—
30C2×#6662C2211yescharacteristic, complemented
31C2×#6658C2211yescharacteristic, complemented
32#91311—24no—
33C2×#6657C2211yescharacteristic, complemented
34C2×#6653C2211yescharacteristic, complemented
35C2×#6648—24no—
36C2×#6648C2212yes—
37C2×#6648C2212yes—
38C5×#808C2212yescomplemented
39C5×#807C2212yescomplemented
40C3×#3942C2212yescomplemented
41C3×#3941C2212yescomplemented
42#90975C2212yescomplemented
43#90969C2212yescomplemented
44#78838—51nomaximal, Hall
45C2×#4050—31no—
46C22×C8×D5—31no—
47#65858—31no—
48#65858—31no—
49C5×#427—31no—
50#65291—31no—
51#65291D311yescharacteristic, complemented
52#65176—32no—
53#65172—32no—
54#65153—32no—
55#65153—32no—
56C23×D15D411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59C22×Dic15D411yescharacteristic
60#6817—22no—
61#6817—22no—
62C2×D60—22no—
63C2×D60C2311yescharacteristic
64C2×C4×D15—22no—
65C2×C4×D15—22no—
66C2×C4×D15—21no—
67C2×C4×D15D412yes—
68C2×C4×D15C2312yes—
69C2×Dic30C2311yescharacteristic
70C2×C3×C22⋊D5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×Dic10C2311yescharacteristic
76C2×#1202—22no—
77C3×C5×C4⋊C4C2312yes—
78C3×C5×C22⋊C4—21no—
79C3×C42×C5—21no—
80#6714—22no—
81#6714—22no—
82C4⋊Dic15—22no—
83C5×#217—21no—
84C5×C4⋊Dic3C2312yes—
85C4×C5×Dic3—21no—
86C2×C5×C3⋊C8D414yescomplemented
87C2×C5×C3⋊C8C2311yescharacteristic
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C3×#168—22no—
90C2×C3×#168C2312yes—
91Dic3⋊Dic5—22no—
92#6667—22no—
93#6665—22no—
94#6662—22no—
95#6658—22no—
96#6657—22no—
97#6653—22no—
98#6648—24no—
99#6648—24no—
100#5828—51no—
101C2×#950—51no—
102C22×D3×C8—51no—
103#5524—51no—
104C3×#416—51no—
105#5113—51no—
106#4998D511yescharacteristic, complemented
107#4813—52no—
108#4807—52no—
109#4778—52no—
110#4775—52no—
111C2×#709—31no—
112C2×#709C2×D311yescharacteristic
113C22×C4×D5—31no—
114C22×C5×C8—31no—
115C5×#117—31no—
116C5×#117C2×D311yescharacteristic
117C22×#168C2×D311yescharacteristic
118C2×Dic20—31no—
119#4050—64no—
120C2×D40—31no—
121C2×#677—31no—
122C2×#677—31no—
123C2×C8×D5—32no—
124C2×C8×D5—32no—
125C2×C8×D5—64no—
126#4043—32no—
127#4043—32no—
128#4041—32no—
129#4041—32no—
130#4032—61no—
131#4032—61no—
132#4028—61no—
133#4028—61no—
134C4×D20—62no—
135C4×D20—62no—
136C5×#107—32no—
137C5×#106—32no—
138#3942—32no—
139#3942C2×D312yescomplemented
140#3941—32no—
141#3941C2×D312yescomplemented
142#3050—151noSylow
143C23×C3×C5C2×D411yescharacteristic
144C22×D15—22no—
145C22×D15—24no—
146C22×D15—21no—
147C22×D15C2×D412yes—
148C22×C3×D5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5C2411yescharacteristic
154#1220—42no—
155C2×Dic15—22no—
156C2×Dic15—21no—
157C2×Dic15C2×D412yes—
158D60—21no—
159D60—21no—
160D60—44no—
161C4×D15—24no—
162C4×D15—22no—
163C4×D15—22no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C2×C5×Dic3—22no—
168C3×C22⋊D5—42no—
169C2×C3×Dic5—21no—
170C3×D20—21no—
171C3×D20—21no—
172C3×C4×D5—42no—
173C3×Dic10—21no—
174C3×Dic10—21no—
175#1202—44no—
176C3×#168—22no—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41—51no—
180C2×#235—51no—
181C22×C4×D3—51no—
182C22×C3×C8—51no—
183C3×#117C2×D511yescharacteristic
184#950—104no—
185#946—52no—
186C2×#216—51no—
187C2×#215—51no—
188#938—52no—
189#937—101no—
190#935—101no—
191C2×#214—51no—
192C2×#213—51no—
193C4×#67—102no—
194#926C2×D511yescharacteristic
195C22×C3⋊C8C2×D511yescharacteristic
196C2×D3×C8—52no—
197C2×D3×C8—52no—
198C2×D3×C8—104no—
199#897—52no—
200#895—52no—
201#886—101no—
202#882—101no—
203C4×D12—102no—
204C3×#103—52no—
205C3×#102—52no—
206#821—52no—
207#816—52no—
208#808C2×D512yescomplemented
209#807C2×D512yescomplemented
210C23×D5—31no—
211C22×C4×C5C22×D311yescharacteristic
212C2×C22⋊D5—21no—
213C2×C22⋊D5—61no—
214C22×Dic5—31no—
215#709—22no—
216#709—22no—
217#709—62no—
218#709—62no—
219C2×D20—31no—
220C2×D20—62no—
221C2×D20—62no—
222C2×D20C22×D311yescharacteristic
223C2×C4×D5—21no—
224C2×C4×D5—32no—
225C2×C4×D5—32no—
226C2×C4×D5—62no—
227C2×C4×D5—62no—
228C2×C4×D5—61no—
229C2×Dic10—31no—
230C2×Dic10C22×D311yescharacteristic
231C2×C5×C8—34no—
232C2×C5×C8—31no—
233C2×C5×C8—31no—
234C5×C4⋊C4—32no—
235C5×C4⋊C4C22×D312yes—
236C5×C22⋊C4—21no—
237C5×C22⋊C4—61no—
238C42×C5—21no—
239C42×C5—61no—
240#685—62no—
241#685—62no—
242#685—62no—
243#685—62no—
244C4⋊Dic5—62no—
245C4⋊Dic5—62no—
246C2×#168—22no—
247C2×#168C22×D312yes—
248Dic20—62no—
249D40—62no—
250#677—62no—
251#677—62no—
252C8×D5—64no—
253C8×D5—64no—
254C2×#135—151no—
255C23×C8—151no—
256#525—151no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—31no—
263#416—51no—
264#416—151no—
265C22×C3×C5—22no—
266C22×C3×C5#12112yes—
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—28no—
269C2×D15—22no—
270C2×D15—22no—
271C2×D15—41no—
272C2×D15—42no—
273C2×D15#13514yescomplemented
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5—42no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—22no—
281Dic15—41no—
282C3×Dic5—41no—
283C5×Dic3—42no—
284C23×D3—51no—
285C3×#41—102no—
286C3×#41—102no—
287C2×C3×Q8—51no—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C22×C3×C4—101no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—102no—
293C2×#67—101no—
294C22×Dic3—51no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×D12—102no—
299C2×C4×D3—52no—
300C2×C4×D3—52no—
301C2×C4×D3—102no—
302C2×C4×D3—102no—
303C2×C4×D3—101no—
304C2×Dic6—51no—
305C2×C3×C8—52no—
306C2×C3×C8—102no—
307C3×C4⋊C4C22×D512yes—
308C3×C22⋊C4—21no—
309C3×C42—21no—
310#217—21no—
311#217—102no—
312#216—102no—
313#215—102no—
314#214—102no—
315#213—102no—
316(C2×D3)⋊C4—102no—
317(C2×D3)⋊C4—102no—
318(C2×D3)⋊C4—102no—
319C4⋊Dic3—102no—
320C4⋊Dic3C22×D512yes—
321Dic3⋊C4—102no—
322C4×Dic3—21no—
323C2×C3⋊C8D2014yescomplemented
324C2×C3⋊C8C22×D511yescharacteristic
325C2×C3⋊C8C22×D511yescharacteristic
326D3×C8—104no—
327D3×C8—104no—
328C23×C5D3×D411yescharacteristic
329C22×D5—21no—
330C22×D5—32no—
331C22×D5—64no—
332C22×D5—62no—
333C22×D5—61no—
334C2×C4×C5—22no—
335C2×C4×C5—62no—
336C2×C4×C5#23512yes—
337C2×C4×C5D3×D412yes—
338C2×C4×C5D3×D411yescharacteristic
339C2×C4×C5C23×D311yescharacteristic
340C22⋊D5—42no—
341C22⋊D5—122no—
342C2×Dic5—21no—
343C2×Dic5—32no—
344C2×Dic5—62no—
345C2×Dic5—61no—
346D20—21no—
347D20—21no—
348D20—61no—
349D20—61no—
350D20—124no—
351D20—124no—
352C4×D5—42no—
353C4×D5—64no—
354C4×D5—62no—
355C4×D5—62no—
356C4×D5—122no—
357Dic10—21no—
358Dic10—21no—
359Dic10—61no—
360Dic10—61no—
361C5×C8—32no—
362C5×C8—32no—
363#168—22no—
364C2×#41—51no—
365C2×#41—151no—
366C23×C4—151no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—31no—
373C22×C8—51no—
374C22×C8—152no—
375C22×C8—152no—
376C22×C8—304no—
377#123—301no—
378#123—301no—
379C22⋊Q8—152no—
380C22⋊Q8—152no—
381#121—152no—
382#121—152no—
383#120—301no—
384#120—301no—
385C4×D4—302no—
386C4×D4—302no—
387#117—31no—
388#117D3×D511yescharacteristic
389#107—32no—
390#106—32no—
391#103—52no—
392#103—152no—
393#102—52no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5C2×#12111yescharacteristic
397C2×C3×C5C2×#13512yes—
398D15—24no—
399D15—81no—
400C3×D5—81no—
401C23×C3—101no—
402C23×C3D4×D511yescharacteristic
403C22×D3—52no—
404C22×D3—104no—
405C22×D3—102no—
406C22×D3—101no—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—101no—
410C3×D4—101no—
411C3×D4—202no—
412C2×C3×C4—22no—
413C2×C3×C4—101no—
414C2×C3×C4—202no—
415C2×C3×C4C2×D2012yes—
416C2×C3×C4D4×D511yescharacteristic
417C2×C3×C4#71312yes—
418C2×C3×C4C23×D511yescharacteristic
419#67—204no—
420#67—202no—
421C2×Dic3—22no—
422C2×Dic3—52no—
423C2×Dic3—102no—
424C2×Dic3—101no—
425D12—101no—
426D12—101no—
427D12—204no—
428C4×D3—102no—
429C4×D3—102no—
430C4×D3—104no—
431C4×D3—202no—
432Dic6—101no—
433Dic6—101no—
434C3×C8—102no—
435C3⋊C8C2×D2012yes—
436C3⋊C8C2×D2012yes—
437C22×C5—22no—
438C22×C5#88412yes—
439C22×C5C2×D3×D411yescharacteristic
440C2×D5—34no—
441C2×D5—41no—
442C2×D5—42no—
443C2×D5—68no—
444C2×D5—62no—
445C2×D5—62no—
446C2×D5—121no—
447C2×D5—122no—
448C4×C5—42no—
449C4×C5—122no—
450C4×C5#88412yes—
451C4×C5C2×#23511yescharacteristic
452C4×C5C2×D3×D411yescharacteristic
453Dic5—41no—
454Dic5—62no—
455Dic5—121no—
456C24—151no—
457#41—102no—
458#41—102no—
459#41—302no—
460#41—302no—
461C2×Q8—51no—
462C2×Q8—151no—
463C2×D4—51no—
464C2×D4—101no—
465C2×D4—151no—
466C2×D4—302no—
467C2×D4—302no—
468C2×D4—301no—
469C22×C4—101no—
470C22×C4—151no—
471C22×C4—152no—
472C22×C4—152no—
473C22×C4—302no—
474C22×C4—302no—
475C22×C4—301no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—52no—
485C2×C8—102no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—32no—
489C4⋊C4—302no—
490C4⋊C4—302no—
491C4⋊C4C2×D3×D512yes—
492C22⋊C4—21no—
493C22⋊C4—61no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—21no—
499C42—61no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—201no—
503C22×C3—202no—
504C22×C3#404112yes—
505C22×C3C2×D4×D511yescharacteristic
506C2×D3—54no—
507C2×D3—108no—
508C2×D3—102no—
509C2×D3—102no—
510C2×D3—201no—
511C2×D3—202no—
512C3×C4—42no—
513C3×C4—201no—
514C3×C4#404112yes—
515C3×C4C22×D2011yescharacteristic
516C3×C4C2×#71311yescharacteristic
517Dic3—42no—
518Dic3—102no—
519Dic3—201no—
520C2×C5—22no—
521C2×C5C2×#88411yescharacteristic
522C2×C5D3×#13512yes—
523D5—64no—
524D5—81no—
525D5—241no—
526C23—101no—
527C23—152no—
528C23—304no—
529C23—302no—
530C23—301no—
531C23#679011yescharacteristic
532Q8—101no—
533Q8—101no—
534Q8—301no—
535Q8—301no—
536D4—101no—
537D4—101no—
538D4—202no—
539D4—301no—
540D4—301no—
541D4—604no—
542D4—604no—
543D4—602no—
544C2×C4—22no—
545C2×C4—62no—
546C2×C4—101no—
547C2×C4—152no—
548C2×C4—202no—
549C2×C4—302no—
550C2×C4—304no—
551C2×C4—302no—
552C2×C4—302no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4#677312yes—
556C2×C4D3×D2012yes—
557C2×C4#679011yescharacteristic
558C2×C4C22×D3×D511yescharacteristic
559C8—32no—
560C8—32no—
561C8—102no—
562C2×C3—22no—
563C2×C3—401no—
564C2×C3C2×#404111yescharacteristic
565C2×C3D5×#13512yes—
566D3—104no—
567D3—401no—
568C5#7883811yescharacteristic, complemented, Sylow
569C22—22no—
570C22—154no—
571C22—201no—
572C22—202no—
573C22—308no—
574C22—302no—
575C22—302no—
576C22—601no—
577C22—602no—
578C22#9145912yes—
579C22C2×#679011yescharacteristic
580C4—42no—
581C4—122no—
582C4—201no—
583C4—302no—
584C4—601no—
585C4#9145912yes—
586C4C2×#677311yescharacteristic
587C4C2×D3×D2011yescharacteristic
588C3#1061091111yescharacteristic, complemented, Sylow
589C2—22no—
590C2—304no—
591C2—401no—
592C2—1201no—
593C2C2×#9145911yescharacteristic
594C2#1175532812yes—
subgroupG/H
centerC2×C4#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756283C2semidirect
2. #11754590C2semidirect
3. C2×#91311C2semidirect
4. C22×#6648C2semidirect
5. C5×#4998C2semidirect
6. C3×#65291C2semidirect
7. #11748393C2semidirect
8. #11747359C2semidirect
9. #11747357C2semidirect
10. #11747329C2semidirect
11. #11747327C2semidirect
30. C2×#6662C22semidirect
31. C2×#6658C22semidirect
33. C2×#6657C22semidirect
34. C2×#6653C22semidirect
38. C5×#808C22semidirect
39. C5×#807C22semidirect
40. C3×#3942C22semidirect
41. C3×#3941C22semidirect
42. #90975C22semidirect
43. #90969C22semidirect
51. #65291D3semidirect
86. C2×C5×C3⋊C8D4semidirect
106. #4998D5semidirect
139. #3942C2×D3semidirect
141. #3941C2×D3semidirect
208. #808C2×D5semidirect
209. #807C2×D5semidirect
273. C2×D15#135semidirect
323. C2×C3⋊C8D20semidirect
500. C3×C5#3050semidirect
568. C5#78838semidirect
588. C3#10610911semidirect

Maximal subgroups

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

subgroupindex
#117562832
#117545902
C2×#913112
C22×#66482
C5×#49982
C3×#652912
#117483932
#117473592
#117473572
#117473292
#117473272
#106109113
#788385