Finite Group Databasebeta

← #14427840

Subgroups — #14427840

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
1C2×#91839C211yesmaximal, characteristic, complemented
2C5×#5828C211yesmaximal, characteristic, complemented
3#11754584C211yesmaximal, characteristic, complemented
4C22×D3×#168C211yesmaximal, characteristic, complemented
5C3×#65522C211yesmaximal, characteristic, complemented
6#11749301C212yesmaximal, complemented
7#11749280C212yesmaximal, complemented
8#11749055C212yesmaximal, complemented
9#11749034C212yesmaximal, complemented
10#11748469C211yesmaximal, characteristic, complemented
11#11748393C211yesmaximal, characteristic, complemented
12#10614653—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16#91839—24no—
17C2×#6718C2211yescharacteristic, complemented
18C2×#6717C2211yescharacteristic, complemented
19C2×#6716C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic, complemented
21C22×C3⋊#168C2211yescharacteristic
22C5×#946C2212yes—
23C5×#938C2212yes—
24C5×#937—21no—
25C5×#935—21no—
26C4×C5×#67—22no—
27C5×#926C2211yescharacteristic
28C3×#4072C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30#91570—21no—
31#91542—21no—
32#91460C2212yes—
33C4×#1203—22no—
34#91365C2212yes—
35C2×D3×#168—24no—
36C2×D3×#168C2212yes—
37C2×D3×#168C2212yes—
38C3×#3967C2212yescomplemented
39C3×#3964C2212yescomplemented
40#90989C2212yescomplemented
41#90986C2212yescomplemented
42#90975C2212yescomplemented
43#90969C2212yescomplemented
44#78838—51nomaximal, Hall
45C5×#525—31no—
46C2×#4096—31no—
47#66125—31no—
48C23×#168—31no—
49#65522D311yescharacteristic, complemented
50#65340—32no—
51#65337—32no—
52#65330—32no—
53#65327—32no—
54#65291—31no—
55#65287—31no—
56C23×C5×D3D411yescharacteristic
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—21no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C2×C5×#67—22no—
71C22×C5×Dic3D411yescharacteristic
72C2×C4×C5×D3—22no—
73C2×C4×C5×D3—22no—
74C2×C4×C5×D3D412yes—
75C2×C4×C5×D3C2312yes—
76C2×#1203—22no—
77#6718—22no—
78#6717—22no—
79#6716—22no—
80#6715—22no—
81C2×C3⋊#168D414yescomplemented
82C2×C3⋊#168C2311yescharacteristic
83C2×C3⋊#168C2311yescharacteristic
84C5×#217—21no—
85C5×#217—22no—
86C5×(C2×D3)⋊C4—22no—
87C5×C4⋊Dic3C2312yes—
88C5×Dic3⋊C4—22no—
89C4×C5×Dic3—21no—
90C3×C22⋊Dic5—21no—
91C3×C4⋊Dic5C2312yes—
92C3×C4×Dic5—21no—
93C2×C3×#168—22no—
94C2×C3×#168C2312yes—
95#6668—22no—
96#6667—22no—
97(C2×D3)⋊Dic5—22no—
98D3×#168—24no—
99D3×#168—24no—
100#5828D511yescharacteristic, complemented
101C2×#950—51no—
102C22×D3×C8—51no—
103#5524—51no—
104C3×#416—51no—
105#5113—51no—
106#4998—51no—
107#4813—52no—
108#4807—52no—
109#4778—52no—
110#4775—52no—
111C2×C5×#41C2×D311yescharacteristic
112C23×C4×C5—31no—
113C2×#709—31no—
114C5×#123—61no—
115C5×C22⋊Q8—32no—
116C5×#121—32no—
117C5×#120—61no—
118C4×C5×D4—62no—
119C5×#117—31no—
120#4099—61no—
121#4096—64no—
122C2×#689—31no—
123C2×#688—31no—
124C2×#687—31no—
125C2×#686—31no—
126#4076—32no—
127#4075—61no—
128C4×C22⋊D5—62no—
129#4072C2×D311yescharacteristic
130#4070—32no—
131C22×#168—31no—
132C22×#168—32no—
133C22×#168—32no—
134C22×#168—64no—
135C22×#168C2×D311yescharacteristic
136#3967C2×D312yescomplemented
137#3964C2×D312yescomplemented
138#3942—32no—
139#3941—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5—21no—
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C5×D3—22no—
147C22×C5×D3—24no—
148C22×C5×D3C2×D412yes—
149C3×C5×Q8—21no—
150C3×C5×Q8—21no—
151C3×C5×D4—21no—
152C3×C5×D4—21no—
153C3×C5×D4—42no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—42no—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5#4112yes—
159C2×C3×C4×C5C2411yescharacteristic
160#1220—42no—
161C2×Dic15—21no—
162D60—21no—
163D60—21no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C5×#67—44no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2×D412yes—
171C4×C5×D3—24no—
172C4×C5×D3—22no—
173C4×C5×D3—22no—
174C2×C3×Dic5—22no—
175#1203—44no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C3×#168—22no—
179C2×C3×#41C2×D511yescharacteristic
180C2×#235—51no—
181C22×C4×D3C2×D511yescharacteristic
182C22×C3×C8—51no—
183C3×#117—51no—
184#950—104no—
185#946C2×D512yes—
186C2×#216—51no—
187C2×#215—51no—
188#938C2×D512yes—
189#937—21no—
190#935—21no—
191C2×#214—51no—
192C2×#213—51no—
193C4×#67—22no—
194#926C2×D511yescharacteristic
195C22×C3⋊C8—51no—
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#808—52no—
209#807—52no—
210C24×C5—31no—
211C5×#41—22no—
212C5×#41—22no—
213C2×C5×Q8C22×D311yescharacteristic
214C2×C5×D4—21no—
215C2×C5×D4—62no—
216C2×C5×D4C22×D311yescharacteristic
217C22×C4×C5—21no—
218C22×C4×C5—31no—
219C22×C4×C5—32no—
220C22×C4×C5—32no—
221C22×C4×C5—62no—
222C22×C4×C5—62no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—62no—
225C2×C22⋊D5—61no—
226#709—62no—
227#709—62no—
228C2×D20—31no—
229C2×C4×D5—61no—
230C2×Dic10—31no—
231C5×C4⋊C4—32no—
232C5×C4⋊C4—62no—
233C5×C22⋊C4—62no—
234C5×C22⋊C4—62no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237C22⋊Dic5—21no—
238C22⋊Dic5—62no—
239#689—62no—
240#688—62no—
241#687—62no—
242#686—62no—
243#685—62no—
244C4⋊Dic5C22×D312yes—
245#683—62no—
246C4×Dic5—21no—
247C2×#168—22no—
248C2×#168—34no—
249C2×#168—31no—
250C2×#168—31no—
251C2×#168—64no—
252C2×#168—64no—
253C2×#168C22×D312yes—
254C2×#135—151no—
255C23×C8—151no—
256#525—31no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—51no—
264#416—151no—
265C22×C3×C5—22no—
266C22×C3×C5—41no—
267C22×C3×C5—42no—
268C22×C3×C5#12112yes—
269C22×C3×C5C22×D411yescharacteristic
270C2×D15—41no—
271C2×D15—42no—
272C2×C5×D3—28no—
273C2×C5×D3—22no—
274C2×C5×D3—22no—
275C2×C5×D3#13514yescomplemented
276C3×C4×C5—41no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—41no—
281C3×Dic5—42no—
282C5×Dic3—22no—
283C5×Dic3—42no—
284C23×D3C22⋊D511yescharacteristic
285C3×#41—22no—
286C3×#41—22no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—22no—
293C2×#67—101no—
294C22×Dic3C22⋊D511yescharacteristic
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×D12—102no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—101no—
302C2×C4×D3C22⋊D512yes—
303C2×C4×D3C22×D512yes—
304C2×Dic6—51no—
305C2×C3×C8—52no—
306C2×C3×C8—102no—
307C3×C4⋊C4—52no—
308C3×C22⋊C4—101no—
309C3×C42—101no—
310#217—21no—
311#217—22no—
312#216—102no—
313#215—102no—
314#214—102no—
315#213—102no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—102no—
318(C2×D3)⋊C4—102no—
319C4⋊Dic3—102no—
320C4⋊Dic3C22×D512yes—
321Dic3⋊C4—22no—
322C4×Dic3—21no—
323C2×C3⋊C8—54no—
324C2×C3⋊C8—51no—
325C2×C3⋊C8—51no—
326D3×C8—104no—
327D3×C8—104no—
328C23×C5—21no—
329C23×C5—32no—
330C23×C5—64no—
331C23×C5—62no—
332C23×C5D3×D411yescharacteristic
333C22×D5—61no—
334C5×Q8—21no—
335C5×Q8—21no—
336C5×D4—21no—
337C5×D4—21no—
338C5×D4—42no—
339C5×D4—124no—
340C2×C4×C5—21no—
341C2×C4×C5—32no—
342C2×C4×C5—42no—
343C2×C4×C5—62no—
344C2×C4×C5—64no—
345C2×C4×C5—62no—
346C2×C4×C5—62no—
347C2×C4×C5—62no—
348C2×C4×C5#23512yes—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5D3×D412yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—124no—
353C22⋊D5—122no—
354C2×Dic5—22no—
355C2×Dic5—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—61no—
360Dic10—61no—
361#168—22no—
362#168—32no—
363#168—32no—
364C2×#41—151no—
365C2×#41D3×D511yescharacteristic
366C23×C4—31no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—51no—
373C22×C8—152no—
374C22×C8—152no—
375C22×C8—151no—
376C22×C8—304no—
377#123—61no—
378#123—301no—
379C22⋊Q8—32no—
380C22⋊Q8—152no—
381#121—32no—
382#121—152no—
383#120—61no—
384#120—301no—
385C4×D4—62no—
386C4×D4—302no—
387#117—31no—
388#117—51no—
389#107—152no—
390#106—152no—
391#103—52no—
392#103—152no—
393#102—52no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5—81no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399D15—81no—
400C5×D3—24no—
401C23×C3—21no—
402C23×C3C2×C22⋊D511yescharacteristic
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—101no—
406C22×D3C2×C22⋊D512yes—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—42no—
412C2×C3×C4—21no—
413C2×C3×C4—42no—
414C2×C3×C4—102no—
415C2×C3×C4D4×D512yes—
416C2×C3×C4#71112yes—
417C2×C3×C4C2×C22⋊D511yescharacteristic
418C2×C3×C4C23×D511yescharacteristic
419#67—44no—
420#67—202no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—101no—
424C2×Dic3C2×C22⋊D512yes—
425D12—101no—
426D12—101no—
427D12—204no—
428C4×D3—22no—
429C4×D3—22no—
430C4×D3—24no—
431C4×D3—202no—
432Dic6—101no—
433Dic6—101no—
434C3×C8—102no—
435C3⋊C8—52no—
436C3⋊C8—52no—
437C22×C5—22no—
438C22×C5—34no—
439C22×C5—41no—
440C22×C5—42no—
441C22×C5—68no—
442C22×C5—62no—
443C22×C5—62no—
444C22×C5#88412yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—121no—
447C2×D5—122no—
448C4×C5—41no—
449C4×C5—62no—
450C4×C5—122no—
451C4×C5#88412yes—
452C4×C5C2×#23511yescharacteristic
453C4×C5C2×D3×D411yescharacteristic
454Dic5—42no—
455Dic5—121no—
456C24—31no—
457#41—22no—
458#41—22no—
459#41—302no—
460#41—302no—
461C2×Q8—151no—
462C2×Q8C2×D3×D511yescharacteristic
463C2×D4—21no—
464C2×D4—62no—
465C2×D4—151no—
466C2×D4—302no—
467C2×D4—301no—
468C2×D4C2×D3×D511yescharacteristic
469C22×C4—21no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—62no—
474C22×C4—62no—
475C22×C4—301no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—52no—
482C2×C8—102no—
483C2×C8—154no—
484C2×C8—151no—
485C2×C8—151no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—32no—
489C4⋊C4—52no—
490C4⋊C4—62no—
491C4⋊C4—302no—
492C22⋊C4—62no—
493C22⋊C4—62no—
494C22⋊C4—61no—
495C22⋊C4—101no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—61no—
499C42—101no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3#408512yes—
505C22×C3C22×C22⋊D511yescharacteristic
506C2×D3—28no—
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—201no—
510C2×D3—202no—
511C2×D3#409614yescomplemented
512C3×C4—41no—
513C3×C4—202no—
514C3×C4#408512yes—
515C3×C4C2×D4×D511yescharacteristic
516C3×C4C2×#71111yescharacteristic
517Dic3—22no—
518Dic3—42no—
519Dic3—201no—
520C2×C5—22no—
521C2×C5—64no—
522C2×C5—81no—
523C2×C5C2×#88411yescharacteristic
524C2×C5D3×#13512yes—
525D5—241no—
526C23—21no—
527C23—32no—
528C23—64no—
529C23—62no—
530C23—301no—
531C23D3×C22⋊D511yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—301no—
535Q8—301no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—124no—
540D4—301no—
541D4—301no—
542D4—604no—
543D4—602no—
544C2×C4—21no—
545C2×C4—32no—
546C2×C4—42no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—102no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4#678212yes—
556C2×C4D3×C22⋊D511yescharacteristic
557C2×C4#679012yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—102no—
560C8—152no—
561C8—152no—
562C2×C3—22no—
563C2×C3—81no—
564C2×C3C2×#408511yescharacteristic
565C2×C3C2×#409612yes—
566D3—24no—
567D3—401no—
568C5#7883811yescharacteristic, complemented, Sylow
569C22—22no—
570C22—34no—
571C22—42no—
572C22—41no—
573C22—68no—
574C22—62no—
575C22—62no—
576C22—602no—
577C22—601no—
578C22#9155812yes—
579C22C2×D3×C22⋊D511yescharacteristic
580C4—41no—
581C4—62no—
582C4—122no—
583C4—202no—
584C4—601no—
585C4#9155812yes—
586C4C2×#678211yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061465311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—64no—
591C2—81no—
592C2—1201no—
593C2D3×#409612yes—
594C2C2×#9155811yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91839C2semidirect
2. C5×#5828C2semidirect
3. #11754584C2semidirect
4. C22×D3×#168C2semidirect
5. C3×#65522C2semidirect
6. #11749301C2semidirect
7. #11749280C2semidirect
8. #11749055C2semidirect
9. #11749034C2semidirect
10. #11748469C2semidirect
11. #11748393C2semidirect
17. C2×#6718C22semidirect
18. C2×#6717C22semidirect
19. C2×#6716C22semidirect
20. C2×#6715C22semidirect
38. C3×#3967C22semidirect
39. C3×#3964C22semidirect
40. #90989C22semidirect
41. #90986C22semidirect
42. #90975C22semidirect
43. #90969C22semidirect
49. #65522D3semidirect
81. C2×C3⋊#168D4semidirect
100. #5828D5semidirect
136. #3967C2×D3semidirect
137. #3964C2×D3semidirect
275. C2×C5×D3#135semidirect
500. C3×C5#3050semidirect
511. C2×D3#4096semidirect
568. C5#78838semidirect
588. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C5×#58282
#117545842
C22×D3×#1682
C3×#655222
#117493012
#117492802
#117490552
#117490342
#117484692
#117483932
#106146533
#788385