Finite Group Databasebeta

← #14427842

Subgroups — #14427842

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
2C3×#66162C211yesmaximal, characteristic, complemented
3#11754564C211yesmaximal, characteristic, complemented
4C22×D5×C3⋊C8C211yesmaximal, characteristic, complemented
5C5×#5233C211yesmaximal, characteristic, complemented
6#11749292C212yesmaximal, complemented
7#11749269C212yesmaximal, complemented
8#11749046C212yesmaximal, complemented
9#11749023C212yesmaximal, complemented
10#11748469C211yesmaximal, characteristic, complemented
11#11748411C211yesmaximal, characteristic, complemented
12#10610569—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16#91839—24no—
17C2×#6718C2211yescharacteristic, complemented
18C2×#6717C2211yescharacteristic, complemented
19C2×#6716C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic, complemented
21C22×C3⋊#168C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4092C2212yes—
25C3×#4084C2212yes—
26C3×#4083—21no—
27C3×#4081—21no—
28C3×C4×C22⋊D5—22no—
29C3×#4072C2211yescharacteristic
30#91564—21no—
31#91546—21no—
32#91450C2212yes—
33C4×#1202—22no—
34#91360C2212yes—
35C2×D5×C3⋊C8—24no—
36C2×D5×C3⋊C8C2212yes—
37C2×D5×C3⋊C8C2212yes—
38C5×#835C2212yescomplemented
39C5×#832C2212yescomplemented
40#90989C2212yescomplemented
41#90986C2212yescomplemented
42#90974C2212yescomplemented
43#90968C2212yescomplemented
44#82922—51nomaximal, Hall
45#66162D311yescharacteristic, complemented
46C2×#4096—31no—
47C22×C8×D5—31no—
48#65858—31no—
49C5×#416—31no—
50#65402—31no—
51#65287—31no—
52#65102—32no—
53#65096—32no—
54#65067—32no—
55#65064—32no—
56C23×C3×D5D411yescharacteristic
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×C3×C22⋊D5—22no—
71C22×C3×Dic5D411yescharacteristic
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5D412yes—
75C2×C3×C4×D5C2312yes—
76C2×#1202—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×C4⋊Dic3C2312yes—
86C4×C5×Dic3—21no—
87C2×C5×C3⋊C8—22no—
88C2×C5×C3⋊C8C2312yes—
89C3×C22⋊Dic5—21no—
90C3×C22⋊Dic5—22no—
91C3×#685—22no—
92C3×C4⋊Dic5C2312yes—
93C3×#683—22no—
94C3×C4×Dic5—21no—
95Dic3⋊Dic5—22no—
96#6667—22no—
97#6665—22no—
98D5×C3⋊C8—24no—
99D5×C3⋊C8—24no—
100C3×#525—51no—
101C2×#950—51no—
102#5791—51no—
103C23×C3⋊C8—51no—
104#5233D511yescharacteristic, complemented
105#5051—52no—
106#5048—52no—
107#5041—52no—
108#5038—52no—
109#5002—51no—
110#4998—51no—
111C2×C5×#41C2×D311yescharacteristic
112C2×#709—31no—
113C22×C4×D5C2×D311yescharacteristic
114C22×C5×C8—31no—
115C5×#117—31no—
116#4096—64no—
117#4092C2×D312yes—
118C2×#689—31no—
119C2×#688—31no—
120#4084C2×D312yes—
121#4083—21no—
122#4081—21no—
123C2×#687—31no—
124C2×#686—31no—
125C4×C22⋊D5—22no—
126#4072C2×D311yescharacteristic
127C22×#168—31no—
128C2×C8×D5—32no—
129C2×C8×D5—32no—
130C2×C8×D5—64no—
131#4043—32no—
132#4041—32no—
133#4032—61no—
134#4028—61no—
135C4×D20—62no—
136C5×#103—32no—
137C5×#102—32no—
138#3953—32no—
139#3948—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5—21no—
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—22no—
147C22×C3×D5—24no—
148C22×C3×D5C2×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—
167C2×C5×Dic3—22no—
168C3×C22⋊D5—44no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5C2×D412yes—
172C3×C4×D5—24no—
173C3×C4×D5—22no—
174C3×C4×D5—22no—
175#1202—44no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C5×C3⋊C8—22no—
179C2×C3×#41C2×D511yescharacteristic
180C23×C3×C4—51no—
181C2×#235—51no—
182C3×#123—101no—
183C3×C22⋊Q8—52no—
184C3×#121—52no—
185C3×#120—101no—
186C3×C4×D4—102no—
187C3×#117—51no—
188#953—101no—
189#950—104no—
190C2×#216—51no—
191C2×#215—51no—
192C2×#214—51no—
193C2×#213—51no—
194#930—52no—
195#929—101no—
196C4×#67—102no—
197#926C2×D511yescharacteristic
198#924—52no—
199C22×C3⋊C8—51no—
200C22×C3⋊C8—52no—
201C22×C3⋊C8—52no—
202C22×C3⋊C8—104no—
203C22×C3⋊C8C2×D511yescharacteristic
204#835C2×D512yescomplemented
205#832C2×D512yescomplemented
206#810—52no—
207#809—52no—
208#808—52no—
209#807—52no—
210C23×D5#6711yescharacteristic
211C5×#41—22no—
212C5×#41—22no—
213C2×C5×Q8C22×D311yescharacteristic
214C2×C5×D4—21no—
215C2×C5×D4C22×D311yescharacteristic
216C22×C4×C5—21no—
217C22×C4×C5C22×D311yescharacteristic
218C2×C22⋊D5—22no—
219C2×C22⋊D5—61no—
220C22×Dic5#6711yescharacteristic
221#709—62no—
222#709—62no—
223C2×D20—31no—
224C2×D20—62no—
225C2×C4×D5—22no—
226C2×C4×D5—22no—
227C2×C4×D5—61no—
228C2×C4×D5#6712yes—
229C2×C4×D5C22×D312yes—
230C2×Dic10—31no—
231C2×C5×C8—32no—
232C2×C5×C8—62no—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236C22⋊Dic5—21no—
237C22⋊Dic5—22no—
238#689—62no—
239#688—62no—
240#687—62no—
241#686—62no—
242#685—22no—
243#685—62no—
244#685—62no—
245C4⋊Dic5—62no—
246C4⋊Dic5C22×D312yes—
247#683—22no—
248C4×Dic5—21no—
249C2×#168—34no—
250C2×#168—31no—
251C2×#168—31no—
252C8×D5—64no—
253C8×D5—64no—
254C2×#135—151no—
255C23×C8—151no—
256#525—51no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—31no—
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×C3×D5—28no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5#13514yescomplemented
276C3×C4×C5—41no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—41no—
281C3×Dic5—22no—
282C3×Dic5—42no—
283C5×Dic3—42no—
284C24×C3—51no—
285C3×#41—22no—
286C3×#41—22no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—102no—
290C2×C3×D4C22×D511yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—51no—
293C22×C3×C4—52no—
294C22×C3×C4—52no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—102no—
299C2×#67—101no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—51no—
305C3×C4⋊C4—52no—
306C3×C4⋊C4—102no—
307C3×C22⋊C4—102no—
308C3×C22⋊C4—102no—
309C3×C22⋊C4—101no—
310C3×C42—101no—
311#217—21no—
312#217—102no—
313#216—102no—
314#215—102no—
315#214—102no—
316#213—102no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3C22×D512yes—
319Dic3⋊C4—102no—
320C4×Dic3—21no—
321C2×C3⋊C8—22no—
322C2×C3⋊C8—54no—
323C2×C3⋊C8—51no—
324C2×C3⋊C8—51no—
325C2×C3⋊C8—104no—
326C2×C3⋊C8—104no—
327C2×C3⋊C8C22×D512yes—
328C23×C5—21no—
329C23×C5C2×#6711yescharacteristic
330C22×D5—22no—
331C22×D5—24no—
332C22×D5—61no—
333C22×D5C2×#6712yes—
334C5×Q8—21no—
335C5×Q8—21no—
336C5×D4—21no—
337C5×D4—21no—
338C5×D4—42no—
339C2×C4×C5—21no—
340C2×C4×C5—42no—
341C2×C4×C5—62no—
342C2×C4×C5D3×D412yes—
343C2×C4×C5#23712yes—
344C2×C4×C5C2×#6711yescharacteristic
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—44no—
347C22⋊D5—122no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—61no—
351C2×Dic5C2×#6712yes—
352D20—61no—
353D20—61no—
354D20—124no—
355C4×D5—24no—
356C4×D5—22no—
357C4×D5—22no—
358C4×D5—122no—
359Dic10—61no—
360Dic10—61no—
361C5×C8—62no—
362#168—32no—
363#168—32no—
364C2×#41—151no—
365C2×#41D3×D511yescharacteristic
366C23×C4—51no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—31no—
373C22×C8—152no—
374C22×C8—152no—
375C22×C8—151no—
376C22×C8—304no—
377#123—101no—
378#123—301no—
379C22⋊Q8—52no—
380C22⋊Q8—152no—
381#121—52no—
382#121—152no—
383#120—101no—
384#120—301no—
385C4×D4—102no—
386C4×D4—302no—
387#117—31no—
388#117—51no—
389#107—152no—
390#106—152no—
391#103—32no—
392#103—152no—
393#102—32no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5—81no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399D15—81no—
400C3×D5—24no—
401C23×C3—21no—
402C23×C3—52no—
403C23×C3—104no—
404C23×C3—102no—
405C23×C3D4×D511yescharacteristic
406C22×D3—101no—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—42no—
412C3×D4—204no—
413C2×C3×C4—21no—
414C2×C3×C4—42no—
415C2×C3×C4—52no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4—102no—
419C2×C3×C4—104no—
420C2×C3×C4—102no—
421C2×C3×C4#70912yes—
422C2×C3×C4D4×D511yescharacteristic
423C2×C3×C4D4×D512yes—
424C2×C3×C4C23×D511yescharacteristic
425#67—204no—
426#67—202no—
427C2×Dic3—22no—
428C2×Dic3—101no—
429D12—101no—
430D12—101no—
431C4×D3—202no—
432Dic6—101no—
433Dic6—101no—
434C3⋊C8—22no—
435C3⋊C8—52no—
436C3⋊C8—52no—
437C22×C5—22no—
438C22×C5—41no—
439C22×C5—42no—
440C22×C5#93912yes—
441C22×C5C22×#6711yescharacteristic
442C2×D5—28no—
443C2×D5—22no—
444C2×D5—22no—
445C2×D5—121no—
446C2×D5—122no—
447C2×D5#95014yescomplemented
448C4×C5—41no—
449C4×C5—122no—
450C4×C5#93912yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C2×#23711yescharacteristic
453Dic5—22no—
454Dic5—42no—
455Dic5—121no—
456C24—51no—
457#41—22no—
458#41—22no—
459#41—302no—
460#41—302no—
461C2×Q8—151no—
462C2×Q8C2×D3×D511yescharacteristic
463C2×D4—21no—
464C2×D4—102no—
465C2×D4—151no—
466C2×D4—302no—
467C2×D4—301no—
468C2×D4C2×D3×D511yescharacteristic
469C22×C4—21no—
470C22×C4—51no—
471C22×C4—52no—
472C22×C4—52no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—301no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—32no—
482C2×C8—62no—
483C2×C8—154no—
484C2×C8—151no—
485C2×C8—151no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—32no—
489C4⋊C4—52no—
490C4⋊C4—102no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—102no—
494C22⋊C4—102no—
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—54no—
505C22×C3—108no—
506C22×C3—102no—
507C22×C3—102no—
508C22×C3#403012yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—201no—
511C2×D3—202no—
512C3×C4—41no—
513C3×C4—102no—
514C3×C4—202no—
515C3×C4#403012yes—
516C3×C4C2×#70911yescharacteristic
517C3×C4C2×D4×D511yescharacteristic
518Dic3—42no—
519Dic3—201no—
520C2×C5—22no—
521C2×C5—81no—
522C2×C5C2×#93911yescharacteristic
523C2×C5C2×#95012yes—
524D5—24no—
525D5—241no—
526C23—21no—
527C23—52no—
528C23—104no—
529C23—102no—
530C23—301no—
531C23D5×#6711yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—301no—
535Q8—301no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—204no—
540D4—301no—
541D4—301no—
542D4—604no—
543D4—602no—
544C2×C4—21no—
545C2×C4—42no—
546C2×C4—52no—
547C2×C4—62no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—104no—
552C2×C4—102no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4#677912yes—
556C2×C4D5×#6711yescharacteristic
557C2×C4#679012yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—62no—
560C8—152no—
561C8—152no—
562C2×C3—22no—
563C2×C3—81no—
564C2×C3—104no—
565C2×C3C2×#403011yescharacteristic
566C2×C3D5×#13512yes—
567D3—401no—
568C5#8292211yescharacteristic, complemented, Sylow
569C22—22no—
570C22—42no—
571C22—41no—
572C22—54no—
573C22—108no—
574C22—102no—
575C22—102no—
576C22—602no—
577C22—601no—
578C22#9155012yes—
579C22C2×D5×#6711yescharacteristic
580C4—41no—
581C4—102no—
582C4—122no—
583C4—202no—
584C4—601no—
585C4#9155012yes—
586C4C2×#677911yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061056911yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—104no—
592C2—1201no—
593C2D5×#95012yes—
594C2C2×#9155011yescharacteristic
subgroupG/H
centerC2×C4D5×#67
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. C3×#66162C2semidirect
3. #11754564C2semidirect
4. C22×D5×C3⋊C8C2semidirect
5. C5×#5233C2semidirect
6. #11749292C2semidirect
7. #11749269C2semidirect
8. #11749046C2semidirect
9. #11749023C2semidirect
10. #11748469C2semidirect
11. #11748411C2semidirect
17. C2×#6718C22semidirect
18. C2×#6717C22semidirect
19. C2×#6716C22semidirect
20. C2×#6715C22semidirect
38. C5×#835C22semidirect
39. C5×#832C22semidirect
40. #90989C22semidirect
41. #90986C22semidirect
42. #90974C22semidirect
43. #90968C22semidirect
45. #66162D3semidirect
81. C2×C3⋊#168D4semidirect
104. #5233D5semidirect
204. #835C2×D5semidirect
205. #832C2×D5semidirect
275. C2×C3×D5#135semidirect
447. C2×D5#950semidirect
500. C3×C5#3050semidirect
568. C5#82922semidirect
588. C3#10610569semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C3×#661622
#117545642
C22×D5×C3⋊C82
C5×#52332
#117492922
#117492692
#117490462
#117490232
#117484692
#117484112
#106105693
#829225