Finite Group Databasebeta

← #14427859

Subgroups — #14427859

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
1C22×C8×D15C211yesmaximal, characteristic, complemented
2#11754592C211yesmaximal, characteristic, complemented
3#11754590C211yesmaximal, characteristic, complemented
4C2×#91297C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748469C211yesmaximal, characteristic, complemented
8#11747954C212yesmaximal, complemented
9#11747928C212yesmaximal, complemented
10#11747926C212yesmaximal, complemented
11#11747924C212yesmaximal, complemented
12#10610569—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C2×C8×D15—24no—
19C2×C8×D15C2212yes—
20C2×C8×D15C2212yes—
21C5×#926C2211yescharacteristic
22C3×#4072C2211yescharacteristic
23#91573—21no—
24#91572—21no—
25#91543—21no—
26#91537—21no—
27#91466C2212yes—
28#91465C2212yes—
29C4×#1203—22no—
30C4×#1202—22no—
31#91390C2212yes—
32#91383C2212yes—
33C2×#6661C2211yescharacteristic, complemented
34C2×#6656C2211yescharacteristic, complemented
35C2×#6655C2211yescharacteristic, complemented
36#91297—24no—
37C2×#6652C2211yescharacteristic, complemented
38C5×#821C2212yescomplemented
39C5×#816C2212yescomplemented
40C3×#3953C2212yescomplemented
41C3×#3948C2212yescomplemented
42#90989C2212yescomplemented
43#90986C2212yescomplemented
44#78838—51nomaximal, Hall
45#66162—31no—
46C2×#4096—31no—
47C22×C8×D5—31no—
48#65858—31no—
49C5×#416—31no—
50#65402D311yescharacteristic, complemented
51#65287—31no—
52#65102—32no—
53#65096—32no—
54#65067—32no—
55#65064—32no—
56C23×D15D411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15D411yescharacteristic
59C2×C4×D15—22no—
60C2×C4×D15—22no—
61C2×C4×D15D412yes—
62C2×C4×D15C2312yes—
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235—22no—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10C2311yescharacteristic
75C2×#1203—22no—
76C2×#1202—22no—
77C2×C3×C5×C8—22no—
78C2×C3×C5×C8C2312yes—
79C2×C3⋊#168D414yescomplemented
80C2×C3⋊#168C2311yescharacteristic
81C2×C3⋊#168C2311yescharacteristic
82C8×D15—24no—
83C8×D15—24no—
84C5×#217—21no—
85C5×C4⋊Dic3C2312yes—
86C4×C5×Dic3—21no—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90Dic3⋊Dic5—22no—
91#6668—22no—
92#6667—22no—
93#6667—22no—
94(C2×D3)⋊Dic5—22no—
95#6665—22no—
96#6661—22no—
97#6656—22no—
98#6655—22no—
99#6652—22no—
100#5828—51no—
101C2×#950—51no—
102C22×D3×C8—51no—
103#5524—51no—
104C3×#416—51no—
105#5113D511yescharacteristic, complemented
106#4998—51no—
107#4813—52no—
108#4807—52no—
109#4778—52no—
110#4775—52no—
111C2×C5×#41—31no—
112C2×#709C2×D311yescharacteristic
113C22×C4×D5—31no—
114C22×C5×C8C2×D311yescharacteristic
115C5×#117—31no—
116#4096—64no—
117#4092—32no—
118C2×#689—31no—
119C2×#688—31no—
120#4084—32no—
121#4083—61no—
122#4081—61no—
123C2×#687—31no—
124C2×#686—31no—
125C4×C22⋊D5—62no—
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#3953C2×D312yescomplemented
139#3948C2×D312yescomplemented
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5C2×D411yescharacteristic
144C22×D15—22no—
145C22×D15—24no—
146C22×D15C2×D412yes—
147C22×C5×D3—21no—
148C22×C3×D5—21no—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5C2411yescharacteristic
153C2×Dic15—22no—
154C2×Dic15C2×D412yes—
155C4×D15—24no—
156C4×D15—22no—
157C4×D15—22no—
158C5×#67—42no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—21no—
161C5×D12—21no—
162C5×D12—21no—
163C4×C5×D3—42no—
164C5×Dic6—21no—
165C5×Dic6—21no—
166C3×C22⋊D5—42no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—21no—
169C3×D20—21no—
170C3×D20—21no—
171C3×C4×D5—42no—
172C3×Dic10—21no—
173C3×Dic10—21no—
174#1203—44no—
175#1202—44no—
176C3×C5×C8—22no—
177C3⋊#168C2×D412yes—
178C3⋊#168C2×D412yes—
179C2×C3×#41—51no—
180C2×#235C2×D511yescharacteristic
181C22×C4×D3—51no—
182C22×C3×C8C2×D511yescharacteristic
183C3×#117—51no—
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⋊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#821C2×D512yescomplemented
207#816C2×D512yescomplemented
208#808—52no—
209#807—52no—
210C23×D5—31no—
211C5×#41—62no—
212C5×#41—62no—
213C2×C5×Q8—31no—
214C2×C5×D4—31no—
215C2×C5×D4—61no—
216C22×C4×C5—61no—
217C22×C4×C5C22×D311yescharacteristic
218C2×C22⋊D5—21no—
219C2×C22⋊D5—62no—
220C22×Dic5—31no—
221#709—22no—
222#709—22no—
223C2×D20—62no—
224C2×D20C22×D311yescharacteristic
225C2×C4×D5—21no—
226C2×C4×D5—32no—
227C2×C4×D5—32no—
228C2×C4×D5—62no—
229C2×C4×D5—62no—
230C2×Dic10C22×D311yescharacteristic
231C2×C5×C8—22no—
232C2×C5×C8C22×D312yes—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236C22⋊Dic5—21no—
237C22⋊Dic5—62no—
238#689—62no—
239#688—62no—
240#687—62no—
241#686—62no—
242#685—62no—
243#685—62no—
244#685—62no—
245C4⋊Dic5—62no—
246C4⋊Dic5C22×D312yes—
247#683—62no—
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—151no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—31no—
264#416—51no—
265C22×C3×C5—22no—
266C22×C3×C5#12112yes—
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—28no—
269C2×D15—22no—
270C2×D15—22no—
271C2×D15#13514yescomplemented
272C2×C5×D3—41no—
273C2×C5×D3—42no—
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5#12112yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C2×#4111yescharacteristic
279Dic15—22no—
280C3×Dic5—41no—
281C3×Dic5—42no—
282C5×Dic3—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—21no—
293C2×#67—102no—
294C22×Dic3—51no—
295#235—22no—
296#235—22no—
297C2×D12—102no—
298C2×D12C22×D511yescharacteristic
299C2×C4×D3—21no—
300C2×C4×D3—52no—
301C2×C4×D3—52no—
302C2×C4×D3—102no—
303C2×C4×D3—102no—
304C2×Dic6C22×D511yescharacteristic
305C2×C3×C8—22no—
306C2×C3×C8C22×D512yes—
307C3×C4⋊C4—52no—
308C3×C22⋊C4—101no—
309C3×C42—101no—
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⋊C8—54no—
324C2×C3⋊C8—51no—
325C2×C3⋊C8—51no—
326D3×C8—104no—
327D3×C8—104no—
328C23×C5—61no—
329C23×C5D3×D411yescharacteristic
330C22×D5—21no—
331C22×D5—32no—
332C22×D5—64no—
333C22×D5—62no—
334C5×Q8—61no—
335C5×Q8—61no—
336C5×D4—61no—
337C5×D4—61no—
338C5×D4—122no—
339C2×C4×C5—61no—
340C2×C4×C5—62no—
341C2×C4×C5—122no—
342C2×C4×C5#23512yes—
343C2×C4×C5D3×D411yescharacteristic
344C2×C4×C5D3×D412yes—
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—42no—
347C22⋊D5—124no—
348C2×Dic5—22no—
349C2×Dic5—21no—
350C2×Dic5—32no—
351C2×Dic5—62no—
352D20—21no—
353D20—21no—
354D20—124no—
355C4×D5—42no—
356C4×D5—64no—
357C4×D5—62no—
358C4×D5—62no—
359Dic10—21no—
360Dic10—21no—
361C5×C8—22no—
362#168—32no—
363#168—32no—
364C2×#41—31no—
365C2×#41—51no—
366C23×C4—151no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—151no—
373C22×C8—152no—
374C22×C8—152no—
375C22×C8—304no—
376C22×C8D3×D511yescharacteristic
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#117—51no—
389#107—152no—
390#106—152no—
391#103—32no—
392#103—52no—
393#102—32no—
394#102—52no—
395C2×C3×C5—22no—
396C2×C3×C5C2×#12111yescharacteristic
397C2×C3×C5C2×#13512yes—
398D15—24no—
399C3×D5—81no—
400C5×D3—81no—
401C23×C3—101no—
402C23×C3D4×D511yescharacteristic
403C22×D3—21no—
404C22×D3—52no—
405C22×D3—104no—
406C22×D3—102no—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—101no—
410C3×D4—101no—
411C3×D4—202no—
412C2×C3×C4—101no—
413C2×C3×C4—102no—
414C2×C3×C4—202no—
415C2×C3×C4#70912yes—
416C2×C3×C4D4×D511yescharacteristic
417C2×C3×C4D4×D512yes—
418C2×C3×C4C23×D511yescharacteristic
419#67—42no—
420#67—204no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—52no—
424C2×Dic3—102no—
425D12—21no—
426D12—21no—
427D12—204no—
428C4×D3—42no—
429C4×D3—102no—
430C4×D3—102no—
431C4×D3—104no—
432Dic6—21no—
433Dic6—21no—
434C3×C8—22no—
435C3⋊C8—52no—
436C3⋊C8—52no—
437C22×C5—22no—
438C22×C5—121no—
439C22×C5—122no—
440C22×C5#88412yes—
441C22×C5C2×D3×D411yescharacteristic
442C2×D5—34no—
443C2×D5—41no—
444C2×D5—42no—
445C2×D5—68no—
446C2×D5—62no—
447C2×D5—62no—
448C4×C5—121no—
449C4×C5—122no—
450C4×C5#88412yes—
451C4×C5C2×#23511yescharacteristic
452C4×C5C2×D3×D411yescharacteristic
453Dic5—41no—
454Dic5—42no—
455Dic5—62no—
456C24—151no—
457#41—62no—
458#41—62no—
459#41—102no—
460#41—102no—
461C2×Q8—31no—
462C2×Q8—51no—
463C2×D4—31no—
464C2×D4—51no—
465C2×D4—61no—
466C2×D4—101no—
467C2×D4—302no—
468C2×D4—302no—
469C22×C4—61no—
470C22×C4—101no—
471C22×C4—151no—
472C22×C4—152no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—22no—
482C2×C8—154no—
483C2×C8—151no—
484C2×C8—151no—
485C2×C8—304no—
486C2×C8—304no—
487C2×C8C2×D3×D512yes—
488C4⋊C4—32no—
489C4⋊C4—52no—
490C4⋊C4—302no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—101no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—61no—
499C42—101no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—201no—
503C22×C3—202no—
504C22×C3#403012yes—
505C22×C3C2×D4×D511yescharacteristic
506C2×D3—41no—
507C2×D3—42no—
508C2×D3—54no—
509C2×D3—108no—
510C2×D3—102no—
511C2×D3—102no—
512C3×C4—201no—
513C3×C4—202no—
514C3×C4#403012yes—
515C3×C4C2×#70911yescharacteristic
516C3×C4C2×D4×D511yescharacteristic
517Dic3—41no—
518Dic3—42no—
519Dic3—102no—
520C2×C5—22no—
521C2×C5—241no—
522C2×C5C2×#88411yescharacteristic
523C2×C5D3×#13512yes—
524D5—64no—
525D5—81no—
526C23—61no—
527C23—101no—
528C23—152no—
529C23—304no—
530C23—302no—
531C23#677711yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—101no—
535Q8—101no—
536D4—61no—
537D4—61no—
538D4—101no—
539D4—101no—
540D4—122no—
541D4—202no—
542D4—604no—
543D4—604no—
544C2×C4—62no—
545C2×C4—61no—
546C2×C4—102no—
547C2×C4—101no—
548C2×C4—122no—
549C2×C4—152no—
550C2×C4—202no—
551C2×C4—302no—
552C2×C4—304no—
553C2×C4—302no—
554C2×C4—302no—
555C2×C4#677112yes—
556C2×C4#677711yescharacteristic
557C2×C4#679012yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—22no—
560C8—152no—
561C8—152no—
562C2×C3—22no—
563C2×C3—401no—
564C2×C3C2×#403011yescharacteristic
565C2×C3D5×#13512yes—
566D3—81no—
567D3—104no—
568C5#7883811yescharacteristic, complemented, Sylow
569C22—22no—
570C22—121no—
571C22—122no—
572C22—154no—
573C22—201no—
574C22—202no—
575C22—308no—
576C22—302no—
577C22—302no—
578C22#9146112yes—
579C22C2×#677711yescharacteristic
580C4—121no—
581C4—122no—
582C4—201no—
583C4—202no—
584C4—302no—
585C4#9146112yes—
586C4C2×#677111yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061056911yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—304no—
592C2—401no—
593C2#1175397812yes—
594C2C2×#9146111yescharacteristic
subgroupG/H
centerC2×C4#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×D15C2semidirect
2. #11754592C2semidirect
3. #11754590C2semidirect
4. C2×#91297C2semidirect
5. C5×#5113C2semidirect
6. C3×#65402C2semidirect
7. #11748469C2semidirect
8. #11747954C2semidirect
9. #11747928C2semidirect
10. #11747926C2semidirect
11. #11747924C2semidirect
33. C2×#6661C22semidirect
34. C2×#6656C22semidirect
35. C2×#6655C22semidirect
37. C2×#6652C22semidirect
38. C5×#821C22semidirect
39. C5×#816C22semidirect
40. C3×#3953C22semidirect
41. C3×#3948C22semidirect
42. #90989C22semidirect
43. #90986C22semidirect
50. #65402D3semidirect
79. C2×C3⋊#168D4semidirect
105. #5113D5semidirect
138. #3953C2×D3semidirect
139. #3948C2×D3semidirect
206. #821C2×D5semidirect
207. #816C2×D5semidirect
271. C2×D15#135semidirect
500. C3×C5#3050semidirect
568. C5#78838semidirect
588. C3#10610569semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D152
#117545922
#117545902
C2×#912972
C5×#51132
C3×#654022
#117484692
#117479542
#117479282
#117479262
#117479242
#106105693
#788385