Finite Group Databasebeta

← #14427841

Subgroups — #14427841

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#11756587C211yesmaximal, characteristic, complemented
2C2×C3×#4096C211yesmaximal, characteristic, complemented
3#11754590C211yesmaximal, characteristic, complemented
4C22×#6648C211yesmaximal, characteristic, complemented
5C5×#5233C211yesmaximal, characteristic, complemented
6#11749299C212yesmaximal, complemented
7#11749277C212yesmaximal, complemented
8#11749053C212yesmaximal, complemented
9#11749031C212yesmaximal, complemented
10#11748458C211yesmaximal, characteristic, complemented
11#11748365C211yesmaximal, characteristic, complemented
12#10610569—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16#91835C2212yes—
17#91827C2212yes—
18#91826—21no—
19#91824—21no—
20C4×#1220—22no—
21#91815C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4096—24no—
25C2×C3×#689C2211yescharacteristic, complemented
26C2×C3×#688C2211yescharacteristic, complemented
27C2×C3×#687C2211yescharacteristic, complemented
28C2×C3×#686C2211yescharacteristic, complemented
29C22×C3×#168C2211yescharacteristic
30#91572—21no—
31#91537—21no—
32#91465C2212yes—
33C4×#1202—22no—
34#91390C2212yes—
35C2×#6648—24no—
36C2×#6648C2212yes—
37C2×#6648C2212yes—
38C5×#835C2212yescomplemented
39C5×#832C2212yescomplemented
40#90988C2212yescomplemented
41#90985C2212yescomplemented
42#90971C2212yescomplemented
43#90965C2212yescomplemented
44#83914—51nomaximal, Hall
45#66162—31no—
46C2×#4096D311yescharacteristic, complemented
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×D15D411yescharacteristic
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—22no—
65C22×Dic15D411yescharacteristic
66C2×C4×D15—22no—
67C2×C4×D15—22no—
68C2×C4×D15D412yes—
69C2×C4×D15C2312yes—
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—
77#6719—21no—
78#6719—22no—
79#6714—22no—
80C4⋊Dic15C2312yes—
81#6712—22no—
82C4×Dic15—21no—
83C5×#217—21no—
84C5×C4⋊Dic3C2312yes—
85C4×C5×Dic3—21no—
86C2×C5×C3⋊C8—22no—
87C2×C5×C3⋊C8C2312yes—
88C3×#689—22no—
89C3×#688—22no—
90C3×#687—22no—
91C3×#686—22no—
92C2×C3×#168D414yescomplemented
93C2×C3×#168C2311yescharacteristic
94C2×C3×#168C2311yescharacteristic
95Dic3⋊Dic5—22no—
96#6667—22no—
97#6665—22no—
98#6648—24no—
99#6648—24no—
100C2×C3×#135—51no—
101#5828—51no—
102#5828—51no—
103C22×D3×C8—51no—
104#5233—51no—
105#5233D511yescharacteristic, complemented
106#5188—52no—
107#5171—52no—
108#5171—52no—
109#5157—52no—
110#5106—51no—
111C2×C5×#41C2×D311yescharacteristic
112C2×#709C2×D311yescharacteristic
113C22×C4×D5—31no—
114C22×C5×C8—31no—
115C5×#117—31no—
116#4096—24no—
117#4092—32no—
118C2×#689C2×D311yescharacteristic, complemented
119C2×#688C2×D311yescharacteristic, complemented
120#4084—32no—
121#4083—61no—
122#4081—61no—
123C2×#687C2×D311yescharacteristic, complemented
124C2×#686C2×D311yescharacteristic, complemented
125C4×C22⋊D5—62no—
126#4072—31no—
127C22×#168C2×D311yescharacteristic
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—22no—
146C22×D15—24no—
147C22×D15C2×D412yes—
148C22×C3×D5—21no—
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—44no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15C2×D412yes—
164C4×D15—24no—
165C4×D15—22no—
166C4×D15—22no—
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×#168C2×D412yes—
177C3×#168C2×D412yes—
178C5×C3⋊C8—22no—
179C2×C3×#41—51no—
180C2×C3×#41C2×D511yescharacteristic
181C22×C4×D3—51no—
182C3×#135—104no—
183C2×C3×Q16—51no—
184C2×C3×SD16—51no—
185C2×C3×SD16—51no—
186C2×C3×D8—51no—
187C22×C3×C8—51no—
188#946—52no—
189#946—52no—
190#938—52no—
191#938—52no—
192#937—101no—
193#937—101no—
194#935—101no—
195#935—101no—
196C4×#67—102no—
197C4×#67—102no—
198#926—51no—
199#926C2×D511yescharacteristic
200C22×C3⋊C8C2×D511yescharacteristic
201C2×D3×C8—52no—
202C2×D3×C8—52no—
203C2×D3×C8—104no—
204#835—52no—
205#835C2×D512yescomplemented
206#832—52no—
207#832C2×D512yescomplemented
208#818—52no—
209#817—52no—
210C23×D5—31no—
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—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—32no—
232C2×C5×C8—62no—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236C22⋊Dic5—62no—
237C22⋊Dic5—61no—
238#689—22no—
239#688—22no—
240#687—22no—
241#686—22no—
242#685—62no—
243#685—62no—
244#685—62no—
245C4⋊Dic5—32no—
246C4⋊Dic5—62no—
247#683—62no—
248C4×Dic5—61no—
249C2×#168#6714yescomplemented
250C2×#168C22×D311yescharacteristic
251C2×#168C22×D311yescharacteristic
252C8×D5—64no—
253C8×D5—64no—
254C2×#135—51no—
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—151no—
265C22×C3×C5—22no—
266C22×C3×C5—41no—
267C22×C3×C5—42no—
268C22×C3×C5#12112yes—
269C22×C3×C5C22×D411yescharacteristic
270C2×D15—28no—
271C2×D15—22no—
272C2×D15—22no—
273C2×D15#13514yescomplemented
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5—41no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—22no—
281Dic15—42no—
282C3×Dic5—41no—
283C5×Dic3—42no—
284C23×D3—51no—
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—102no—
288C3×#41—102no—
289C2×C3×Q8—51no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4—51no—
293C2×C3×D4—101no—
294C2×C3×D4C22×D511yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—102no—
299C2×#67—102no—
300C22×Dic3—51no—
301C2×C4×D3—52no—
302C2×C4×D3—52no—
303C2×C4×D3—102no—
304C2×C4×D3—102no—
305C3×Q16—102no—
306C3×SD16—102no—
307C3×SD16—102no—
308C3×D8—102no—
309C2×C3×C8—54no—
310C2×C3×C8—51no—
311C2×C3×C8—51no—
312#217—21no—
313#217—102no—
314#217—102no—
315#217—101no—
316(C2×D3)⋊C4—102no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—52no—
319C4⋊Dic3C22×D512yes—
320Dic3⋊C4—102no—
321Dic3⋊C4—102no—
322C4×Dic3—21no—
323C4×Dic3—101no—
324C2×C3⋊C8—22no—
325C2×C3⋊C8C22×D512yes—
326D3×C8—104no—
327D3×C8—104no—
328C23×C5—21no—
329C23×C5D3×D411yescharacteristic
330C22×D5—21no—
331C22×D5—32no—
332C22×D5—64no—
333C22×D5—62no—
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×D411yescharacteristic
343C2×C4×C5#23712yes—
344C2×C4×C5C2×#6712yes—
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—42no—
347C22⋊D5—124no—
348C2×Dic5—21no—
349C2×Dic5—32no—
350C2×Dic5—62no—
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—62no—
362#168C2×#6712yes—
363#168C2×#6712yes—
364C2×#41—51no—
365C2×#41D3×D511yescharacteristic
366C23×C4—151no—
367#135—104no—
368C2×Q16—51no—
369C2×SD16—51no—
370C2×SD16—51no—
371C2×D8—51no—
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#117—151no—
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—24no—
400C3×D5—81no—
401C23×C3—21no—
402C23×C3—101no—
403C23×C3D4×D511yescharacteristic
404C22×D3—52no—
405C22×D3—104no—
406C22×D3—102no—
407C3×Q8—21no—
408C3×Q8—21no—
409C3×Q8—101no—
410C3×Q8—101no—
411C3×D4—21no—
412C3×D4—21no—
413C3×D4—42no—
414C3×D4—101no—
415C3×D4—101no—
416C3×D4—202no—
417C2×C3×C4—21no—
418C2×C3×C4—42no—
419C2×C3×C4—101no—
420C2×C3×C4—202no—
421C2×C3×C4#70912yes—
422C2×C3×C4D4×D512yes—
423C2×C3×C4D4×D511yescharacteristic
424C2×C3×C4C23×D511yescharacteristic
425#67—204no—
426#67—204no—
427C2×Dic3—22no—
428C2×Dic3—52no—
429C2×Dic3—102no—
430C2×Dic3—102no—
431C4×D3—102no—
432C4×D3—102no—
433C4×D3—104no—
434C3×C8—52no—
435C3×C8—52no—
436C3⋊C8—22no—
437C22×C5—22no—
438C22×C5—42no—
439C22×C5—41no—
440C22×C5#93812yes—
441C22×C5C2×D3×D411yescharacteristic
442C2×D5—34no—
443C2×D5—42no—
444C2×D5—41no—
445C2×D5—68no—
446C2×D5—62no—
447C2×D5—62no—
448C4×C5—41no—
449C4×C5—122no—
450C4×C5#93812yes—
451C4×C5C2×#23711yescharacteristic
452C4×C5C22×#6711yescharacteristic
453Dic5—41no—
454Dic5—62no—
455Dic5—122no—
456C24—151no—
457#41—22no—
458#41—22no—
459#41—102no—
460#41—102no—
461C2×Q8—51no—
462C2×Q8C2×D3×D511yescharacteristic
463C2×D4—21no—
464C2×D4—51no—
465C2×D4—101no—
466C2×D4—302no—
467C2×D4—302no—
468C2×D4C2×D3×D511yescharacteristic
469C22×C4—21no—
470C22×C4—101no—
471C22×C4—151no—
472C22×C4—152no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—102no—
478SD16—102no—
479SD16—102no—
480D8—102no—
481C2×C8—32no—
482C2×C8—54no—
483C2×C8—51no—
484C2×C8—51no—
485C2×C8—62no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—32no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—302no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—61no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3—201no—
505C22×C3—202no—
506C22×C3#403012yes—
507C22×C3C2×D4×D511yescharacteristic
508C2×D3—54no—
509C2×D3—108no—
510C2×D3—102no—
511C2×D3—102no—
512C3×C4—41no—
513C3×C4—201no—
514C3×C4#403012yes—
515C3×C4C2×#70911yescharacteristic
516C3×C4C2×D4×D511yescharacteristic
517Dic3—42no—
518Dic3—102no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—81no—
522C2×C5D3×#13512yes—
523C2×C5C2×#93811yescharacteristic
524D5—64no—
525D5—81no—
526C23—21no—
527C23—101no—
528C23—152no—
529C23—304no—
530C23—302no—
531C23#679011yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—101no—
535Q8—101no—
536D4—21no—
537D4—21no—
538D4—42no—
539D4—101no—
540D4—101no—
541D4—202no—
542D4—604no—
543D4—604no—
544C2×C4—21no—
545C2×C4—42no—
546C2×C4—62no—
547C2×C4—101no—
548C2×C4—152no—
549C2×C4—202no—
550C2×C4—302no—
551C2×C4—302no—
552C2×C4—304no—
553C2×C4—302no—
554C2×C4—302no—
555C2×C4#677912yes—
556C2×C4D5×#6712yes—
557C2×C4#679011yescharacteristic
558C2×C4C22×D3×D511yescharacteristic
559C8—52no—
560C8—52no—
561C8—62no—
562C2×C3—22no—
563C2×C3—81no—
564C2×C3—401no—
565C2×C3C2×#403011yescharacteristic
566C2×C3D5×#13512yes—
567D3—104no—
568C5#8391411yescharacteristic, complemented, Sylow
569C22—22no—
570C22—42no—
571C22—41no—
572C22—154no—
573C22—202no—
574C22—201no—
575C22—308no—
576C22—302no—
577C22—302no—
578C22#9153312yes—
579C22C2×#679011yescharacteristic
580C4—41no—
581C4—122no—
582C4—201no—
583C4—302no—
584C4—602no—
585C4#9153312yes—
586C4C2×#677911yescharacteristic
587C4C2×D5×#6711yescharacteristic
588C3#1061056911yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—304no—
592C2—401no—
593C2#1175532812yes—
594C2C2×#9153311yescharacteristic
subgroupG/H
centerC2×C4#6790
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. #11756587C2semidirect
2. C2×C3×#4096C2semidirect
3. #11754590C2semidirect
4. C22×#6648C2semidirect
5. C5×#5233C2semidirect
6. #11749299C2semidirect
7. #11749277C2semidirect
8. #11749053C2semidirect
9. #11749031C2semidirect
10. #11748458C2semidirect
11. #11748365C2semidirect
25. C2×C3×#689C22semidirect
26. C2×C3×#688C22semidirect
27. C2×C3×#687C22semidirect
28. C2×C3×#686C22semidirect
38. C5×#835C22semidirect
39. C5×#832C22semidirect
40. #90988C22semidirect
41. #90985C22semidirect
42. #90971C22semidirect
43. #90965C22semidirect
46. C2×#4096D3semidirect
92. C2×C3×#168D4semidirect
105. #5233D5semidirect
118. C2×#689C2×D3semidirect
119. C2×#688C2×D3semidirect
123. C2×#687C2×D3semidirect
124. C2×#686C2×D3semidirect
205. #835C2×D5semidirect
207. #832C2×D5semidirect
249. C2×#168#67semidirect
273. C2×D15#135semidirect
500. C3×C5#3050semidirect
568. C5#83914semidirect
588. C3#10610569semidirect

Maximal subgroups

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

subgroupindex
#117565872
C2×C3×#40962
#117545902
C22×#66482
C5×#52332
#117492992
#117492772
#117490532
#117490312
#117484582
#117483652
#106105693
#839145