Finite Group Databasebeta

← #14427860

Subgroups — #14427860

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×C5×D3×C8C211yesmaximal, characteristic, complemented
2#11754584C211yesmaximal, characteristic, complemented
3#11754577C211yesmaximal, characteristic, complemented
4C2×#91311C211yesmaximal, characteristic, complemented
5#11751214C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748451C211yesmaximal, characteristic, complemented
8#11747947C212yesmaximal, complemented
9#11747946C212yesmaximal, complemented
10#11747909C212yesmaximal, complemented
11#11747908C212yesmaximal, complemented
12#10615473—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17#91815C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C2×C5×D3×C8—24no—
20C2×C5×D3×C8C2212yes—
21C2×C5×D3×C8C2212yes—
22C3×#4072C2211yescharacteristic
23#91570—21no—
24#91568—21no—
25#91542—21no—
26#91536—21no—
27#91460C2212yes—
28#91456C2212yes—
29C4×#1203—22no—
30C4×#1201—22no—
31#91369C2212yes—
32#91365C2212yes—
33C2×#6662C2211yescharacteristic, complemented
34C2×#6658C2211yescharacteristic, complemented
35#91311—24no—
36C2×#6657C2211yescharacteristic, complemented
37C2×#6653C2211yescharacteristic, complemented
38#91105C2212yescomplemented
39#91100C2212yescomplemented
40C3×#3953C2212yescomplemented
41C3×#3948C2212yescomplemented
42#90990C2212yescomplemented
43#90987C2212yescomplemented
44#78838—51nomaximal, Hall
45C23×C5×C8—31no—
46#66125—31no—
47#66125—31no—
48C2×#4050—31no—
49#65405—32no—
50#65404—32no—
51#65403—32no—
52#65403—32no—
53#65402—31no—
54#65402D311yescharacteristic, complemented
55#65395—31no—
56C23×C5×D3D411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C5×Dic3D411yescharacteristic
65C2×C4×C5×D3—22no—
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3D412yes—
68C2×C4×C5×D3C2312yes—
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×#1201—22no—
77C2×C3×C5×C8—22no—
78C2×C3×C5×C8C2312yes—
79#6719—21no—
80C4⋊Dic15C2312yes—
81C4×Dic15—21no—
82C2×C5×C3⋊C8D414yescomplemented
83C2×C5×C3⋊C8C2311yescharacteristic
84C2×C5×C3⋊C8C2311yescharacteristic
85C5×D3×C8—24no—
86C5×D3×C8—24no—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90#6669—22no—
91#6668—22no—
92#6667—22no—
93(C2×D3)⋊Dic5—22no—
94(C2×D3)⋊Dic5—22no—
95#6665—22no—
96#6662—22no—
97#6658—22no—
98#6657—22no—
99#6653—22no—
100#5828—51no—
101C2×#950—51no—
102C22×D3×C8D511yescharacteristic, complemented
103#5524—51no—
104C3×#416—51no—
105#5113—51no—
106#4998—51no—
107#4813—52no—
108#4807—52no—
109#4778—52no—
110#4775—52no—
111C23×C4×C5—31no—
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×C5×C8—31no—
115C22×C5×C8—32no—
116C22×C5×C8—32no—
117C22×C5×C8—64no—
118C22×C5×C8C2×D311yescharacteristic
119#4099—61no—
120#4099—61no—
121#4076—32no—
122#4076—32no—
123#4075—61no—
124#4075—61no—
125C4×C22⋊D5—62no—
126C4×C22⋊D5—62no—
127#4072—31no—
128#4072C2×D311yescharacteristic
129#4070—32no—
130#4070—32no—
131C2×Dic20—31no—
132#4050—64no—
133C2×D40—31no—
134C2×#677—31no—
135C2×#677—31no—
136#3953—32no—
137#3953C2×D312yescomplemented
138#3950—32no—
139#3949—32no—
140#3948—32no—
141#3948C2×D312yescomplemented
142#3050—151noSylow
143C23×C3×C5C2×D411yescharacteristic
144C22×D15—21no—
145C22×C5×D3—22no—
146C22×C5×D3—24no—
147C22×C5×D3C2×D412yes—
148C22×C3×D5—21no—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5C2411yescharacteristic
153#1220—42no—
154C2×Dic15—22no—
155C2×Dic15—21no—
156D60—21no—
157D60—21no—
158C4×D15—42no—
159Dic30—21no—
160Dic30—21no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3C2×D412yes—
163C4×C5×D3—24no—
164C4×C5×D3—22no—
165C4×C5×D3—22no—
166C3×C22⋊D5—42no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—22no—
169C3×D20—21no—
170C3×D20—21no—
171C3×C4×D5—42no—
172C3×Dic10—21no—
173C3×Dic10—21no—
174#1203—44no—
175#1201—44no—
176C3×C5×C8—22no—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41—51no—
180C2×#235—51no—
181C22×C4×D3C2×D511yescharacteristic
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#926—51no—
195C22×C3⋊C8C2×D511yescharacteristic
196C2×D3×C8—24no—
197C2×D3×C8C2×D512yes—
198C2×D3×C8C2×D512yes—
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—
211C22×C4×C5—31no—
212C22×C4×C5—32no—
213C22×C4×C5—32no—
214C22×C4×C5—62no—
215C22×C4×C5—62no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—21no—
218C2×C22⋊D5—62no—
219C2×C22⋊D5—62no—
220C2×C22⋊D5—61no—
221#709—22no—
222#709—22no—
223#709—62no—
224#709—62no—
225C2×D20—31no—
226C2×D20C22×D311yescharacteristic
227C2×C4×D5—21no—
228C2×C4×D5—61no—
229C2×Dic10—31no—
230C2×Dic10C22×D311yescharacteristic
231C2×C5×C8—22no—
232C2×C5×C8—34no—
233C2×C5×C8—31no—
234C2×C5×C8—31no—
235C2×C5×C8—64no—
236C2×C5×C8—64no—
237C2×C5×C8C22×D312yes—
238C22⋊Dic5—21no—
239C22⋊Dic5—62no—
240C22⋊Dic5—62no—
241C22⋊Dic5—61no—
242#685—62no—
243#685—62no—
244C4⋊Dic5—32no—
245C4⋊Dic5C22×D312yes—
246#683—62no—
247#683—62no—
248C4×Dic5—21no—
249C4×Dic5—61no—
250Dic20—62no—
251D40—62no—
252#677—62no—
253#677—62no—
254C2×#135—151no—
255C23×C8—31no—
256#525—151no—
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#12112yes—
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—41no—
269C2×D15—42no—
270C2×C5×D3—28no—
271C2×C5×D3—22no—
272C2×C5×D3—22no—
273C2×C5×D3#13514yescomplemented
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5#12112yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C2×#4111yescharacteristic
279Dic15—41no—
280Dic15—42no—
281C3×Dic5—41no—
282C3×Dic5—42no—
283C5×Dic3—22no—
284C23×D3D2011yescharacteristic
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—101no—
293C2×#67—102no—
294C22×Dic3D2011yescharacteristic
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×D3D2012yes—
303C2×C4×D3C22×D512yes—
304C2×Dic6—51no—
305C2×C3×C8—22no—
306C2×C3×C8C22×D512yes—
307C3×C4⋊C4—52no—
308C3×C22⋊C4—101no—
309C3×C42—101no—
310#217—101no—
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—52no—
320C4⋊Dic3—102no—
321Dic3⋊C4—102no—
322C4×Dic3—101no—
323C2×C3⋊C8C22⋊D514yescomplemented
324C2×C3⋊C8C22×D511yescharacteristic
325C2×C3⋊C8C22×D511yescharacteristic
326D3×C8—24no—
327D3×C8—24no—
328C23×C5—32no—
329C23×C5—64no—
330C23×C5—62no—
331C23×C5D3×D411yescharacteristic
332C22×D5—21no—
333C22×D5—61no—
334C2×C4×C5—32no—
335C2×C4×C5—62no—
336C2×C4×C5—64no—
337C2×C4×C5—62no—
338C2×C4×C5—62no—
339C2×C4×C5#23512yes—
340C2×C4×C5D3×D411yescharacteristic
341C2×C4×C5D3×D412yes—
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—42no—
344C22⋊D5—124no—
345C22⋊D5—124no—
346C22⋊D5—122no—
347C2×Dic5—22no—
348C2×Dic5—21no—
349C2×Dic5—62no—
350C2×Dic5—61no—
351D20—21no—
352D20—21no—
353D20—61no—
354D20—61no—
355C4×D5—42no—
356C4×D5—122no—
357Dic10—21no—
358Dic10—21no—
359Dic10—61no—
360Dic10—61no—
361C5×C8—22no—
362C5×C8—32no—
363C5×C8—32no—
364C2×#41—51no—
365C2×#41—151no—
366C23×C4—31no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—31no—
373C22×C8—32no—
374C22×C8—32no—
375C22×C8—64no—
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—51no—
388#117—151no—
389#107—152no—
390#106—152no—
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—81no—
399C3×D5—81no—
400C5×D3—24no—
401C23×C3—101no—
402C23×C3C2×D2011yescharacteristic
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—101no—
406C22×D3C2×D2012yes—
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×C4C2×D2011yescharacteristic
416C2×C3×C4#70912yes—
417C2×C3×C4C2×C22⋊D512yes—
418C2×C3×C4C23×D511yescharacteristic
419#67—202no—
420#67—204no—
421C2×Dic3—22no—
422C2×Dic3—102no—
423C2×Dic3—101no—
424C2×Dic3C2×D2012yes—
425D12—101no—
426D12—101no—
427D12—204no—
428C4×D3—22no—
429C4×D3—22no—
430C4×D3—24no—
431C4×D3—202no—
432Dic6—101no—
433Dic6—101no—
434C3×C8—22no—
435C3⋊C8C2×C22⋊D512yes—
436C3⋊C8C2×C22⋊D512yes—
437C22×C5—22no—
438C22×C5—34no—
439C22×C5—68no—
440C22×C5—62no—
441C22×C5—62no—
442C22×C5#88412yes—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—41no—
445C2×D5—42no—
446C2×D5—121no—
447C2×D5—122no—
448C4×C5—62no—
449C4×C5#88412yes—
450C4×C5C2×#23511yescharacteristic
451C4×C5C2×D3×D411yescharacteristic
452Dic5—41no—
453Dic5—42no—
454Dic5—121no—
455Dic5—122no—
456C24—31no—
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—31no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—101no—
475C22×C4—301no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—22no—
482C2×C8—34no—
483C2×C8—31no—
484C2×C8—31no—
485C2×C8—64no—
486C2×C8—64no—
487C2×C8C2×D3×D512yes—
488C4⋊C4—52no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4—302no—
492C22⋊C4—101no—
493C22⋊C4—302no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—101no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—202no—
503C22×C3—201no—
504C22×C3#407612yes—
505C22×C3C22×D2011yescharacteristic
506C2×D3—28no—
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—202no—
510C2×D3—201no—
511C2×D3#405014yescomplemented
512C3×C4—202no—
513C3×C4—201no—
514C3×C4#407612yes—
515C3×C4C2×#70911yescharacteristic
516C3×C4C22×C22⋊D511yescharacteristic
517Dic3—22no—
518Dic3—202no—
519Dic3—201no—
520C2×C5—22no—
521C2×C5—64no—
522C2×C5C2×#88411yescharacteristic
523C2×C5D3×#13512yes—
524D5—81no—
525D5—241no—
526C23—32no—
527C23—64no—
528C23—62no—
529C23—101no—
530C23—301no—
531C23D3×D2011yescharacteristic
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—32no—
545C2×C4—62no—
546C2×C4—64no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—102no—
550C2×C4—101no—
551C2×C4—202no—
552C2×C4—302no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4#677112yes—
556C2×C4D3×D2011yescharacteristic
557C2×C4D3×C22⋊D512yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—22no—
560C8—32no—
561C8—32no—
562C2×C3—22no—
563C2×C3—401no—
564C2×C3C2×#405012yes—
565C2×C3C2×#407611yescharacteristic
566D3—24no—
567D3—401no—
568C5#7883811yescharacteristic, complemented, Sylow
569C22—22no—
570C22—34no—
571C22—68no—
572C22—62no—
573C22—62no—
574C22—201no—
575C22—202no—
576C22—601no—
577C22—602no—
578C22#9145412yes—
579C22C2×D3×D2011yescharacteristic
580C4—62no—
581C4—201no—
582C4—202no—
583C4—601no—
584C4—602no—
585C4#9145412yes—
586C4C2×#677111yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061547311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—64no—
591C2—401no—
592C2—1201no—
593C2D3×#405012yes—
594C2C2×#9145411yescharacteristic
subgroupG/H
centerC2×C4D3×D20
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×C5×D3×C8C2semidirect
2. #11754584C2semidirect
3. #11754577C2semidirect
4. C2×#91311C2semidirect
5. #11751214C2semidirect
6. C3×#65402C2semidirect
7. #11748451C2semidirect
8. #11747947C2semidirect
9. #11747946C2semidirect
10. #11747909C2semidirect
11. #11747908C2semidirect
33. C2×#6662C22semidirect
34. C2×#6658C22semidirect
36. C2×#6657C22semidirect
37. C2×#6653C22semidirect
38. #91105C22semidirect
39. #91100C22semidirect
40. C3×#3953C22semidirect
41. C3×#3948C22semidirect
42. #90990C22semidirect
43. #90987C22semidirect
54. #65402D3semidirect
82. C2×C5×C3⋊C8D4semidirect
102. C22×D3×C8D5semidirect
137. #3953C2×D3semidirect
141. #3948C2×D3semidirect
273. C2×C5×D3#135semidirect
323. C2×C3⋊C8C22⋊D5semidirect
500. C3×C5#3050semidirect
511. C2×D3#4050semidirect
568. C5#78838semidirect
588. C3#10615473semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×C82
#117545842
#117545772
C2×#913112
#117512142
C3×#654022
#117484512
#117479472
#117479462
#117479092
#117479082
#106154733
#788385