Finite Group Databasebeta

← #14438691

Subgroups — #14438691

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754572C211yesmaximal, characteristic
2C2×#91388C211yesmaximal, characteristic, complemented
3#11751234C211yesmaximal, characteristic, complemented
4C5×#5133C211yesmaximal, characteristic, complemented
5C3×M16×Dic5C211yesmaximal, characteristic, complemented
6#11748394C211yesmaximal, characteristic, complemented
7#11748390C211yesmaximal, characteristic, complemented
8#11748025C212yesmaximal, complemented
9#11747998C212yesmaximal, complemented
10#11747985C212yesmaximal, complemented
11#11747963C212yesmaximal, complemented
12#10610610—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic5C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91566—21no—
21#91566—21no—
22C2×Dic3⋊Dic5—21no—
23C2×#6669—21no—
24#91451C2211yescharacteristic
25C4×#1203—21no—
26C4×#1203—21no—
27#91388—21no—
28#91388—21no—
29#91388C2212yes—
30#91388C2212yes—
31#91376C2211yescharacteristic
32#91375C2211yescharacteristic
33#91373C2211yescharacteristic
34#91105C2212yes—
35#91100C2212yes—
36C5×#821C2212yes—
37C5×#816C2212yes—
38C3×#3947C2212yes—
39C3×C8×Dic5C2212yes—
40#90975C2212yes—
41#90973C2212yes—
42#90969C2212yes—
43#90967C2212yes—
44#78529—51nomaximal, Hall
45#66166—31no—
46C2×#4036—31no—
47C5×#417—31no—
48#65521—31no—
49#65422—31no—
50M16×Dic5D311yescharacteristic, complemented
51#65255—31no—
52#65089—32no—
53#65086—32no—
54#65057—32no—
55#65053—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C22×C5×Dic3—21no—
66C5×#235—22no—
67C5×#235—22no—
68C2×C5×D12C2311yescharacteristic
69C2×C4×C5×D3—21no—
70C2×C5×Dic6C2311yescharacteristic
71C22×C3×Dic5D411yescharacteristic
72C22×C3×Dic5D411yescharacteristic
73C2×#1203—21no—
74C2×#1203—21no—
75C3×C5×M16—22no—
76C2×C3×C5×C8C2312yes—
77C4⋊Dic15—21no—
78C4⋊Dic15C2312yes—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C3×C4×Dic5D411yescharacteristic
82C3×C4×Dic5D411yescharacteristic
83C3×C4×Dic5C2311yescharacteristic
84C3×C4×Dic5C2311yescharacteristic
85C3×#681—22no—
86C2×C3×#168C2312yes—
87Dic3⋊Dic5—22no—
88Dic3⋊Dic5—22no—
89#6669—22no—
90#6669—22no—
91#6668—21no—
92#6668—21no—
93#6667—21no—
94#6667—21no—
95(C2×D3)⋊Dic5—21no—
96(C2×D3)⋊Dic5—21no—
97#5477—51no—
98C2×#870—51no—
99C3×C4×M16—51no—
100#5133—51no—
101#5133—51no—
102#5133—51no—
103#5133D511yescharacteristic, complemented
104#4713—52no—
105#4703—52no—
106#4697—52no—
107#4697—52no—
108C2×C5×#41—31no—
109C2×#709—31no—
110C2×C5×M16C2×D311yescharacteristic
111C2×C5×C4⋊C4—31no—
112#4093—31no—
113#4090—31no—
114#4086—31no—
115#4085—61no—
116#4085—61no—
117#4082—31no—
118C4×C22⋊D5—61no—
119C4×C22⋊D5—61no—
120C2×C4⋊Dic5—31no—
121C2×C4⋊Dic5—61no—
122C2×#683—61no—
123C2×C4×Dic5C2×D311yescharacteristic
124C2×#681C2×D311yescharacteristic
125#4036—32no—
126#4036—32no—
127#4036—61no—
128#4036—61no—
129C5×#103—32no—
130C5×#102—32no—
131#3967—32no—
132#3964—32no—
133#3953—32no—
134#3948—32no—
135#3947C2×D312yes—
136C8×Dic5C2×D312yes—
137#3942—32no—
138#3941—32no—
139#3142—151noSylow
140C23×C3×C5C2×D411yescharacteristic
141C22×D15—21no—
142C22×C5×D3—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—42no—
148C2×Dic15—21no—
149C2×Dic15—22no—
150C2×Dic15—42no—
151D60—21no—
152D60—21no—
153C4×D15—42no—
154Dic30—21no—
155Dic30—21no—
156C5×#67—42no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—42no—
160C5×D12—21no—
161C5×D12—21no—
162C4×C5×D3—42no—
163C5×Dic6—21no—
164C5×Dic6—21no—
165C2×C3×Dic5—41no—
166C2×C3×Dic5—41no—
167C2×C3×Dic5C2×D411yescharacteristic
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2×D411yescharacteristic
171#1203—42no—
172#1203—42no—
173C3×C5×C8—22no—
174C3×#168—22no—
175C2×#235—51no—
176C2×#235C2×D511yescharacteristic
177C2×C3×M16—51no—
178C2×C3×M16C2×D511yescharacteristic
179C2×C3×C42—51no—
180#930—101no—
181#930—101no—
182C2×C4⋊Dic3—51no—
183C2×C4⋊Dic3C2×D511yescharacteristic
184C2×Dic3⋊C4—101no—
185C2×Dic3⋊C4—101no—
186#875—51no—
187#875—51no—
188#874—51no—
189C4×D12—101no—
190C4×D12—101no—
191#870—52no—
192#870—52no—
193#870—101no—
194#870—101no—
195#869—51no—
196C3×#97—52no—
197C3×C4×C8—52no—
198#821—52no—
199#821—52no—
200#821—52no—
201#821C2×D512yes—
202#816—52no—
203#816—52no—
204#816—52no—
205#816C2×D512yes—
206C5×#41—62no—
207C5×#41—62no—
208C2×C5×Q8—31no—
209C2×C5×D4—31no—
210C2×C5×D4—61no—
211C22×C4×C5—61no—
212C22×C4×C5—61no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—61no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—61no—
217C22×Dic5—61no—
218C22×Dic5D1211yescharacteristic
219C22×Dic5D1211yescharacteristic
220#709—62no—
221#709—62no—
222C2×D20—31no—
223C2×C4×D5—61no—
224C2×Dic10—31no—
225C5×M16—22no—
226C2×C5×C8C22×D312yes—
227C5×C4⋊C4—32no—
228C5×C4⋊C4—61no—
229C22⋊Dic5—61no—
230C22⋊Dic5—61no—
231#685—61no—
232#685—61no—
233C4⋊Dic5—32no—
234C4⋊Dic5—61no—
235C4⋊Dic5—62no—
236C4⋊Dic5—62no—
237#683—61no—
238#683—61no—
239#683—62no—
240#683—62no—
241C4×Dic5D1211yescharacteristic
242C4×Dic5D1211yescharacteristic
243C4×Dic5C22×D311yescharacteristic
244C4×Dic5C22×D311yescharacteristic
245#681—22no—
246C2×#168C22×D312yes—
247#532—151no—
248C2×#125—151no—
249#491—152no—
250#490—152no—
251#488—152no—
252#488—152no—
253#417—31no—
254#417—151no—
255#417—151no—
256#417—151no—
257C4×M16—51no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12412yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×D15—41no—
263C2×D15—41no—
264C2×D15—41no—
265C2×C5×D3—41no—
266C2×C5×D3—41no—
267C2×C5×D3—41no—
268C3×C4×C5#12412yes—
269C3×C4×C5C2×#4111yescharacteristic
270C3×C4×C5C2×#4111yescharacteristic
271Dic15—41no—
272Dic15—42no—
273C3×Dic5—21no—
274C3×Dic5—21no—
275C3×Dic5—21no—
276C3×Dic5—21no—
277C5×Dic3—41no—
278C5×Dic3—42no—
279C22×C3×C4—51no—
280C22×C3×C4—51no—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—21no—
283C2×#67—101no—
284C22×Dic3—21no—
285C22×Dic3—101no—
286#235—22no—
287#235—22no—
288#235—102no—
289#235—102no—
290C2×D12—51no—
291C2×D12—101no—
292C2×D12—101no—
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—101no—
296C2×Dic6—51no—
297C2×Dic6C22×D511yescharacteristic
298C3×M16—22no—
299C3×M16—102no—
300C2×C3×C8—52no—
301C2×C3×C8C22×D512yes—
302C3×C42—51no—
303C3×C42—51no—
304C3×C42—51no—
305C3×C42—51no—
306(C2×D3)⋊C4—101no—
307(C2×D3)⋊C4—101no—
308(C2×D3)⋊C4—101no—
309(C2×D3)⋊C4—101no—
310C4⋊Dic3—21no—
311C4⋊Dic3—52no—
312C4⋊Dic3—101no—
313C4⋊Dic3—101no—
314C4⋊Dic3—101no—
315C4⋊Dic3C22×D512yes—
316Dic3⋊C4—102no—
317Dic3⋊C4—102no—
318Dic3⋊C4—102no—
319Dic3⋊C4—102no—
320C23×C5—61no—
321C23×C5C2×D1211yescharacteristic
322C22×D5—61no—
323C5×Q8—61no—
324C5×Q8—61no—
325C5×D4—61no—
326C5×D4—61no—
327C5×D4—122no—
328C2×C4×C5—62no—
329C2×C4×C5—61no—
330C2×C4×C5—122no—
331C2×C4×C5—122no—
332C2×C4×C5C2×D1211yescharacteristic
333C2×C4×C5#23512yes—
334C2×C4×C5#23512yes—
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—122no—
337C22⋊D5—122no—
338C22⋊D5—122no—
339C2×Dic5—41no—
340C2×Dic5—41no—
341C2×Dic5—62no—
342C2×Dic5—61no—
343C2×Dic5—122no—
344C2×Dic5C2×D1211yescharacteristic
345C2×Dic5C2×D1211yescharacteristic
346C2×Dic5C2×D1211yescharacteristic
347C2×Dic5C2×D1211yescharacteristic
348D20—61no—
349D20—61no—
350C4×D5—122no—
351Dic10—61no—
352Dic10—61no—
353C5×C8—22no—
354#168—22no—
355C2×#41—31no—
356C2×#41—151no—
357C2×M16—51no—
358C2×M16D3×D511yescharacteristic
359C4⋊Q8—151no—
360#127—151no—
361#125—152no—
362#125—152no—
363#125—301no—
364#125—301no—
365#124—151no—
366#124—151no—
367#121—301no—
368#121—301no—
369C4×D4—301no—
370C4×D4—301no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—151no—
373C2×C4⋊C4—301no—
374C2×C4⋊C4—301no—
375C2×C42—51no—
376#103—32no—
377#103—152no—
378#103—152no—
379#103—152no—
380#102—32no—
381#102—152no—
382#102—152no—
383#102—152no—
384#97—52no—
385C4×C8—52no—
386C2×C3×C5—22no—
387C2×C3×C5C2×#12411yescharacteristic
388C2×C3×C5#57511yescharacteristic
389C2×C3×C5#57511yescharacteristic
390D15—81no—
391C5×D3—81no—
392C23×C3D4×D511yescharacteristic
393C22×D3—21no—
394C22×D3—101no—
395C2×C3×C4—51no—
396C2×C3×C4—51no—
397C2×C3×C4—51no—
398C2×C3×C4—51no—
399C2×C3×C4—201no—
400C2×C3×C4—201no—
401C2×C3×C4#70912yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4#71112yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—42no—
406#67—202no—
407C2×Dic3—22no—
408C2×Dic3—21no—
409C2×Dic3—42no—
410C2×Dic3—102no—
411C2×Dic3—101no—
412C2×Dic3—202no—
413D12—21no—
414D12—21no—
415D12—101no—
416D12—101no—
417D12—202no—
418D12—202no—
419C4×D3—42no—
420C4×D3—202no—
421Dic6—21no—
422Dic6—21no—
423Dic6—101no—
424Dic6—101no—
425C3×C8—22no—
426C3×C8—102no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—121no—
430C22×C5—121no—
431C22×C5—121no—
432C22×C5#87512yes—
433C22×C5C22×D1211yescharacteristic
434C2×D5—121no—
435C2×D5—121no—
436C2×D5—121no—
437C4×C5—121no—
438C4×C5—122no—
439C4×C5#87512yes—
440C4×C5C2×#23511yescharacteristic
441C4×C5C2×#23511yescharacteristic
442Dic5—21no—
443Dic5—21no—
444Dic5—21no—
445Dic5—21no—
446Dic5—121no—
447Dic5—122no—
448#41—62no—
449#41—62no—
450#41—302no—
451#41—302no—
452C2×Q8—31no—
453C2×Q8—151no—
454C2×D4—31no—
455C2×D4—61no—
456C2×D4—151no—
457C2×D4—301no—
458C2×D4—301no—
459C2×D4—301no—
460C22×C4—51no—
461C22×C4—51no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—301no—
465C22×C4—301no—
466C22×C4C2×D3×D511yescharacteristic
467M16—22no—
468M16—102no—
469C2×C8—52no—
470C2×C8C2×D3×D512yes—
471C4⋊C4—32no—
472C4⋊C4—61no—
473C4⋊C4—152no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—302no—
477C4⋊C4—302no—
478C4⋊C4—301no—
479C4⋊C4—301no—
480C4⋊C4—301no—
481C22⋊C4—301no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C42—51no—
486C42—51no—
487C42—51no—
488C42—51no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3#403112yes—
493C22×C3C2×D4×D511yescharacteristic
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—201no—
498C2×D3—201no—
499C2×D3—201no—
500C3×C4—101no—
501C3×C4—101no—
502C3×C4—101no—
503C3×C4—101no—
504C3×C4#403112yes—
505C3×C4C2×#70911yescharacteristic
506C3×C4C2×#71111yescharacteristic
507Dic3—41no—
508Dic3—42no—
509Dic3—201no—
510Dic3—202no—
511C2×C5—22no—
512C2×C5—241no—
513C2×C5C2×#87511yescharacteristic
514C2×C5#574811yescharacteristic
515C2×C5#574811yescharacteristic
516D5—241no—
517C23—61no—
518C23—301no—
519C23D5×D1211yescharacteristic
520Q8—61no—
521Q8—61no—
522Q8—301no—
523Q8—301no—
524D4—61no—
525D4—61no—
526D4—122no—
527D4—301no—
528D4—301no—
529D4—602no—
530D4—602no—
531D4—602no—
532C2×C4—51no—
533C2×C4—51no—
534C2×C4—51no—
535C2×C4—51no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—122no—
539C2×C4—122no—
540C2×C4—201no—
541C2×C4—201no—
542C2×C4—301no—
543C2×C4—302no—
544C2×C4—602no—
545C2×C4—602no—
546C2×C4#677112yes—
547C2×C4D5×D1211yescharacteristic
548C2×C4#678212yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—22no—
551C8—102no—
552C2×C3—22no—
553C2×C3C2×#403111yescharacteristic
554C2×C3#6610711yescharacteristic
555C2×C3#6611111yescharacteristic
556D3—81no—
557D3—401no—
558C5#7852911yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—601no—
565C22—601no—
566C22—601no—
567C22#9135012yes—
568C22C2×D5×D1211yescharacteristic
569C4—101no—
570C4—101no—
571C4—101no—
572C4—101no—
573C4—122no—
574C4—121no—
575C4—602no—
576C4—601no—
577C4#9135012yes—
578C4C2×#677111yescharacteristic
579C4C2×#678211yescharacteristic
580C3#1061061011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—241no—
583C2—1201no—
584C2#1175402111yescharacteristic
585C2#1175402211yescharacteristic
586C2C2×#9135011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radical#11754572C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91388C2semidirect
3. #11751234C2semidirect
4. C5×#5133C2semidirect
5. C3×M16×Dic5C2semidirect
6. #11748394C2semidirect
7. #11748390C2semidirect
8. #11748025C2semidirect
9. #11747998C2semidirect
10. #11747985C2semidirect
11. #11747963C2semidirect
50. M16×Dic5D3semidirect
103. #5133D5semidirect
489. C3×C5#3142semidirect
558. C5#78529semidirect
580. C3#10610610semidirect

Maximal subgroups

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

subgroupindex
#117545722
C2×#913882
#117512342
C5×#51332
C3×M16×Dic52
#117483942
#117483902
#117480252
#117479982
#117479852
#117479632
#106106103
#785295