Finite Group Databasebeta

← #14426247

Subgroups — #14426247

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91275C212yesmaximal, complemented
2#11752550C211yesmaximal, characteristic, complemented
3C4×#6769C211yesmaximal, characteristic, complemented
4#11750944C211yesmaximal, characteristic, complemented
5C5×D3×C4⋊C8C211yesmaximal, characteristic, complemented
6C3×#65138C211yesmaximal, characteristic, complemented
7#11747841C212yesmaximal, complemented
8#11747798C212yesmaximal, complemented
9#11747643C212yesmaximal, complemented
10#11747085C211yesmaximal, characteristic, complemented
11#11747064C211yesmaximal, characteristic, complemented
12#10610752—31nomaximal, Hall
13C2×#6769C2212yes—
14C2×#6769C2211yescharacteristic
15C2×D120C2212yes—
16#91763C2211yescharacteristic
17C4×D60C2211yescharacteristic
18C2×C5×D3×C8C2212yes—
19C42×C5×D3C2211yescharacteristic
20C2×C3×Dic20C2212yes—
21C3×#4015C2211yescharacteristic
22C3×C4×Dic10C2211yescharacteristic
23#91460—21no—
24#91460—21no—
25#91446—21no—
26C4×#1203—21no—
27#91428—21no—
28#91428—21no—
29#91428C2211yescharacteristic
30#91403—21no—
31C4×#1200—21no—
32#91374C2212yes—
33#91338C2211yescharacteristic
34Dic3×Dic10C2211yescharacteristic
35C2×#6658C2212yes—
36C2×#6658C2212yes—
37#91275—28no—
38C3×C5×C4⋊C8C2211yescharacteristic
39#91105C2212yes—
40C5×Dic3⋊C8C2212yes—
41C5×C4⋊(C3⋊C8)C2211yescharacteristic
42C3×#3948C2212yes—
43#90971C2212yes—
44#90968C2212yes—
45#80475—51nomaximal, Hall
46C2×#4050—32no—
47#65811—31no—
48C4×#709—31no—
49C2×C5×C4⋊C8—31no—
50#65402—32no—
51#65138D311yescharacteristic, complemented
52#65137—31no—
53#65134—32no—
54#65133—32no—
55#65132—31no—
56#65130—31no—
57C2×D60—21no—
58C2×D60—21no—
59C2×D60C2312yes—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×C5×D3D411yescharacteristic
63C2×C4×C5×D3D411yescharacteristic
64C2×C4×C5×D3C2311yescharacteristic
65C2×C3×Dic10C2312yes—
66C2×C3×Dic10C2311yescharacteristic
67C2×#1203—21no—
68C2×#1203—22no—
69C2×#1200—21no—
70C2×#1200—21no—
71C2×#1200—22no—
72#6769—22no—
73#6769—24no—
74#6769—24no—
75#6769D414yescomplemented
76C2×C3×C5×C8C2312yes—
77C3×C42×C5C2311yescharacteristic
78#6714—21no—
79C4⋊Dic15C2311yescharacteristic
80D120—24no—
81C4×C5×Dic3D411yescharacteristic
82C4×C5×Dic3D411yescharacteristic
83C4×C5×Dic3C2311yescharacteristic
84C2×C5×C3⋊C8C2312yes—
85C5×D3×C8—24no—
86C3×C4⋊Dic5—21no—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2311yescharacteristic
89C3×#683—21no—
90C3×C4×Dic5—21no—
91C3×Dic20—24no—
92#6668—21no—
93#6667—21no—
94#6667—22no—
95#6667—22no—
96(C2×D3)⋊Dic5—21no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6658—24no—
100#6658—24no—
101C2×#919—52no—
102#5725—51no—
103C4×#239—51no—
104C3×#462—51no—
105#5185—52no—
106#5083—51no—
107#5027—51no—
108#4843—51no—
109D3×C4⋊C8D511yescharacteristic, complemented
110#4819—52no—
111#4804—52no—
112C2×#709—31no—
113C2×#709—32no—
114C22×C5×C8—32no—
115C2×C42×C5—31no—
116#4076—61no—
117#4076—61no—
118C4×C22⋊D5—61no—
119C4×C22⋊D5—61no—
120#4072—31no—
121C2×Dic20C2×D312yes—
122#4050—68no—
123C2×D40—32no—
124C2×#677—32no—
125C2×#677—32no—
126#4021—32no—
127#4020—31no—
128C4×D20—31no—
129C4×D20—31no—
130C4×D20—61no—
131C4×D20—61no—
132#4018—61no—
133C42×D5—61no—
134#4015C2×D311yescharacteristic
135C4×Dic10—31no—
136C4×Dic10C2×D311yescharacteristic
137C5×C4⋊C8—32no—
138C5×C4⋊C8—31no—
139C5×C4⋊C8C2×D311yescharacteristic
140#3953—32no—
141#3953—32no—
142#3948—32no—
143#3948C2×D312yes—
144#3035—151noSylow
145C22×D15—21no—
146C22×D15—22no—
147C22×C5×D3C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—21no—
152D60—22no—
153D60—21no—
154D60—22no—
155D60—42no—
156D60—42no—
157D60C2×D412yes—
158C4×D15—42no—
159C2×C5×Dic3C2×D411yescharacteristic
160C2×C5×Dic3C2×D411yescharacteristic
161C2×C5×Dic3C2×D411yescharacteristic
162C4×C5×D3—22no—
163C4×C5×D3—41no—
164C4×C5×D3C2×D412yes—
165C4×C5×D3#4112yes—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—22no—
169C3×Dic10—21no—
170C3×Dic10—22no—
171C3×Dic10—22no—
172C3×Dic10C2×D412yes—
173#1203—24no—
174#1203—44no—
175#1200—24no—
176#1200—42no—
177#1200—44no—
178C3×C5×C8—22no—
179C5×C3⋊C8—22no—
180C2×#239—51no—
181C2×#239—52no—
182C2×C3×Q16—52no—
183C3×C4⋊Q8—51no—
184C3×C4×Q8—51no—
185#947—52no—
186Q8×Dic3—51no—
187C2×#215—52no—
188C2×#215—52no—
189#919—108no—
190C2×D24—52no—
191C2×D3×C8C2×D512yes—
192#895—101no—
193#895—101no—
194#893—51no—
195#893—101no—
196#893—101no—
197#893—101no—
198#892—51no—
199#892—101no—
200#874—51no—
201C4×D12—51no—
202C4×D12—101no—
203C42×D3—101no—
204C42×D3C2×D511yescharacteristic
205C3×C4⋊C8C2×D511yescharacteristic
206C3×#103—52no—
207#835—52no—
208#821—52no—
209Dic3⋊C8C2×D512yes—
210#809—52no—
211C4⋊(C3⋊C8)C2×D511yescharacteristic
212C22×C4×C5—31no—
213C22×C4×C5—31no—
214C22×C4×C5—31no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—62no—
217#709—34no—
218#709—62no—
219#709—64no—
220#709—64no—
221C2×D20—31no—
222C2×D20—32no—
223C2×D20—61no—
224C2×D20—61no—
225C2×C4×D5—61no—
226C2×C4×D5—62no—
227C2×C4×D5—61no—
228C2×C4×D5—61no—
229C2×Dic10C22×D312yes—
230C2×Dic10C22×D311yescharacteristic
231C2×C5×C8—32no—
232C2×C5×C8—64no—
233C2×C5×C8C22×D312yes—
234C42×C5—31no—
235C42×C5—31no—
236C42×C5—31no—
237C42×C5C22×D311yescharacteristic
238C22⋊Dic5—61no—
239#685—61no—
240#685—62no—
241#685—62no—
242#685—61no—
243C4⋊Dic5—21no—
244C4⋊Dic5—21no—
245C4⋊Dic5—31no—
246C4⋊Dic5C22×D311yescharacteristic
247#683—21no—
248#683—61no—
249C4×Dic5—21no—
250C4×Dic5—61no—
251C4×Dic5—61no—
252Dic20—24no—
253D40—64no—
254#677—64no—
255#677—64no—
256C2×#135—152no—
257#532—151no—
258C4×#41—151no—
259#464—152no—
260#463—152no—
261#462—51no—
262#461—151no—
263#460—151no—
264#459—151no—
265C2×C4⋊C8—31no—
266#416—152no—
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—22no—
269C2×D15—41no—
270C2×D15—41no—
271C2×D15—42no—
272C2×D15—42no—
273C2×D15—42no—
274C2×C5×D3—21no—
275C2×C5×D3—21no—
276C2×C5×D3#12112yes—
277C3×C4×C5—21no—
278C3×C4×C5#13512yescomplemented
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C2×#4111yescharacteristic
281Dic15—41no—
282C3×Dic5—22no—
283C3×Dic5—42no—
284C3×Dic5—41no—
285C5×Dic3—21no—
286C5×Dic3—21no—
287C5×Dic3#12112yes—
288C2×C3×Q8—51no—
289C2×C3×Q8—52no—
290#239—54no—
291#239—102no—
292#239—104no—
293#239—104no—
294C2×D12—51no—
295C2×D12—52no—
296C2×D12—101no—
297C2×D12—102no—
298C2×D12—101no—
299C2×D12—101no—
300C2×C4×D3—101no—
301C2×C4×D3—101no—
302C2×C4×D3—101no—
303C2×C4×D3—102no—
304C2×C4×D3D2011yescharacteristic
305C2×C4×D3D2011yescharacteristic
306C2×C4×D3C22×D511yescharacteristic
307C3×Q16—104no—
308C2×C3×C8C22×D512yes—
309C3×C4⋊C4—51no—
310C3×C4⋊C4—101no—
311C3×C4⋊C4—101no—
312C3×C4⋊C4—101no—
313C3×C42—101no—
314C3×C42C22×D511yescharacteristic
315#215—104no—
316#215—104no—
317(C2×D3)⋊C4—101no—
318(C2×D3)⋊C4—101no—
319(C2×D3)⋊C4—101no—
320(C2×D3)⋊C4—102no—
321(C2×D3)⋊C4—102no—
322C4⋊Dic3—51no—
323C4⋊Dic3—101no—
324C4×Dic3—101no—
325C4×Dic3—101no—
326C4×Dic3D2011yescharacteristic
327C4×Dic3D2011yescharacteristic
328C4×Dic3C22×D511yescharacteristic
329C2×C3⋊C8C22×D512yes—
330D24—104no—
331D3×C8—24no—
332C23×C5—31no—
333C22×D5—61no—
334C22×D5—62no—
335C2×C4×C5—31no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—31no—
339C2×C4×C5—31no—
340C2×C4×C5—62no—
341C2×C4×C5—121no—
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5D3×D411yescharacteristic
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—64no—
346C22⋊D5—124no—
347C2×Dic5—21no—
348C2×Dic5—21no—
349C2×Dic5—22no—
350C2×Dic5—61no—
351D20—32no—
352D20—62no—
353D20—61no—
354D20—62no—
355D20—122no—
356D20—122no—
357C4×D5—64no—
358C4×D5—124no—
359C4×D5—122no—
360C4×D5—122no—
361Dic10—21no—
362Dic10—22no—
363Dic10—22no—
364Dic10D3×D412yes—
365C5×C8—22no—
366C5×C8—62no—
367C2×#41—151no—
368C2×#41—152no—
369#135—308no—
370C2×Q16—52no—
371C2×SD16—152no—
372C2×SD16—152no—
373C2×D8—152no—
374C22×C8—32no—
375C4⋊Q8—51no—
376#127—151no—
377#124—152no—
378#121—301no—
379#121—301no—
380C4×Q8—51no—
381C4×Q8—151no—
382C4×D4—151no—
383C4×D4—151no—
384C4×D4—301no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4—301no—
388#117—151no—
389#117—301no—
390C2×C42—31no—
391C2×C42—301no—
392C4⋊C8—32no—
393C4⋊C8—31no—
394C4⋊C8D3×D511yescharacteristic
395#103—52no—
396#103—152no—
397#102—152no—
398#102—152no—
399C2×C3×C5C2×#12111yescharacteristic
400C2×C3×C5C2×#13511yescharacteristic
401C2×C3×C5#57511yescharacteristic
402D15—42no—
403D15—82no—
404C5×D3—22no—
405C22×D3—101no—
406C22×D3—102no—
407C22×D3C2×D2011yescharacteristic
408C3×Q8—52no—
409C3×Q8—101no—
410C3×Q8—102no—
411C3×Q8—102no—
412C2×C3×C4—101no—
413C2×C3×C4—101no—
414C2×C3×C4—102no—
415C2×C3×C4C2×D2011yescharacteristic
416C2×C3×C4C2×D2011yescharacteristic
417C2×C3×C4C23×D511yescharacteristic
418C2×Dic3—101no—
419C2×Dic3C2×D2011yescharacteristic
420C2×Dic3C2×D2011yescharacteristic
421C2×Dic3C2×D2011yescharacteristic
422D12—52no—
423D12—104no—
424D12—102no—
425D12—101no—
426D12—102no—
427D12—202no—
428D12—204no—
429D12—202no—
430C4×D3—22no—
431C4×D3—41no—
432C4×D3—104no—
433C4×D3—202no—
434C4×D3—202no—
435C4×D3—204no—
436C4×D3D4×D512yes—
437C4×D3#71312yes—
438C3×C8—22no—
439C3⋊C8—22no—
440C22×C5—32no—
441C22×C5—61no—
442C22×C5—61no—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—62no—
445C2×D5—121no—
446C2×D5—121no—
447C2×D5—122no—
448C2×D5—122no—
449C2×D5—122no—
450C4×C5—21no—
451C4×C5—32no—
452C4×C5—61no—
453C4×C5—61no—
454C4×C5#91912yescomplemented
455C4×C5C2×D3×D411yescharacteristic
456C4×C5D3×#4111yescharacteristic
457Dic5—22no—
458Dic5—41no—
459Dic5—42no—
460Dic5—121no—
461#41—154no—
462#41—302no—
463#41—304no—
464#41—304no—
465C2×Q8—51no—
466C2×Q8—52no—
467C2×D4—151no—
468C2×D4—152no—
469C2×D4—301no—
470C2×D4—302no—
471C2×D4—301no—
472C2×D4—301no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—301no—
477C22×C4—301no—
478C22×C4—302no—
479C22×C4—301no—
480Q16—104no—
481SD16—304no—
482SD16—304no—
483D8—304no—
484C2×C8—32no—
485C2×C8—64no—
486C2×C8C2×D3×D512yes—
487C4⋊C4—51no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—151no—
492C4⋊C4—301no—
493C22⋊C4—301no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—301no—
497C22⋊C4—301no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—101no—
502C42—301no—
503C42—301no—
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3C22×D2011yescharacteristic
507C2×D3—21no—
508C2×D3—21no—
509C2×D3—102no—
510C2×D3—201no—
511C2×D3—201no—
512C2×D3—202no—
513C2×D3—202no—
514C2×D3—202no—
515C2×D3#404112yes—
516C3×C4—21no—
517C3×C4—102no—
518C3×C4—201no—
519C3×C4—202no—
520C3×C4#405012yescomplemented
521C3×C4C2×D4×D511yescharacteristic
522C3×C4C2×#71311yescharacteristic
523Dic3—21no—
524Dic3—21no—
525Dic3—201no—
526Dic3#404112yes—
527C2×C5—62no—
528C2×C5D3×#12111yescharacteristic
529C2×C5C2×#91911yescharacteristic
530C2×C5#577711yescharacteristic
531D5—122no—
532D5—242no—
533C23—31no—
534C23—301no—
535C23—302no—
536Q8—52no—
537Q8—101no—
538Q8—102no—
539Q8—102no—
540D4—152no—
541D4—304no—
542D4—302no—
543D4—301no—
544D4—302no—
545D4—602no—
546D4—604no—
547D4—602no—
548C2×C4—31no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—62no—
554C2×C4—101no—
555C2×C4—101no—
556C2×C4—102no—
557C2×C4—121no—
558C2×C4—304no—
559C2×C4—301no—
560C2×C4—604no—
561C2×C4—602no—
562C2×C4—602no—
563C2×C4D3×D2011yescharacteristic
564C2×C4D3×D2011yescharacteristic
565C2×C4C22×D3×D511yescharacteristic
566C8—22no—
567C8—62no—
568C2×C3C2×#404111yescharacteristic
569C2×C3C2×#405011yescharacteristic
570C2×C3#6608211yescharacteristic
571D3—22no—
572D3—202no—
573D3—402no—
574C5#8047511yescharacteristic, complemented, Sylow
575C22—32no—
576C22—61no—
577C22—61no—
578C22—302no—
579C22—601no—
580C22—601no—
581C22—602no—
582C22—602no—
583C22—602no—
584C22C2×D3×D2011yescharacteristic
585C4—21no—
586C4—32no—
587C4—61no—
588C4—61no—
589C4—102no—
590C4—201no—
591C4—202no—
592C4—601no—
593C4#9127512yescomplemented
594C4D3×D4×D511yescharacteristic
595C4D3×#71311yescharacteristic
596C3#1061075211yescharacteristic, complemented, Sylow
597C2—62no—
598C2—602no—
599C2—1202no—
600C2D3×#404111yescharacteristic
601C2C2×#9127511yescharacteristic
602C2#1175402811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#91275C2semidirect
2. #11752550C2semidirect
3. C4×#6769C2semidirect
4. #11750944C2semidirect
5. C5×D3×C4⋊C8C2semidirect
6. C3×#65138C2semidirect
7. #11747841C2semidirect
8. #11747798C2semidirect
9. #11747643C2semidirect
10. #11747085C2semidirect
11. #11747064C2semidirect
51. #65138D3semidirect
75. #6769D4semidirect
109. D3×C4⋊C8D5semidirect
278. C3×C4×C5#135semidirect
454. C4×C5#919semidirect
505. C3×C5#3035semidirect
520. C3×C4#4050semidirect
574. C5#80475semidirect
593. C4#91275semidirect
596. C3#10610752semidirect

Maximal subgroups

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

subgroupindex
C2×#912752
#117525502
C4×#67692
#117509442
C5×D3×C4⋊C82
C3×#651382
#117478412
#117477982
#117476432
#117470852
#117470642
#106107523
#804755