Finite Group Databasebeta

← #14426246

Subgroups — #14426246

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×#91273C212yesmaximal, complemented
2#11752542C211yesmaximal, characteristic, complemented
3C4×#6765C211yesmaximal, characteristic, complemented
4#11750950C211yesmaximal, characteristic, complemented
5C5×D3×C4⋊C8C211yesmaximal, characteristic, complemented
6C3×#65132C211yesmaximal, characteristic, complemented
7#11748137C212yesmaximal, complemented
8#11747972C212yesmaximal, complemented
9#11747756C212yesmaximal, complemented
10#11747083C211yesmaximal, characteristic, complemented
11#11747062C211yesmaximal, characteristic, complemented
12#10610752—31nomaximal, Hall
13C2×#6765C2212yes—
14C2×#6765C2211yescharacteristic
15C2×Dic60C2212yes—
16#91758C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C2×C5×D3×C8C2212yes—
19C42×C5×D3C2211yescharacteristic
20C2×C3×D40C2212yes—
21C3×#4020C2211yescharacteristic
22C3×C4×D20C2211yescharacteristic
23#91456—21no—
24#91456—21no—
25#91441—21no—
26C4×#1201—21no—
27Dic3×D20—21no—
28Dic3×D20—21no—
29Dic3×D20C2211yescharacteristic
30#91393—21no—
31C4×D5×Dic3—21no—
32#91364C2212yes—
33#91340C2211yescharacteristic
34#91338C2211yescharacteristic
35C2×#6657C2212yes—
36C2×#6657C2212yes—
37#91273—28no—
38C3×C5×C4⋊C8C2211yescharacteristic
39#91100C2212yes—
40C5×Dic3⋊C8C2212yes—
41C5×C4⋊(C3⋊C8)C2211yescharacteristic
42C3×#3953C2212yes—
43#90974C2212yes—
44#90965C2212yes—
45#80331—51nomaximal, Hall
46C2×#4050—32no—
47#65811—31no—
48C4×#709—31no—
49C2×C5×C4⋊C8—31no—
50#65402—32no—
51#65138—31no—
52#65137—31no—
53#65134—32no—
54#65133—32no—
55#65132D311yescharacteristic, complemented
56#65130—31no—
57C2×Dic30C2312yes—
58C2×Dic30C2311yescharacteristic
59C2×C4×C5×D3D411yescharacteristic
60C2×C4×C5×D3D411yescharacteristic
61C2×C4×C5×D3C2311yescharacteristic
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20C2312yes—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×#1201—21no—
68C2×#1201—22no—
69C2×D5×Dic3—21no—
70C2×D5×Dic3—22no—
71C2×D5×Dic3—21no—
72#6765—22no—
73#6765—24no—
74#6765—24no—
75#6765D414yescomplemented
76C2×C3×C5×C8C2312yes—
77C3×C42×C5C2311yescharacteristic
78C4⋊Dic15—21no—
79C4⋊Dic15—21no—
80C4⋊Dic15C2311yescharacteristic
81#6712—21no—
82C4×Dic15—21no—
83Dic60—24no—
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3D411yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C2×C5×C3⋊C8C2312yes—
88C5×D3×C8—24no—
89C3×#685—21no—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×D40—24no—
92#6669—21no—
93(C2×D3)⋊Dic5—21no—
94#6665—21no—
95#6665—22no—
96#6665—22no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6657—24no—
100#6657—24no—
101C2×#912—52no—
102#5716—51no—
103C4×#237—51no—
104C3×#459—51no—
105#5153—52no—
106#5075—51no—
107#5019—51no—
108#4849—51no—
109D3×C4⋊C8D511yescharacteristic, complemented
110#4772—52no—
111#4767—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×Dic20—32no—
122#4050—68no—
123C2×D40C2×D312yes—
124C2×#677—32no—
125C2×#677—32no—
126#4021—32no—
127#4020C2×D311yescharacteristic
128C4×D20—31no—
129C4×D20—61no—
130C4×D20—61no—
131C4×D20C2×D311yescharacteristic
132#4018—61no—
133C42×D5—61no—
134#4015—31no—
135C4×Dic10—31no—
136C4×Dic10—31no—
137C5×C4⋊C8—32no—
138C5×C4⋊C8—31no—
139C5×C4⋊C8C2×D311yescharacteristic
140#3953—32no—
141#3953C2×D312yes—
142#3948—32no—
143#3948—32no—
144#3035—151noSylow
145C22×C5×D3C2×D411yescharacteristic
146C22×C3×D5—21no—
147C22×C3×D5—22no—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—21no—
152C2×Dic15—21no—
153C2×Dic15—22no—
154Dic30—21no—
155Dic30—22no—
156Dic30—22no—
157Dic30C2×D412yes—
158C2×C5×Dic3C2×D411yescharacteristic
159C2×C5×Dic3C2×D411yescharacteristic
160C2×C5×Dic3C2×D411yescharacteristic
161C4×C5×D3—22no—
162C4×C5×D3—41no—
163C4×C5×D3C2×D412yes—
164C4×C5×D3#4112yes—
165C2×C3×Dic5—21no—
166C3×D20—22no—
167C3×D20—21no—
168C3×D20—22no—
169C3×D20—42no—
170C3×D20—42no—
171C3×D20C2×D412yes—
172C3×C4×D5—42no—
173#1201—24no—
174#1201—44no—
175D5×Dic3—24no—
176D5×Dic3—42no—
177D5×Dic3—44no—
178C3×C5×C8—22no—
179C5×C3⋊C8—22no—
180C2×#237—51no—
181C2×#237—52no—
182C2×C3×D8—52no—
183C3×#127—51no—
184C3×C4×D4—51no—
185#938—101no—
186#938—101no—
187#936—52no—
188D4×Dic3—51no—
189D4×Dic3—101no—
190D4×Dic3—101no—
191C2×#214—52no—
192C2×#214—52no—
193C4×#67—101no—
194C2×C4×Dic3—101no—
195#912—108no—
196C2×Dic12—52no—
197C2×D3×C8C2×D512yes—
198#892—51no—
199#887—51no—
200#67⋊C4—101no—
201#877—101no—
202C42×D3C2×D511yescharacteristic
203#869—51no—
204C4×Dic6—51no—
205C3×C4⋊C8C2×D511yescharacteristic
206C3×#102—52no—
207#832—52no—
208#816—52no—
209Dic3⋊C8C2×D512yes—
210#810—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—21no—
222C2×D20—21no—
223C2×D20C22×D312yes—
224C2×D20C22×D311yescharacteristic
225C2×C4×D5—21no—
226C2×C4×D5—61no—
227C2×C4×D5—62no—
228C2×C4×D5—61no—
229C2×Dic10—31no—
230C2×Dic10—32no—
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—21no—
240#685—61no—
241#685—62no—
242#685—62no—
243C4⋊Dic5—31no—
244C4⋊Dic5—61no—
245C4⋊Dic5—61no—
246C4⋊Dic5C22×D311yescharacteristic
247#683—61no—
248#683—61no—
249C4×Dic5—61no—
250C4×Dic5—61no—
251C4×Dic5—61no—
252Dic20—64no—
253D40—24no—
254#677—64no—
255#677—64no—
256C2×#135—152no—
257#532—151no—
258C4×#41—151no—
259#464—152no—
260#463—152no—
261#462—151no—
262#461—151no—
263#460—151no—
264#459—51no—
265C2×C4⋊C8—31no—
266#416—152no—
267C22×C3×C5C22×D411yescharacteristic
268C2×C5×D3—21no—
269C2×C5×D3—21no—
270C2×C5×D3#12112yes—
271C2×C3×D5—22no—
272C2×C3×D5—41no—
273C2×C3×D5—41no—
274C2×C3×D5—42no—
275C2×C3×D5—42no—
276C2×C3×D5—42no—
277C3×C4×C5—21no—
278C3×C4×C5#13512yescomplemented
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C2×#4111yescharacteristic
281Dic15—22no—
282Dic15—42no—
283Dic15—41no—
284C3×Dic5—41no—
285C5×Dic3—21no—
286C5×Dic3—21no—
287C5×Dic3#12112yes—
288C2×C3×D4—51no—
289C2×C3×D4—52no—
290C2×C3×D4—101no—
291C2×C3×D4—101no—
292C22×C3×C4—101no—
293C2×#67—101no—
294C2×#67—102no—
295C22×Dic3—101no—
296C22×Dic3—101no—
297C22×Dic3—102no—
298#237—54no—
299#237—104no—
300#237—102no—
301#237—104no—
302C2×C4×D3D2011yescharacteristic
303C2×C4×D3D2011yescharacteristic
304C2×C4×D3C22×D511yescharacteristic
305C2×Dic6—51no—
306C2×Dic6—52no—
307C3×D8—104no—
308C2×C3×C8C22×D512yes—
309C3×C4⋊C4—51no—
310C3×C22⋊C4—101no—
311C3×C42C22×D511yescharacteristic
312#217—101no—
313#217—102no—
314#217—102no—
315#214—104no—
316#214—104no—
317(C2×D3)⋊C4—101no—
318C4⋊Dic3—51no—
319C4⋊Dic3—101no—
320C4⋊Dic3—101no—
321Dic3⋊C4—101no—
322Dic3⋊C4—101no—
323C4×Dic3—101no—
324C4×Dic3—101no—
325C4×Dic3—101no—
326C4×Dic3D2011yescharacteristic
327C4×Dic3D2011yescharacteristic
328C4×Dic3C22×D511yescharacteristic
329C2×C3⋊C8C22×D512yes—
330Dic12—104no—
331D3×C8—24no—
332C23×C5—31no—
333C22×D5—21no—
334C22×D5—22no—
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—61no—
349C2×Dic5—61no—
350C2×Dic5—62no—
351D20—22no—
352D20—21no—
353D20—22no—
354D20—42no—
355D20—42no—
356D20D3×D412yes—
357C4×D5—42no—
358C4×D5—64no—
359C4×D5—124no—
360C4×D5—122no—
361Dic10—32no—
362Dic10—61no—
363Dic10—62no—
364Dic10—62no—
365C5×C8—22no—
366C5×C8—62no—
367C2×#41—151no—
368C2×#41—152no—
369#135—308no—
370C2×Q16—152no—
371C2×SD16—152no—
372C2×SD16—152no—
373C2×D8—52no—
374C22×C8—32no—
375C4⋊Q8—151no—
376#127—51no—
377#124—152no—
378#121—301no—
379#121—301no—
380C4×Q8—151no—
381C4×Q8—151no—
382C4×D4—51no—
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—152no—
396#103—152no—
397#102—52no—
398#102—152no—
399C2×C3×C5C2×#12111yescharacteristic
400C2×C3×C5C2×#13511yescharacteristic
401C2×C3×C5#57511yescharacteristic
402C3×D5—42no—
403C3×D5—82no—
404C5×D3—22no—
405C23×C3—101no—
406C23×C3—102no—
407C22×D3C2×D2011yescharacteristic
408C3×D4—52no—
409C3×D4—102no—
410C3×D4—101no—
411C3×D4—102no—
412C3×D4—202no—
413C3×D4—202no—
414C2×C3×C4—101no—
415C2×C3×C4—202no—
416C2×C3×C4C2×D2011yescharacteristic
417C2×C3×C4C2×D2011yescharacteristic
418C2×C3×C4C23×D511yescharacteristic
419#67—104no—
420#67—204no—
421C2×Dic3—101no—
422C2×Dic3—104no—
423C2×Dic3—101no—
424C2×Dic3—102no—
425C2×Dic3—202no—
426C2×Dic3—204no—
427C2×Dic3C2×D2011yescharacteristic
428C2×Dic3C2×D2011yescharacteristic
429C2×Dic3C2×D2011yescharacteristic
430C4×D3—22no—
431C4×D3—41no—
432C4×D3D4×D512yes—
433C4×D3#71312yes—
434Dic6—52no—
435Dic6—101no—
436Dic6—102no—
437Dic6—102no—
438C3×C8—22no—
439C3⋊C8—22no—
440C22×C5—32no—
441C22×C5—61no—
442C22×C5—61no—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—22no—
445C2×D5—41no—
446C2×D5—41no—
447C2×D5—42no—
448C2×D5—42no—
449C2×D5—42no—
450C4×C5—21no—
451C4×C5—32no—
452C4×C5—61no—
453C4×C5—61no—
454C4×C5#91212yescomplemented
455C4×C5C2×D3×D411yescharacteristic
456C4×C5D3×#4111yescharacteristic
457Dic5—41no—
458Dic5—62no—
459Dic5—121no—
460Dic5—122no—
461#41—154no—
462#41—302no—
463#41—304no—
464#41—304no—
465C2×Q8—151no—
466C2×Q8—152no—
467C2×D4—51no—
468C2×D4—52no—
469C2×D4—101no—
470C2×D4—101no—
471C2×D4—301no—
472C2×D4—302no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—101no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4—302no—
480Q16—304no—
481SD16—304no—
482SD16—304no—
483D8—104no—
484C2×C8—32no—
485C2×C8—64no—
486C2×C8C2×D3×D512yes—
487C4⋊C4—51no—
488C4⋊C4—151no—
489C4⋊C4—301no—
490C4⋊C4—301no—
491C4⋊C4—301no—
492C4⋊C4—301no—
493C22⋊C4—101no—
494C22⋊C4—301no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—301no—
502C42—301no—
503C42—301no—
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3—102no—
507C22×C3—201no—
508C22×C3—201no—
509C22×C3—202no—
510C22×C3—202no—
511C22×C3—202no—
512C22×C3C22×D2011yescharacteristic
513C2×D3—21no—
514C2×D3—21no—
515C2×D3#404112yes—
516C3×C4—21no—
517C3×C4—201no—
518C3×C4#405012yescomplemented
519C3×C4C2×D4×D511yescharacteristic
520C3×C4C2×#71311yescharacteristic
521Dic3—21no—
522Dic3—21no—
523Dic3—102no—
524Dic3—201no—
525Dic3—202no—
526Dic3#404112yes—
527C2×C5—62no—
528C2×C5D3×#12111yescharacteristic
529C2×C5C2×#91211yescharacteristic
530C2×C5#577311yescharacteristic
531D5—42no—
532D5—82no—
533C23—31no—
534C23—101no—
535C23—102no—
536Q8—152no—
537Q8—301no—
538Q8—302no—
539Q8—302no—
540D4—52no—
541D4—102no—
542D4—101no—
543D4—102no—
544D4—202no—
545D4—202no—
546D4—304no—
547D4—604no—
548C2×C4—31no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—62no—
554C2×C4—101no—
555C2×C4—121no—
556C2×C4—202no—
557C2×C4—304no—
558C2×C4—301no—
559C2×C4—301no—
560C2×C4—302no—
561C2×C4—604no—
562C2×C4—602no—
563C2×C4D3×D2011yescharacteristic
564C2×C4D3×D2011yescharacteristic
565C2×C4C22×D3×D511yescharacteristic
566C8—22no—
567C8—62no—
568C2×C3—202no—
569C2×C3—402no—
570C2×C3C2×#404111yescharacteristic
571C2×C3C2×#405011yescharacteristic
572C2×C3#6608211yescharacteristic
573D3—22no—
574C5#8033111yescharacteristic, complemented, Sylow
575C22—32no—
576C22—61no—
577C22—61no—
578C22—102no—
579C22—201no—
580C22—201no—
581C22—202no—
582C22—202no—
583C22—202no—
584C22C2×D3×D2011yescharacteristic
585C4—21no—
586C4—32no—
587C4—61no—
588C4—61no—
589C4—201no—
590C4—302no—
591C4—601no—
592C4—602no—
593C4#9127312yescomplemented
594C4D3×D4×D511yescharacteristic
595C4D3×#71311yescharacteristic
596C3#1061075211yescharacteristic, complemented, Sylow
597C2—62no—
598C2—202no—
599C2—402no—
600C2D3×#404111yescharacteristic
601C2C2×#9127311yescharacteristic
602C2#1175402911yescharacteristic
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×#91273C2semidirect
2. #11752542C2semidirect
3. C4×#6765C2semidirect
4. #11750950C2semidirect
5. C5×D3×C4⋊C8C2semidirect
6. C3×#65132C2semidirect
7. #11748137C2semidirect
8. #11747972C2semidirect
9. #11747756C2semidirect
10. #11747083C2semidirect
11. #11747062C2semidirect
55. #65132D3semidirect
75. #6765D4semidirect
109. D3×C4⋊C8D5semidirect
278. C3×C4×C5#135semidirect
454. C4×C5#912semidirect
505. C3×C5#3035semidirect
518. C3×C4#4050semidirect
574. C5#80331semidirect
593. C4#91273semidirect
596. C3#10610752semidirect

Maximal subgroups

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

subgroupindex
C2×#912732
#117525422
C4×#67652
#117509502
C5×D3×C4⋊C82
C3×#651322
#117481372
#117479722
#117477562
#117470832
#117470622
#106107523
#803315