Finite Group Databasebeta

← #14426256

Subgroups — #14426256

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×#91269C212yesmaximal, complemented
2#11752674C211yesmaximal, characteristic, complemented
3C4×#6772C211yesmaximal, characteristic, complemented
4#11750949C211yesmaximal, characteristic, complemented
5C5×#4841C211yesmaximal, characteristic, complemented
6C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
7#11747857C212yesmaximal, complemented
8#11747770C212yesmaximal, complemented
9#11747642C212yesmaximal, complemented
10#11747105C211yesmaximal, characteristic, complemented
11#11747037C211yesmaximal, characteristic, complemented
12#10612158—31nomaximal, Hall
13C2×#6773C2212yes—
14C2×#6772C2211yescharacteristic
15C2×#6706C2212yes—
16#91763C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C2×C5×#204C2212yes—
19C4×C5×D12C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C2×C3×C8×D5C2212yes—
22C3×C42×D5C2211yescharacteristic
23#91450—21no—
24#91450—21no—
25#91440—21no—
26C4×#1201—21no—
27#91418—21no—
28#91418—21no—
29Dic5×D12C2211yescharacteristic
30#91398—21no—
31C4×D3×Dic5—21no—
32#91375C2212yes—
33#91358C2211yescharacteristic
34#91333C2211yescharacteristic
35C2×#6663C2212yes—
36C2×#6654C2212yes—
37#91269—28no—
38C3×C5×C4⋊C8C2211yescharacteristic
39#91105C2212yes—
40C5×#816C2212yes—
41C3×#3946C2212yes—
42C3×C4⋊#168C2211yescharacteristic
43#90973C2212yes—
44#90969C2212yes—
45#79021—51nomaximal, Hall
46C2×#4062—32no—
47#66059—31no—
48C4×#711—31no—
49C5×#461—31no—
50#65454—32no—
51#65379—31no—
52#65304—31no—
53#65137—31no—
54D5×C4⋊C8D311yescharacteristic, complemented
55#65093—32no—
56#65087—32no—
57C2×D60—21no—
58C2×D60—21no—
59C2×D60C2312yes—
60C2×Dic30C2311yescharacteristic
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2312yes—
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×#1202—22no—
68C2×#1201—21no—
69C2×#1200—22no—
70C2×D3×Dic5—21no—
71C2×D3×Dic5—21no—
72#6773—24no—
73#6773—24no—
74#6772—22no—
75#6772D414yescomplemented
76C2×C3×C5×C8C2312yes—
77C3×C42×C5C2311yescharacteristic
78C4⋊Dic15C2311yescharacteristic
79#6712—21no—
80C4×Dic15—21no—
81#6706—24no—
82C5×(C2×D3)⋊C4—21no—
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3—21no—
85C5×C4⋊Dic3C2311yescharacteristic
86C5×#204—24no—
87C3×C4×Dic5D411yescharacteristic
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5C2311yescharacteristic
90C2×C3×#168C2312yes—
91C3×C8×D5—24no—
92#6669—21no—
93#6667—22no—
94#6667—22no—
95(C2×D3)⋊Dic5—21no—
96#6665—21no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6663—24no—
100#6654—24no—
101C2×#904—52no—
102#5477—51no—
103C4×#235—51no—
104C2×C3×C4⋊C8—51no—
105#5113—52no—
106#4849—51no—
107#4848—51no—
108#4845—52no—
109#4844—52no—
110#4843—51no—
111#4841D511yescharacteristic, complemented
112C2×#713—32no—
113C2×#711—31no—
114C2×C5×SD16—32no—
115C5×C4⋊Q8—31no—
116C4×C5×D4—31no—
117#4093—32no—
118C2×#689—32no—
119D4×Dic5—31no—
120C2×#686—32no—
121C4×C22⋊D5—61no—
122C2×C4×Dic5—61no—
123#4062—68no—
124C2×#677—32no—
125C2×C8×D5C2×D312yes—
126#4041—61no—
127#4041—61no—
128#4039—61no—
129#4039—61no—
130#4038—31no—
131#4033—31no—
132#4027—61no—
133#4023—61no—
134#4020—31no—
135C42×D5C2×D311yescharacteristic
136C4×Dic10—31no—
137C5×C4⋊C8C2×D311yescharacteristic
138C5×#103—32no—
139#3967—32no—
140#3953—32no—
141#3946C2×D312yes—
142#3941—32no—
143C4⋊#168C2×D311yescharacteristic
144#3035—151noSylow
145C22×D15—22no—
146C22×C5×D3—21no—
147C22×C3×D5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2411yescharacteristic
151C2×Dic15—21no—
152C2×Dic15—21no—
153D60—22no—
154D60—22no—
155D60—42no—
156D60—42no—
157Dic30—21no—
158Dic30C2×D412yes—
159C2×C5×Dic3—21no—
160C2×C5×Dic3—22no—
161C5×D12—21no—
162C5×D12C2×D412yes—
163C4×C5×D3—42no—
164C5×Dic6—22no—
165C5×Dic6—22no—
166C2×C3×Dic5C2×D411yescharacteristic
167C2×C3×Dic5C2×D411yescharacteristic
168C2×C3×Dic5C2×D411yescharacteristic
169C3×C4×D5—22no—
170C3×C4×D5—41no—
171C3×C4×D5C2×D412yes—
172C3×C4×D5#4112yes—
173#1202—44no—
174#1201—24no—
175#1200—44no—
176D3×Dic5—24no—
177D3×Dic5—42no—
178C3×C5×C8—22no—
179C3×#168—22no—
180C2×#235—51no—
181C2×#235—52no—
182C22×C3×C8—52no—
183C2×C3×C42—51no—
184#930—101no—
185#930—101no—
186C4×#67—101no—
187C4×#67—101no—
188#926—51no—
189C2×Dic12—52no—
190#904—108no—
191C2×D24—52no—
192C2×#204—52no—
193C2×#204C2×D512yes—
194#875—52no—
195#874—51no—
196C4×D12—51no—
197C4×D12—101no—
198C4×D12—101no—
199C4×D12C2×D511yescharacteristic
200#872—101no—
201C42×D3—101no—
202#869C2×D511yescharacteristic
203C4×Dic6—51no—
204C4×Dic6—51no—
205C3×C4⋊C8—52no—
206C3×C4⋊C8—51no—
207C3×C4⋊C8C2×D511yescharacteristic
208#821—52no—
209#821—52no—
210#816—52no—
211#816C2×D512yes—
212C2×C5×Q8—32no—
213C2×C5×D4—31no—
214C22×C4×C5—61no—
215C2×C22⋊D5—61no—
216C22×Dic5—61no—
217C22×Dic5—61no—
218#713—64no—
219#713—64no—
220#711—34no—
221#711—62no—
222C2×D20—32no—
223C2×D20—62no—
224C2×D20—61no—
225C2×D20—61no—
226C2×C4×D5—62no—
227C2×C4×D5D1211yescharacteristic
228C2×C4×D5D1211yescharacteristic
229C2×C4×D5C22×D311yescharacteristic
230C2×Dic10—31no—
231C5×SD16—64no—
232C2×C5×C8C22×D312yes—
233C5×C4⋊C4—31no—
234C5×C4⋊C4—61no—
235C5×C4⋊C4—61no—
236C5×C22⋊C4—61no—
237C42×C5C22×D311yescharacteristic
238C22⋊Dic5—61no—
239#689—64no—
240#686—64no—
241#685—61no—
242#685—62no—
243#685—62no—
244C4⋊Dic5—31no—
245#683—61no—
246#683—61no—
247C4×Dic5—61no—
248C4×Dic5—61no—
249C4×Dic5—61no—
250C4×Dic5D1211yescharacteristic
251C4×Dic5D1211yescharacteristic
252C4×Dic5C22×D311yescharacteristic
253C2×#168C22×D312yes—
254#677—64no—
255C8×D5—24no—
256C2×#135—152no—
257#532—151no—
258C4×#41—151no—
259#464—152no—
260#463—152no—
261#462—151no—
262#461—31no—
263#460—151no—
264#459—151no—
265C2×C4⋊C8—51no—
266#416—152no—
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—42no—
269C2×D15—42no—
270C2×D15—42no—
271C2×C5×D3—22no—
272C2×C5×D3—41no—
273C2×C5×D3—41no—
274C2×C3×D5—21no—
275C2×C3×D5—21no—
276C2×C3×D5#12112yes—
277C3×C4×C5—21no—
278C3×C4×C5#13512yescomplemented
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C2×#4111yescharacteristic
281Dic15—22no—
282Dic15—41no—
283C3×Dic5—21no—
284C3×Dic5—21no—
285C3×Dic5#12112yes—
286C5×Dic3—42no—
287C5×Dic3—41no—
288C22×C3×C4—51no—
289C22×C3×C4—51no—
290C22×C3×C4—51no—
291C2×#67—102no—
292C2×#67—101no—
293#235—54no—
294#235—104no—
295#235—104no—
296#235—102no—
297C2×D12—52no—
298C2×D12—101no—
299C2×D12—101no—
300C2×D12C22×D511yescharacteristic
301C2×C4×D3—21no—
302C2×C4×D3—101no—
303C2×C4×D3—102no—
304C2×C4×D3—101no—
305C2×Dic6—51no—
306C2×Dic6C22×D512yes—
307C2×C3×C8—52no—
308C2×C3×C8—104no—
309C2×C3×C8C22×D512yes—
310C3×C42—51no—
311C3×C42—51no—
312C3×C42—51no—
313C3×C42C22×D511yescharacteristic
314#217—101no—
315(C2×D3)⋊C4—21no—
316(C2×D3)⋊C4—102no—
317(C2×D3)⋊C4—102no—
318(C2×D3)⋊C4—101no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—51no—
322C4⋊Dic3C22×D511yescharacteristic
323Dic3⋊C4—101no—
324Dic3⋊C4—101no—
325C4×Dic3—101no—
326C4×Dic3—101no—
327C4×Dic3—101no—
328Dic12—104no—
329D24—104no—
330#204—24no—
331#204—104no—
332C23×C5—61no—
333C22×D5—62no—
334C22×D5C2×D1211yescharacteristic
335C5×Q8—62no—
336C5×Q8—62no—
337C5×D4—32no—
338C5×D4—61no—
339C2×C4×C5—61no—
340C2×C4×C5—62no—
341C2×C4×C5—122no—
342C2×C4×C5C2×D1211yescharacteristic
343C2×C4×C5C2×D1211yescharacteristic
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—64no—
346C2×Dic5—61no—
347C2×Dic5—64no—
348C2×Dic5—61no—
349C2×Dic5—122no—
350C2×Dic5C2×D1211yescharacteristic
351C2×Dic5C2×D1211yescharacteristic
352C2×Dic5C2×D1211yescharacteristic
353D20—62no—
354D20—62no—
355D20—122no—
356D20—124no—
357D20—122no—
358C4×D5—22no—
359C4×D5—41no—
360C4×D5—124no—
361C4×D5D3×D412yes—
362C4×D5#23912yes—
363Dic10—32no—
364Dic10—61no—
365C5×C8—22no—
366#168—22no—
367C2×#41—151no—
368C2×#41—152no—
369#135—308no—
370C2×Q16—152no—
371C2×SD16—32no—
372C2×SD16—152no—
373C2×D8—152no—
374C22×C8—52no—
375C4⋊Q8—31no—
376#127—151no—
377#124—152no—
378#121—301no—
379#121—301no—
380C4×Q8—151no—
381C4×Q8—151no—
382C4×D4—31no—
383C4×D4—151no—
384C4×D4—301no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4—301no—
388#117—151no—
389#117—301no—
390C2×C42—51no—
391C2×C42—301no—
392C4⋊C8—52no—
393C4⋊C8—51no—
394C4⋊C8D3×D511yescharacteristic
395#103—32no—
396#103—152no—
397#102—152no—
398#102—152no—
399C2×C3×C5C2×#12111yescharacteristic
400C2×C3×C5C2×#13511yescharacteristic
401C2×C3×C5#57511yescharacteristic
402D15—82no—
403C3×D5—22no—
404C5×D3—42no—
405C23×C3—51no—
406C22×D3—21no—
407C22×D3—102no—
408C2×C3×C4—51no—
409C2×C3×C4—52no—
410C2×C3×C4—52no—
411C2×C3×C4—51no—
412C2×C3×C4—51no—
413C2×C3×C4—102no—
414C2×C3×C4—201no—
415C2×C3×C4D4×D511yescharacteristic
416C2×C3×C4D4×D511yescharacteristic
417C2×C3×C4C23×D511yescharacteristic
418#67—104no—
419#67—204no—
420C2×Dic3—21no—
421C2×Dic3—22no—
422C2×Dic3—101no—
423C2×Dic3—101no—
424D12—21no—
425D12—102no—
426D12—102no—
427D12—202no—
428D12—202no—
429D12D4×D512yes—
430C4×D3—42no—
431C4×D3—104no—
432C4×D3—204no—
433C4×D3—202no—
434Dic6—22no—
435Dic6—22no—
436Dic6—52no—
437Dic6—101no—
438C3×C8—22no—
439C3×C8—102no—
440C22×C5—62no—
441C22×C5—121no—
442C22×C5—121no—
443C22×C5C22×D1211yescharacteristic
444C2×D5—21no—
445C2×D5—21no—
446C2×D5—122no—
447C2×D5—122no—
448C2×D5—122no—
449C2×D5#89512yes—
450C4×C5—21no—
451C4×C5—121no—
452C4×C5—122no—
453C4×C5#90412yescomplemented
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C2×#23911yescharacteristic
456Dic5—21no—
457Dic5—21no—
458Dic5—62no—
459Dic5—121no—
460Dic5#89512yes—
461#41—154no—
462#41—302no—
463#41—304no—
464#41—304no—
465C2×Q8—32no—
466C2×Q8—151no—
467C2×D4—31no—
468C2×D4—152no—
469C2×D4—302no—
470C2×D4—301no—
471C2×D4—301no—
472C2×D4—301no—
473C22×C4—51no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—61no—
477C22×C4—302no—
478C22×C4—301no—
479C22×C4—301no—
480Q16—304no—
481SD16—64no—
482SD16—304no—
483D8—304no—
484C2×C8—52no—
485C2×C8—104no—
486C2×C8C2×D3×D512yes—
487C4⋊C4—31no—
488C4⋊C4—61no—
489C4⋊C4—61no—
490C4⋊C4—151no—
491C4⋊C4—301no—
492C4⋊C4—301no—
493C22⋊C4—61no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—301no—
497C22⋊C4—301no—
498C42—51no—
499C42—51no—
500C42—51no—
501C42—301no—
502C42—301no—
503C42—301no—
504C42C2×D3×D511yescharacteristic
505C3×C5#303511yescharacteristic, complemented, Hall
506C22×C3—52no—
507C22×C3—101no—
508C22×C3—101no—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—22no—
511C2×D3—41no—
512C2×D3—41no—
513C2×D3—202no—
514C2×D3—202no—
515C2×D3—202no—
516C3×C4—21no—
517C3×C4—52no—
518C3×C4—101no—
519C3×C4—101no—
520C3×C4#406212yescomplemented
521C3×C4C2×D4×D511yescharacteristic
522C3×C4D5×#4111yescharacteristic
523Dic3—41no—
524Dic3—42no—
525Dic3—102no—
526Dic3—201no—
527C2×C5—122no—
528C2×C5C2×#89511yescharacteristic
529C2×C5C2×#90411yescharacteristic
530C2×C5#574811yescharacteristic
531D5—22no—
532D5—242no—
533C23—51no—
534C23—61no—
535C23—302no—
536Q8—62no—
537Q8—62no—
538Q8—152no—
539Q8—301no—
540D4—32no—
541D4—61no—
542D4—304no—
543D4—302no—
544D4—302no—
545D4—602no—
546D4—604no—
547D4—602no—
548C2×C4—51no—
549C2×C4—52no—
550C2×C4—52no—
551C2×C4—51no—
552C2×C4—51no—
553C2×C4—61no—
554C2×C4—62no—
555C2×C4—102no—
556C2×C4—122no—
557C2×C4—201no—
558C2×C4—304no—
559C2×C4—301no—
560C2×C4—301no—
561C2×C4—604no—
562C2×C4—602no—
563C2×C4D5×D1211yescharacteristic
564C2×C4D5×D1211yescharacteristic
565C2×C4C22×D3×D511yescharacteristic
566C8—22no—
567C8—102no—
568C2×C3—102no—
569C2×C3D5×#12111yescharacteristic
570C2×C3C2×#406211yescharacteristic
571C2×C3#6611111yescharacteristic
572D3—42no—
573D3—402no—
574C5#7902111yescharacteristic, complemented, Sylow
575C22—52no—
576C22—62no—
577C22—101no—
578C22—101no—
579C22—121no—
580C22—121no—
581C22—602no—
582C22—602no—
583C22—602no—
584C22C2×D5×D1211yescharacteristic
585C4—21no—
586C4—52no—
587C4—101no—
588C4—101no—
589C4—121no—
590C4—122no—
591C4—302no—
592C4—601no—
593C4#9126912yescomplemented
594C4D3×D4×D511yescharacteristic
595C4D5×#23911yescharacteristic
596C3#1061215811yescharacteristic, complemented, Sylow
597C2—102no—
598C2—122no—
599C2—1202no—
600C2D5×#89511yescharacteristic
601C2C2×#9126911yescharacteristic
602C2#1175402111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
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×#91269C2semidirect
2. #11752674C2semidirect
3. C4×#6772C2semidirect
4. #11750949C2semidirect
5. C5×#4841C2semidirect
6. C3×D5×C4⋊C8C2semidirect
7. #11747857C2semidirect
8. #11747770C2semidirect
9. #11747642C2semidirect
10. #11747105C2semidirect
11. #11747037C2semidirect
54. D5×C4⋊C8D3semidirect
75. #6772D4semidirect
111. #4841D5semidirect
278. C3×C4×C5#135semidirect
453. C4×C5#904semidirect
505. C3×C5#3035semidirect
520. C3×C4#4062semidirect
574. C5#79021semidirect
593. C4#91269semidirect
596. C3#10612158semidirect

Maximal subgroups

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

subgroupindex
C2×#912692
#117526742
C4×#67722
#117509492
C5×#48412
C3×D5×C4⋊C82
#117478572
#117477702
#117476422
#117471052
#117470372
#106121583
#790215