Finite Group Databasebeta

← #14424197

Subgroups — #14424197

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92095C211yesmaximal, characteristic, complemented
2C22×C3×C5×D8C211yesmaximal, characteristic, complemented
3#11756564C211yesmaximal, characteristic, complemented
4C2×#91821C211yesmaximal, characteristic, complemented
5#11751316C211yesmaximal, characteristic, complemented
6#11751259C214yesmaximal, complemented
7#11751257C214yesmaximal, complemented
8#11751214C211yesmaximal, characteristic, complemented
9#11751211C211yesmaximal, characteristic, complemented
10#10615564—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic, complemented
13C22×#1220—22no—
14#92095—24no—
15#92095—24no—
16C2×#6819—21no—
17C2×#6819C2212yescomplemented
18C2×D4×D15—21no—
19C2×D4×D15C2212yescomplemented
20C2×#6817C2211yescharacteristic
21C2×#6817C2211yescharacteristic
22C2×C3×C5×D8—24no—
23C2×C3×C5×D8C2214yescomplemented
24C22×C3×C5×C8C2211yescharacteristic, complemented
25#91842—22no—
26#91829—21no—
27#91827C2214yescomplemented
28#91825—21no—
29C2×#6716C2212yescomplemented
30#91821—24no—
31C2×#6715C2212yescomplemented
32#91815C2211yescharacteristic, complemented
33C2×#6710C2211yescharacteristic, complemented
34#91116C2214yescomplemented
35#91105C2212yescomplemented
36#91104C2214yescomplemented
37#91100C2212yescomplemented
38#83833—51nomaximal, Hall
39C2×#4144—31no—
40C22×C5×D8D311yescharacteristic, complemented
41#66139—31no—
42C2×#4078—31no—
43#65504—31no—
44#65447—34no—
45#65445—34no—
46#65402—31no—
47#65399—31no—
48C24×C3×C5—21no—
49C24×C3×C5—21no—
50C23×D15—22no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4D414yescomplemented
57C2×C3×C5×D4C2312yes—
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—216no—
61C2×#1220—21no—
62C2×#1220—22no—
63C2×#1220—24no—
64C2×#1220—22no—
65C2×#1220D412yes—
66C22×Dic15—22no—
67#6819—28no—
68#6819—24no—
69#6819—24no—
70D4×D15—28no—
71D4×D15—24no—
72D4×D15—24no—
73#6817—22no—
74#6817—22no—
75#6817—22no—
76#6817D414yescomplemented
77C2×D60D411yescharacteristic
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×C4×D15C2312yes—
81C2×Dic30D411yescharacteristic
82C2×Dic30C2311yescharacteristic
83C3×C5×D8—28no—
84C2×C3×C5×C8—22no—
85C2×C3×C5×C8C2312yes—
86#6719—21no—
87#6719—24no—
88#6716—24no—
89#6715—24no—
90C4⋊Dic15C2312yes—
91C4×Dic15—21no—
92#6710—22no—
93C2×C3⋊#168C2312yes—
94C2×#1004—51no—
95C22×C3×D8D511yescharacteristic, complemented
96#5805—51no—
97C2×#932—51no—
98#5215—51no—
99#5158—54no—
100#5156—54no—
101#5113—51no—
102#5110—51no—
103C22×C5×D4C2×D311yescharacteristic
104C22×C5×D4C2×D311yescharacteristic, complemented
105C22×C22⋊D5—62no—
106#4144—64no—
107#4144—64no—
108C2×#711—32no—
109C2×#711—61no—
110C2×D4×D5—32no—
111C2×D4×D5—61no—
112C2×#709—31no—
113C2×#709—31no—
114C2×C5×D8—24no—
115C2×C5×D8C2×D314yescomplemented
116C22×C5×C8C2×D311yescharacteristic, complemented
117#4099—62no—
118#4086—61no—
119#4084—34no—
120#4082—61no—
121C2×#687—32no—
122#4078—64no—
123C2×#686—32no—
124#4072—31no—
125C2×#681—31no—
126#3964—34no—
127#3953—32no—
128#3952—34no—
129#3948—32no—
130#3008—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—24no—
133C23×C3×C5—22no—
134C23×C3×C5—42no—
135C23×C3×C5—82no—
136C23×C3×C5—82no—
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C22×D15—28no—
140C22×D15—84no—
141C22×D15C2×D412yes—
142C3×C5×D4—24no—
143C3×C5×D4—22no—
144C3×C5×D4—22no—
145C3×C5×D4—22no—
146C3×C5×D4—42no—
147C3×C5×D4C2×D414yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5C2411yescharacteristic
152#1220—28no—
153#1220—28no—
154#1220—24no—
155#1220—24no—
156#1220—84no—
157C2×Dic15—28no—
158C2×Dic15—21no—
159C2×Dic15—22no—
160C2×Dic15C2×D412yes—
161D60—22no—
162D60—21no—
163D60C2×D412yes—
164C4×D15—24no—
165C4×D15—22no—
166C4×D15—22no—
167Dic30—22no—
168Dic30—21no—
169Dic30C2×D412yes—
170C3×C5×C8—22no—
171C3⋊#168—22no—
172C22×C3×D4C2×D511yescharacteristic
173C22×C3×D4C2×D511yescharacteristic, complemented
174C22×#67—102no—
175#1004—104no—
176#1004—104no—
177C2×#237—52no—
178C2×#237—101no—
179C2×D3×D4—52no—
180C2×D3×D4—101no—
181C2×#235—51no—
182C2×#235—51no—
183C2×C3×D8—24no—
184C2×C3×D8C2×D514yescomplemented
185C22×C3×C8C2×D511yescharacteristic, complemented
186#953—102no—
187#940—101no—
188#938—54no—
189#936—101no—
190C2×#214—52no—
191#932—104no—
192C2×#213—52no—
193#926—51no—
194C2×#208—51no—
195#832—54no—
196#821—52no—
197(C2×D3)⋊C8—54no—
198#816—52no—
199C24×C5—21no—
200C24×C5—21no—
201C23×D5—62no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—21no—
206C2×C5×D4—22no—
207C2×C5×D4#6714yescomplemented
208C2×C5×D4C22×D312yes—
209C2×C5×D4C22×D312yes—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—32no—
212C2×C22⋊D5—62no—
213C2×C22⋊D5—62no—
214C2×C22⋊D5—616no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—64no—
217C22×Dic5—62no—
218#711—64no—
219#711—68no—
220#711—64no—
221D4×D5—64no—
222D4×D5—68no—
223D4×D5—64no—
224#709—34no—
225#709—62no—
226#709—62no—
227#709—62no—
228C2×D20—31no—
229C2×D20—31no—
230C2×C4×D5—32no—
231C2×C4×D5—61no—
232C2×Dic10—31no—
233C2×Dic10—31no—
234C5×D8—28no—
235C2×C5×C8—22no—
236C2×C5×C8C22×D312yes—
237C22⋊Dic5—64no—
238C22⋊Dic5—61no—
239#687—64no—
240#686—64no—
241C4⋊Dic5—32no—
242C4×Dic5—61no—
243#681—62no—
244C2×#168—32no—
245C2×H(5,𝔽2)—151no—
246C2×AGL(1,ℤ/8)—151no—
247C22×D8D1511yescharacteristic, complemented
248#535—151no—
249#449—154no—
250#447—154no—
251#418—151no—
252#416—151no—
253#408—151no—
254C22×C3×C5—22no—
255C22×C3×C5—24no—
256C22×C3×C5—44no—
257C22×C3×C5—42no—
258C22×C3×C5—44no—
259C22×C3×C5—84no—
260C22×C3×C5—84no—
261C22×C3×C5#12012yes—
262C22×C3×C5C22×D411yescharacteristic
263C2×D15—22no—
264C2×D15—22no—
265C2×D15—24no—
266C2×D15—42no—
267C2×D15—88no—
268C3×C4×C5#12012yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272Dic15—22no—
273Dic15—42no—
274C24×C3—21no—
275C24×C3—21no—
276C23×D3—102no—
277C2×C3×D4—21no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—21no—
281C2×C3×D4—22no—
282C2×C3×D4C22⋊D514yescomplemented
283C2×C3×D4C22×D512yes—
284C2×C3×D4C22×D512yes—
285C22×C3×C4C22×D511yescharacteristic
286C2×#67—52no—
287C2×#67—102no—
288C2×#67—102no—
289C2×#67—1016no—
290C2×#67—101no—
291C2×#67—104no—
292C22×Dic3—102no—
293#237—104no—
294#237—108no—
295#237—104no—
296D3×D4—104no—
297D3×D4—108no—
298D3×D4—104no—
299#235—54no—
300#235—102no—
301#235—102no—
302#235—102no—
303C2×D12—51no—
304C2×D12—51no—
305C2×C4×D3—52no—
306C2×C4×D3—101no—
307C2×Dic6—51no—
308C2×Dic6—51no—
309C3×D8—28no—
310C2×C3×C8—22no—
311C2×C3×C8C22×D512yes—
312#217—104no—
313#217—101no—
314#214—104no—
315#213—104no—
316C4⋊Dic3—52no—
317C4×Dic3—101no—
318#208—102no—
319C2×C3⋊C8—52no—
320C23×C5—22no—
321C23×C5—24no—
322C23×C5—22no—
323C23×C5—42no—
324C23×C5—82no—
325C23×C5—82no—
326C23×C5D3×D411yescharacteristic
327C22×D5—32no—
328C22×D5—61no—
329C22×D5—68no—
330C22×D5—244no—
331C5×D4—24no—
332C5×D4—22no—
333C5×D4—22no—
334C5×D4—22no—
335C5×D4—42no—
336C5×D4C2×#6714yes—
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5D3×D412yes—
339C2×C4×C5C2×#6712yes—
340C2×C4×C5C23×D311yescharacteristic
341C22⋊D5—68no—
342C22⋊D5—68no—
343C22⋊D5—64no—
344C22⋊D5—64no—
345C22⋊D5—244no—
346C2×Dic5—32no—
347C2×Dic5—68no—
348C2×Dic5—61no—
349C2×Dic5—62no—
350D20—32no—
351D20—62no—
352D20—61no—
353C4×D5—64no—
354C4×D5—62no—
355C4×D5—62no—
356Dic10—32no—
357Dic10—62no—
358Dic10—61no—
359C5×C8—22no—
360#168—62no—
361H(5,𝔽2)—304no—
362H(5,𝔽2)—304no—
363C2×#41—151no—
364C2×#41—152no—
365C2×#41—151no—
366C2×#41—301no—
367C22×D4—152no—
368C22×D4—301no—
369C22×D4—302no—
370C22×D4C2×D1511yescharacteristic
371C22×D4C2×D1511yescharacteristic, complemented
372AGL(1,ℤ/8)—304no—
373C2×SD16—152no—
374C2×D8—24no—
375C2×D8—152no—
376C2×D8C2×D1514yescomplemented
377C2×M16—151no—
378C22×C8C2×D1511yescharacteristic, complemented
379#127—301no—
380#124—301no—
381#121—154no—
382#120—302no—
383#117—151no—
384#103—152no—
385#102—154no—
386#102—152no—
387C22⋊C8—154no—
388C2×C3×C5—22no—
389C2×C3×C5—44no—
390C2×C3×C5—82no—
391C2×C3×C5C2×#12011yescharacteristic
392C2×C3×C5#57612yes—
393D15—42no—
394D15—42no—
395C23×C3—22no—
396C23×C3—24no—
397C23×C3—22no—
398C23×C3—42no—
399C23×C3—82no—
400C23×C3—82no—
401C23×C3D4×D511yescharacteristic
402C22×D3—52no—
403C22×D3—101no—
404C22×D3—108no—
405C22×D3—404no—
406C3×D4—22no—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—24no—
410C3×D4—42no—
411C3×D4C2×C22⋊D514yes—
412C2×C3×C4D4×D512yes—
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4C2×C22⋊D512yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—108no—
417#67—108no—
418#67—104no—
419#67—104no—
420#67—404no—
421C2×Dic3—52no—
422C2×Dic3—108no—
423C2×Dic3—101no—
424C2×Dic3—102no—
425D12—52no—
426D12—101no—
427D12—102no—
428C4×D3—102no—
429C4×D3—102no—
430C4×D3—104no—
431Dic6—52no—
432Dic6—101no—
433Dic6—102no—
434C3×C8—22no—
435C3⋊C8—102no—
436C22×C5—22no—
437C22×C5—24no—
438C22×C5—44no—
439C22×C5—44no—
440C22×C5—42no—
441C22×C5—84no—
442C22×C5—84no—
443C22×C5#93712yes—
444C22×C5C2×D3×D411yescharacteristic
445C2×D5—64no—
446C2×D5—62no—
447C2×D5—62no—
448C2×D5—122no—
449C2×D5—248no—
450C4×C5#93712yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C22×#6711yescharacteristic
453Dic5—62no—
454Dic5—62no—
455Dic5—122no—
456C24—21no—
457C24—21no—
458C24—302no—
459#41—154no—
460#41—304no—
461#41—308no—
462#41—304no—
463#41—302no—
464#41—302no—
465#41—302no—
466C2×Q8—151no—
467C2×Q8—151no—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—152no—
474C2×D4—151no—
475C2×D4—151no—
476C2×D4—302no—
477C2×D4—304no—
478C2×D4—308no—
479C2×D4—302no—
480C2×D4—3016no—
481C2×D4—301no—
482C2×D4—304no—
483C2×D4—304no—
484C2×D4#122014yescomplemented
485C2×D4C22×D1512yes—
486C2×D4C22×D1512yes—
487C22×C4—152no—
488C22×C4—302no—
489C22×C4—301no—
490C22×C4C22×D1511yescharacteristic
491SD16—304no—
492D8—28no—
493D8—304no—
494M16—302no—
495C2×C8—22no—
496C2×C8—152no—
497C2×C8C22×D1512yes—
498C4⋊C4—152no—
499C22⋊C4—304no—
500C22⋊C4—301no—
501C42—301no—
502C3×C5#300811yescharacteristic, complemented, Hall
503C22×C3—22no—
504C22×C3—24no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—42no—
508C22×C3—84no—
509C22×C3—84no—
510C22×C3#408312yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—104no—
513C2×D3—102no—
514C2×D3—102no—
515C2×D3—202no—
516C2×D3—408no—
517C3×C4#408312yes—
518C3×C4C2×D4×D511yescharacteristic
519C3×C4C22×C22⋊D511yescharacteristic
520Dic3—102no—
521Dic3—102no—
522Dic3—202no—
523C2×C5—22no—
524C2×C5—44no—
525C2×C5—82no—
526C2×C5#575712yes—
527C2×C5C2×#93711yescharacteristic
528D5—122no—
529D5—122no—
530C23—22no—
531C23—24no—
532C23—22no—
533C23—42no—
534C23—82no—
535C23—82no—
536C23—152no—
537C23—308no—
538C23—301no—
539C23—1204no—
540C23D4×D1511yescharacteristic
541Q8—152no—
542Q8—302no—
543Q8—301no—
544D4—24no—
545D4—22no—
546D4—22no—
547D4—22no—
548D4—42no—
549D4—152no—
550D4—308no—
551D4—308no—
552D4—304no—
553D4—304no—
554D4—302no—
555D4—301no—
556D4—1204no—
557D4C2×#122014yes—
558C2×C4—152no—
559C2×C4—308no—
560C2×C4—301no—
561C2×C4—304no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4D4×D1511yescharacteristic
566C2×C4D4×D1512yes—
567C2×C4C2×#122012yes—
568C2×C4C23×D1511yescharacteristic
569C8—22no—
570C8—302no—
571C2×C3—22no—
572C2×C3—44no—
573C2×C3—82no—
574C2×C3#6609112yes—
575C2×C3C2×#408311yescharacteristic
576D3—202no—
577D3—202no—
578C5#8383311yescharacteristic, complemented, Sylow
579C22—22no—
580C22—24no—
581C22—44no—
582C22—42no—
583C22—44no—
584C22—84no—
585C22—84no—
586C22—302no—
587C22—302no—
588C22—304no—
589C22—602no—
590C22—1208no—
591C22#9182612yes—
592C22C2×D4×D1511yescharacteristic
593C4—302no—
594C4—302no—
595C4—602no—
596C4#9182612yes—
597C4C2×D4×D1511yescharacteristic
598C4C22×#122011yescharacteristic
599C3#1061556411yescharacteristic, complemented, Sylow
600C2—22no—
601C2—44no—
602C2—82no—
603C2—602no—
604C2—602no—
605C2#1175651612yes—
606C2C2×#9182611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×D8C2
socleC22×C3×C5C22×D4
hypercenterC22×D8D15
hypocenterC3×C5#3008
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#92095C2semidirect
2. C22×C3×C5×D8C2semidirect
3. #11756564C2semidirect
4. C2×#91821C2semidirect
5. #11751316C2semidirect
6. #11751259C2semidirect
7. #11751257C2semidirect
8. #11751214C2semidirect
9. #11751211C2semidirect
12. C22×C3×C5×D4C22semidirect
17. C2×#6819C22semidirect
19. C2×D4×D15C22semidirect
23. C2×C3×C5×D8C22semidirect
24. C22×C3×C5×C8C22semidirect
27. #91827C22semidirect
29. C2×#6716C22semidirect
31. C2×#6715C22semidirect
32. #91815C22semidirect
33. C2×#6710C22semidirect
34. #91116C22semidirect
35. #91105C22semidirect
36. #91104C22semidirect
37. #91100C22semidirect
40. C22×C5×D8D3semidirect
56. C2×C3×C5×D4D4semidirect
76. #6817D4semidirect
95. C22×C3×D8D5semidirect
104. C22×C5×D4C2×D3semidirect
115. C2×C5×D8C2×D3semidirect
116. C22×C5×C8C2×D3semidirect
173. C22×C3×D4C2×D5semidirect
184. C2×C3×D8C2×D5semidirect
185. C22×C3×C8C2×D5semidirect
207. C2×C5×D4#67semidirect
247. C22×D8D15semidirect
282. C2×C3×D4C22⋊D5semidirect
371. C22×D4C2×D15semidirect
376. C2×D8C2×D15semidirect
378. C22×C8C2×D15semidirect
484. C2×D4#1220semidirect
502. C3×C5#3008semidirect
578. C5#83833semidirect
599. C3#10615564semidirect

Maximal subgroups

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

subgroupindex
C2×#920952
C22×C3×C5×D82
#117565642
C2×#918212
#117513162
#117512592
#117512572
#117512142
#117512112
#106155643
#838335