Finite Group Databasebeta

← #14424253

Subgroups — #14424253

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×#92017C211yesmaximal, characteristic, complemented
2#11756564C211yesmaximal, characteristic, complemented
3C2×C5×#932C211yesmaximal, characteristic, complemented
4C22×C3×#686C211yesmaximal, characteristic, complemented
5#11749158C214yesmaximal, complemented
6#11749153C214yesmaximal, complemented
7#11748388C211yesmaximal, characteristic, complemented
8#11748367C211yesmaximal, characteristic, complemented
9#11748349C211yesmaximal, characteristic, complemented
10#10615678—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic, complemented
12C2×#6817C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C2×D5×#67—22no—
16#92017—24no—
17#92017—24no—
18C2×#6777C2212yescomplemented
19C2×D3×D20—21no—
20C2×#6766C2212yescomplemented
21C2×#6765—21no—
22#91842—22no—
23#91829—21no—
24#91827C2214yescomplemented
25#91825—21no—
26#91815C2211yescharacteristic, complemented
27C2×C5×#214C2212yescomplemented
28C5×#932—24no—
29C2×C5×#213C2212yescomplemented
30C2×C5×#208C2211yescharacteristic, complemented
31C2×C3×#686—24no—
32C2×C3×#686C2214yescomplemented
33C22×C3×#168C2211yescharacteristic, complemented
34#90973C2212yescomplemented
35#90967C2212yescomplemented
36#90965C2214yescomplemented
37#90957C2214yescomplemented
38#83833—51nomaximal, Hall
39C2×#4149—31no—
40C2×C5×AGL(1,ℤ/8)—31no—
41#66139—31no—
42C22×#686D311yescharacteristic, complemented
43#65522—31no—
44#65461—34no—
45#65445—34no—
46#65420—31no—
47#65418—31no—
48C24×C3×C5—21no—
49C23×C3×D5—21no—
50C22×D3×D5—22no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—21no—
54C2×C3×C5×D4C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—24no—
57C2×#1220D412yes—
58#6817—22no—
59#6817—22no—
60C2×D60D411yescharacteristic
61C2×C4×D15C2312yes—
62C2×Dic30D411yescharacteristic
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235D414yescomplemented
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×D20—21no—
70C2×C3×D20—22no—
71C2×C3×D20D414yescomplemented
72C2×C3×D20C2312yes—
73D5×#67—216no—
74C2×#1202—22no—
75C2×#1201—22no—
76C2×D5×Dic3—22no—
77#6777—24no—
78#6777—24no—
79D3×D20—28no—
80#6766—24no—
81#6766—24no—
82#6765—28no—
83#6719—21no—
84#6719—24no—
85C4⋊Dic15C2312yes—
86C4×Dic15—21no—
87C5×#214—24no—
88C5×#213—24no—
89C5×#208—22no—
90C2×C5×C3⋊C8C2312yes—
91C3×#686—28no—
92C2×C3×#168—22no—
93C2×C3×#168C2312yes—
94C2×#1004—51no—
95C22×C3×D8—51no—
96#5805—51no—
97C2×#932D511yescharacteristic, complemented
98#5215—51no—
99#5158—54no—
100#5156—54no—
101#5113—51no—
102#5110—51no—
103C2×C5×#41—31no—
104C22×C5×D4C2×D311yescharacteristic, complemented
105#4149—64no—
106#4149—64no—
107C2×#713—32no—
108C2×D4×D5—32no—
109C2×D4×D5—62no—
110C2×#709—31no—
111C2×#709—61no—
112C22×D20—61no—
113C22×D20C2×D311yescharacteristic
114C5×AGL(1,ℤ/8)—64no—
115C2×C5×SD16—32no—
116C2×C5×D8—32no—
117C2×C5×M16—31no—
118#4099—62no—
119#4086—61no—
120#4084—34no—
121#4082—61no—
122C2×#686—24no—
123C2×#686C2×D314yescomplemented
124#4072—31no—
125C22×#168C2×D311yescharacteristic, complemented
126#3967—32no—
127#3964—32no—
128#3953—34no—
129#3952—34no—
130#3008—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—42no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D411yescharacteristic
135C22×D15C2×D412yes—
136C22×C5×D3—21no—
137C22×C3×D5—22no—
138C22×C3×D5—24no—
139C22×C3×D5—82no—
140C2×D3×D5—28no—
141C2×D3×D5—84no—
142C3×C5×D4—22no—
143C3×C5×D4—22no—
144C3×C5×D4—42no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—24no—
150#1220—84no—
151C2×Dic15—22no—
152C2×Dic15C2×D412yes—
153D60—22no—
154C4×D15—22no—
155C4×D15—22no—
156Dic30—22no—
157C5×#67—24no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12C2×D412yes—
161C4×C5×D3—24no—
162C5×Dic6—21no—
163C5×Dic6C2×D412yes—
164C3×D20—24no—
165C3×D20—22no—
166C3×D20C2×D414yes—
167#1202—28no—
168#1201—28no—
169D5×Dic3—28no—
170C3×#168—22no—
171C5×C3⋊C8—22no—
172C22×C3×D4—51no—
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×#235C2×D511yescharacteristic
183C2×C3×D8—54no—
184C2×C3×D8—104no—
185C22×C3×C8—51no—
186#953—102no—
187#940—101no—
188#938—54no—
189#936—101no—
190C2×#214C2×D512yescomplemented
191#932—24no—
192C2×#213C2×D512yescomplemented
193#926—51no—
194C2×#208C2×D511yescharacteristic, complemented
195#832—54no—
196#821—52no—
197(C2×D3)⋊C8—54no—
198#816—52no—
199C24×C5—21no—
200C23×D5—21no—
201C23×D5—62no—
202C5×#41—34no—
203C5×#41—62no—
204C2×C5×Q8—31no—
205C2×C5×D4—22no—
206C2×C5×D4—21no—
207C2×C5×D4—22no—
208C2×C5×D4—31no—
209C2×C5×D4—61no—
210C2×C5×D4C22×D312yes—
211C22×C4×C5—61no—
212C22×C4×C5C22×D311yescharacteristic
213C2×C22⋊D5—32no—
214C2×C22⋊D5—62no—
215C2×C22⋊D5—64no—
216#713—64no—
217#713—64no—
218D4×D5—64no—
219D4×D5—616no—
220D4×D5—64no—
221#709—68no—
222#709—62no—
223#709—62no—
224C2×D20—21no—
225C2×D20—22no—
226C2×D20—31no—
227C2×D20—68no—
228C2×D20—62no—
229C2×D20#6714yescomplemented
230C2×D20C22×D312yes—
231C2×C4×D5—32no—
232C2×C4×D5—62no—
233C2×Dic10—31no—
234C5×SD16—64no—
235C5×D8—64no—
236C5×M16—62no—
237C2×C5×C8—32no—
238C22⋊Dic5—64no—
239C22⋊Dic5—61no—
240#686—28no—
241C4⋊Dic5—32no—
242C4×Dic5—61no—
243C2×#168—22no—
244C2×#168C22×D312yes—
245C2×H(5,𝔽2)—151no—
246C2×AGL(1,ℤ/8)—31no—
247C22×D8—51no—
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—42no—
256C22×C3×C5—44no—
257C22×C3×C5—84no—
258C22×C3×C5#12012yes—
259C22×C3×C5C22×D411yescharacteristic
260C2×D15—22no—
261C2×D15—24no—
262C2×C5×D3—22no—
263C2×C5×D3—42no—
264C2×C3×D5—24no—
265C2×C3×D5—44no—
266C2×C3×D5—84no—
267D3×D5—88no—
268C3×C4×C5#12012yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272Dic15—42no—
273C5×Dic3—22no—
274C24×C3—21no—
275C24×C3—101no—
276C23×D3—102no—
277C2×C3×D4—22no—
278C2×C3×D4—21no—
279C2×C3×D4—22no—
280C2×C3×D4—54no—
281C2×C3×D4—52no—
282C2×C3×D4—101no—
283C2×C3×D4—102no—
284C2×C3×D4C22×D512yes—
285C22×C3×C4C22×D511yescharacteristic
286C2×#67—21no—
287C2×#67—52no—
288C2×#67—102no—
289C2×#67—102no—
290C2×#67—1016no—
291C2×#67—104no—
292C22×Dic3—102no—
293#237—104no—
294#237—108no—
295#237—104no—
296D3×D4—108no—
297D3×D4—104no—
298D3×D4—104no—
299#235—22no—
300#235—102no—
301#235—102no—
302#235C22⋊D514yescomplemented
303C2×D12—51no—
304C2×D12C22×D511yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—52no—
307C2×Dic6—51no—
308C2×Dic6C22×D511yescharacteristic
309C3×D8—108no—
310C2×C3×C8—52no—
311C2×C3×C8—102no—
312#217—104no—
313#217—101no—
314#214—24no—
315#213—24no—
316C4⋊Dic3—52no—
317C4×Dic3—101no—
318#208—22no—
319C2×C3⋊C8C22×D512yes—
320C23×C5—22no—
321C23×C5—42no—
322C23×C5—61no—
323C23×C5—82no—
324C23×C5D3×D411yescharacteristic
325C22×D5—22no—
326C22×D5—24no—
327C22×D5—32no—
328C22×D5—68no—
329C22×D5—82no—
330C22×D5—244no—
331C5×Q8—32no—
332C5×Q8—61no—
333C5×D4—22no—
334C5×D4—22no—
335C5×D4—32no—
336C5×D4—42no—
337C5×D4—64no—
338C5×D4—61no—
339C2×C4×C5—61no—
340C2×C4×C5—64no—
341C2×C4×C5D3×D412yes—
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5C2×#6712yes—
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—68no—
346C22⋊D5—64no—
347C22⋊D5—244no—
348C2×Dic5—32no—
349C2×Dic5—62no—
350D20—24no—
351D20—22no—
352D20—68no—
353D20—62no—
354D20C2×#6714yes—
355C4×D5—68no—
356C4×D5—62no—
357C4×D5—62no—
358Dic10—62no—
359C5×C8—62no—
360#168—22no—
361H(5,𝔽2)—304no—
362H(5,𝔽2)—304no—
363C2×#41—31no—
364C2×#41—151no—
365C2×#41—152no—
366C2×#41—301no—
367C22×D4—51no—
368C22×D4—152no—
369C22×D4—301no—
370C22×D4—302no—
371C22×D4D3×D511yescharacteristic, complemented
372AGL(1,ℤ/8)—64no—
373C2×SD16—32no—
374C2×D8—32no—
375C2×D8—54no—
376C2×D8—104no—
377C2×M16—31no—
378C22×C8—51no—
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—82no—
390C2×C3×C5C2×#12011yescharacteristic
391C2×C3×C5#57612yes—
392D15—42no—
393C3×D5—44no—
394C5×D3—42no—
395C23×C3—22no—
396C23×C3—42no—
397C23×C3—82no—
398C23×C3—102no—
399C23×C3—104no—
400C23×C3—402no—
401C23×C3D4×D511yescharacteristic
402C22×D3—21no—
403C22×D3—52no—
404C22×D3—108no—
405C22×D3—404no—
406C3×D4—22no—
407C3×D4—22no—
408C3×D4—42no—
409C3×D4—54no—
410C3×D4—102no—
411C3×D4—104no—
412C2×C3×C4D4×D512yes—
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4C2×C22⋊D512yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—24no—
417#67—108no—
418#67—108no—
419#67—104no—
420#67—404no—
421C2×Dic3—21no—
422C2×Dic3—52no—
423C2×Dic3—108no—
424C2×Dic3—102no—
425D12—21no—
426D12—102no—
427D12C2×C22⋊D512yes—
428C4×D3—24no—
429C4×D3—102no—
430C4×D3—102no—
431Dic6—21no—
432Dic6—102no—
433Dic6C2×C22⋊D512yes—
434C3×C8—102no—
435C3⋊C8—22no—
436C22×C5—22no—
437C22×C5—44no—
438C22×C5—42no—
439C22×C5—62no—
440C22×C5—84no—
441C22×C5—122no—
442C22×C5#93712yes—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—24no—
445C2×D5—44no—
446C2×D5—64no—
447C2×D5—62no—
448C2×D5—84no—
449C2×D5—248no—
450C4×C5—62no—
451C4×C5#93712yes—
452C4×C5C2×D3×D411yescharacteristic
453C4×C5C22×#6711yescharacteristic
454Dic5—62no—
455Dic5—122no—
456C24—21no—
457C24—101no—
458C24—302no—
459#41—34no—
460#41—62no—
461#41—308no—
462#41—304no—
463#41—304no—
464#41—302no—
465#41—302no—
466C2×Q8—31no—
467C2×Q8—151no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—31no—
472C2×D4—54no—
473C2×D4—52no—
474C2×D4—61no—
475C2×D4—102no—
476C2×D4—101no—
477C2×D4—152no—
478C2×D4—151no—
479C2×D4—308no—
480C2×D4—302no—
481C2×D4—302no—
482C2×D4—304no—
483C2×D4—304no—
484C2×D4—3016no—
485C2×D4—304no—
486C2×D4C2×D3×D512yes—
487C22×C4—61no—
488C22×C4—152no—
489C22×C4—302no—
490C22×C4C2×D3×D511yescharacteristic
491SD16—64no—
492D8—64no—
493D8—108no—
494M16—62no—
495C2×C8—32no—
496C2×C8—52no—
497C2×C8—102no—
498C4⋊C4—152no—
499C22⋊C4—304no—
500C22⋊C4—301no—
501C42—301no—
502C3×C5#300811yescharacteristic, complemented, Hall
503C22×C3—22no—
504C22×C3—44no—
505C22×C3—42no—
506C22×C3—84no—
507C22×C3—104no—
508C22×C3—204no—
509C22×C3—404no—
510C22×C3#408312yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—22no—
513C2×D3—42no—
514C2×D3—104no—
515C2×D3—102no—
516C2×D3—408no—
517C3×C4#408312yes—
518C3×C4C2×D4×D511yescharacteristic
519C3×C4C22×C22⋊D511yescharacteristic
520Dic3—22no—
521Dic3—102no—
522Dic3—202no—
523C2×C5—22no—
524C2×C5—82no—
525C2×C5—122no—
526C2×C5#575712yes—
527C2×C5C2×#93711yescharacteristic
528D5—44no—
529D5—122no—
530C23—22no—
531C23—42no—
532C23—61no—
533C23—82no—
534C23—102no—
535C23—104no—
536C23—152no—
537C23—308no—
538C23—402no—
539C23—1204no—
540C23#679011yescharacteristic
541Q8—32no—
542Q8—61no—
543Q8—302no—
544D4—22no—
545D4—22no—
546D4—32no—
547D4—42no—
548D4—54no—
549D4—64no—
550D4—61no—
551D4—102no—
552D4—104no—
553D4—308no—
554D4—308no—
555D4—304no—
556D4—302no—
557D4—1204no—
558C2×C4—61no—
559C2×C4—64no—
560C2×C4—152no—
561C2×C4—308no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4D5×#6712yes—
566C2×C4D3×C22⋊D512yes—
567C2×C4#679011yescharacteristic
568C2×C4C22×D3×D511yescharacteristic
569C8—62no—
570C8—102no—
571C2×C3—22no—
572C2×C3—82no—
573C2×C3—204no—
574C2×C3#6610812yes—
575C2×C3C2×#408311yescharacteristic
576D3—42no—
577D3—202no—
578C5#8383311yescharacteristic, complemented, Sylow
579C22—22no—
580C22—42no—
581C22—44no—
582C22—62no—
583C22—84no—
584C22—104no—
585C22—122no—
586C22—204no—
587C22—302no—
588C22—304no—
589C22—404no—
590C22—1208no—
591C22#9157712yes—
592C22C2×#679011yescharacteristic
593C4—62no—
594C4—302no—
595C4—602no—
596C4#9157712yes—
597C4C2×D5×#6711yescharacteristic
598C4C2×D3×C22⋊D511yescharacteristic
599C3#1061567811yescharacteristic, complemented, Sylow
600C2—22no—
601C2—82no—
602C2—122no—
603C2—204no—
604C2—602no—
605C2#1175470312yes—
606C2C2×#9157711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3008
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#92017C2semidirect
2. #11756564C2semidirect
3. C2×C5×#932C2semidirect
4. C22×C3×#686C2semidirect
5. #11749158C2semidirect
6. #11749153C2semidirect
7. #11748388C2semidirect
8. #11748367C2semidirect
9. #11748349C2semidirect
11. C22×C3×C5×D4C22semidirect
18. C2×#6777C22semidirect
20. C2×#6766C22semidirect
24. #91827C22semidirect
26. #91815C22semidirect
27. C2×C5×#214C22semidirect
29. C2×C5×#213C22semidirect
30. C2×C5×#208C22semidirect
32. C2×C3×#686C22semidirect
33. C22×C3×#168C22semidirect
34. #90973C22semidirect
35. #90967C22semidirect
36. #90965C22semidirect
37. #90957C22semidirect
42. C22×#686D3semidirect
65. C5×#235D4semidirect
71. C2×C3×D20D4semidirect
97. C2×#932D5semidirect
104. C22×C5×D4C2×D3semidirect
123. C2×#686C2×D3semidirect
125. C22×#168C2×D3semidirect
173. C22×C3×D4C2×D5semidirect
190. C2×#214C2×D5semidirect
192. C2×#213C2×D5semidirect
194. C2×#208C2×D5semidirect
229. C2×D20#67semidirect
302. #235C22⋊D5semidirect
371. C22×D4D3×D5semidirect
502. C3×C5#3008semidirect
578. C5#83833semidirect
599. C3#10615678semidirect

Maximal subgroups

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

subgroupindex
C2×#920172
#117565642
C2×C5×#9322
C22×C3×#6862
#117491582
#117491532
#117483882
#117483672
#117483492
#106156783
#838335