Finite Group Databasebeta

← #14458554

Subgroups — #14458554

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×D20C211yesmaximal, characteristic
2#11752648C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4C5×#4842C211yesmaximal, characteristic, complemented
5C3×#65123C211yesmaximal, characteristic, complemented
6#11748115C212yesmaximal, complemented
7D5×#821C212yesmaximal, complemented
8#11747897C212yesmaximal, complemented
9#11747614C212yesmaximal, complemented
10C4×#6659C211yesmaximal, characteristic, complemented
11#11746912C211yesmaximal, characteristic, complemented
12#10612806—31nomaximal, Hall
13C2×D3×D20—21no—
14C2×D5×D12C2212yes—
15C2×#6706C2212yescomplemented
16#91763C2211yescharacteristic
17C4×Dic30C2211yescharacteristic, complemented
18C4×C5×D12C2211yescharacteristic
19C5×#869C2211yescharacteristic, complemented
20C2×C3×C8×D5C2212yescomplemented
21C3×C4×D20C2211yescharacteristic
22#91476—22no—
23#91460—21no—
24#91450C2212yes—
25#91434—21no—
26#91421—22no—
27D5×C4⋊Dic3C2212yescomplemented
28#91384—21no—
29#91360C2212yescomplemented
30C2×#6659C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic, complemented
32#91105C2212yescomplemented
33C5×#821C2212yes—
34C5×#817C2212yescomplemented
35C3×#3952C2212yescomplemented
36C3×C4×#168C2211yescharacteristic, complemented
37#90985C2211yescharacteristic, complemented
38#90975C2211yescharacteristic, complemented
39#90969C2212yescomplemented
40#90969C2212yescomplemented
41#90967C2211yescharacteristic
42#79439—51nomaximal, Hall
43#66064—31no—
44D4×D20—31no—
45C5×#476—31no—
46#65377—31no—
47C4×#687—31no—
48#65153—32no—
49#65152—32no—
50#65137—31no—
51#65123D311yescharacteristic, complemented
52#65065—32no—
53D5×#102—32no—
54C22×D3×D5—22no—
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×Dic30C2311yescharacteristic
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6—21no—
62C2×C3×D20D411yescharacteristic
63C2×C3×C4×D5C2312yes—
64C2×#1203—22no—
65C2×#1202—22no—
66C2×D5×Dic3—22no—
67D3×D20—44no—
68D5×D12—24no—
69D5×D12—42no—
70C2×C3×C5×C8C2312yes—
71C3×C42×C5C2311yescharacteristic
72C4⋊Dic15C2311yescharacteristic
73#6712—21no—
74C4×Dic15—21no—
75#6706—42no—
76C5×(C2×D3)⋊C4—21no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C5×C4⋊Dic3C2311yescharacteristic
80C3×#685D412yes—
81C3×C4⋊Dic5D411yescharacteristic
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84C3×C8×D5—42no—
85Dic3⋊Dic5—22no—
86#6668—22no—
87#6667—22no—
88#6665—22no—
89#6659—22no—
90D4×D12—51no—
91#5543—51no—
92C3×C8×D4—51no—
93#5114—52no—
94C2×#821—52no—
95#4848—51no—
96#4842D511yescharacteristic, complemented
97#4735—52no—
98#4731—52no—
99#4694—51no—
100C4×#204—51no—
101C2×D4×D5—32no—
102C22×D20—61no—
103C5×C4⋊Q8—31no—
104C4×C5×D4—31no—
105#4092—62no—
106C2×#687—31no—
107#4076—61no—
108C2×#677—32no—
109C2×C8×D5C2×D312yescomplemented
110#4043—32no—
111#4041—32no—
112#4039—61no—
113D5×C4⋊C4—32no—
114#4036—61no—
115#4028—62no—
116#4020—31no—
117C4×D20C2×D311yescharacteristic
118C4×Dic10—31no—
119C5×#106—32no—
120C5×C4⋊C8C2×D311yescharacteristic, complemented
121C5×#102—32no—
122#3964—31no—
123#3953—32no—
124#3952C2×D312yescomplemented
125#3942—31no—
126#3941—32no—
127#3941—32no—
128#3940—31no—
129C4×#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C22×D15—22no—
132C22×C5×D3—21no—
133C22×C3×D5C2×D412yes—
134C2×D3×D5—44no—
135C2×D3×D5—44no—
136C2×D3×D5—82no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141C2×Dic15—21no—
142D60—22no—
143D60—22no—
144D60—42no—
145D60—81no—
146Dic30—21no—
147Dic30—21no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—21no—
150C5×D12—21no—
151C5×D12#4112yes—
152C4×C5×D3—42no—
153C5×Dic6—81no—
154C2×C3×Dic5C2×D412yes—
155C3×D20SD1614yescomplemented
156C3×C4×D5—22no—
157C3×C4×D5—22no—
158#1203—44no—
159#1202—44no—
160D5×Dic3—82no—
161C3×C5×C8—22no—
162C3×#168—21no—
163C3×#168—21no—
164C2×D3×D4—101no—
165C22×D12—52no—
166C22×C3×C8—52no—
167C3×C4×D4—51no—
168D4×Dic3—101no—
169#930—52no—
170C2×C4⋊Dic3—52no—
171#924—52no—
172C2×#204—51no—
173C2×#204—52no—
174#895—101no—
175#890—101no—
176#882—102no—
177#878—102no—
178#874—51no—
179C4×D12C2×D511yescharacteristic
180#869C2×D511yescharacteristic, complemented
181C4×Dic6—51no—
182C3×C4⋊C8C2×D511yescharacteristic, complemented
183C3×C22⋊C8—52no—
184C3×C4×C8—51no—
185#821—51no—
186#821—52no—
187#821—52no—
188#821—52no—
189#821C2×D512yes—
190#817—51no—
191#817C2×D512yescomplemented
192#816—51no—
193C23×D5—62no—
194C2×C5×Q8—61no—
195C2×C5×D4—31no—
196C22×C4×C5—61no—
197C2×C22⋊D5—62no—
198D4×D5—64no—
199D4×D5—122no—
200C2×D20—32no—
201C2×D20—62no—
202C2×D20—61no—
203C2×D20—61no—
204C2×D20—124no—
205C2×D20D1211yescharacteristic
206C2×C4×D5—62no—
207C2×C4×D5C22×D312yes—
208C2×Dic10—31no—
209C2×C5×C8C22×D312yes—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—32no—
212C5×C4⋊C4—61no—
213C5×C22⋊C4—61no—
214C42×C5C22×D311yescharacteristic
215#687—62no—
216#685—62no—
217#685—62no—
218#685D1212yes—
219C4⋊Dic5—31no—
220C4⋊Dic5—62no—
221C4⋊Dic5D1211yescharacteristic
222#683—61no—
223#683—62no—
224C4×Dic5—61no—
225C2×#168C22×D311yescharacteristic
226C2×#168C22×D311yescharacteristic
227#677—122no—
228C8×D5—42no—
229#554—151no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—31no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—51no—
239C2×#102—152no—
240C22×C3×C5C22×D411yescharacteristic
241C2×D15—42no—
242C2×D15—42no—
243C2×D15—42no—
244C2×C5×D3—22no—
245C2×C5×D3—41no—
246C2×C5×D3—41no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5C2×SD1614yes—
250D3×D5—88no—
251C3×C4×C5—21no—
252C3×C4×C5C2×SD1612yes—
253C3×C4×C5C2×#4111yescharacteristic
254C3×C4×C5H(5,𝔽2)11yescharacteristic
255Dic15—41no—
256Dic15—41no—
257C3×Dic5—22no—
258C5×Dic3—41no—
259C5×Dic3—42no—
260C23×D3—102no—
261C2×C3×D4—51no—
262C22×C3×C4—52no—
263C2×#67—102no—
264C22×Dic3—102no—
265D3×D4—204no—
266C2×D12—52no—
267C2×D12—104no—
268C2×D12—102no—
269C2×D12—101no—
270C2×D12—101no—
271C2×D12—202no—
272C2×D12C22×D511yescharacteristic
273C2×C4×D3—21no—
274C2×Dic6—21no—
275C2×Dic6—51no—
276C2×C3×C8—51no—
277C2×C3×C8—51no—
278C2×C3×C8—202no—
279C2×C3×C8C22×D512yes—
280C3×C4⋊C4—51no—
281C3×C22⋊C4—52no—
282C3×C42C22×D511yescharacteristic
283#217—102no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—102no—
286C4⋊Dic3—21no—
287C4⋊Dic3—51no—
288C4⋊Dic3—102no—
289C4⋊Dic3C22×D511yescharacteristic
290C4⋊Dic3C22×D512yes—
291Dic3⋊C4—102no—
292Dic3⋊C4—101no—
293C4×Dic3—101no—
294#204—102no—
295#204—202no—
296C23×C5—61no—
297C22×D5—62no—
298C22×D5—124no—
299C22×D5—124no—
300C22×D5—242no—
301C22×D5C2×D1212yes—
302C5×Q8—241no—
303C5×D4—32no—
304C5×D4—61no—
305C2×C4×C5—62no—
306C2×C4×C5—61no—
307C2×C4×C5—122no—
308C2×C4×C5C2×D1211yescharacteristic
309C2×C4×C5C2×D1211yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C2×Dic5—61no—
313C2×Dic5—61no—
314C2×Dic5C2×D1212yes—
315D20—62no—
316D20—62no—
317D20—124no—
318D20—122no—
319D20—241no—
320D20#20414yescomplemented
321C4×D5—22no—
322C4×D5—22no—
323C4×D5—242no—
324Dic10—61no—
325Dic10—61no—
326C5×C8—22no—
327#168—21no—
328#168—21no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—52no—
334C4⋊Q8—31no—
335#127—151no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—151no—
343C4×D4—31no—
344C4×D4—51no—
345C4×D4—301no—
346C2×C4⋊C4—152no—
347#106—32no—
348#106—151no—
349C4⋊C8D3×D511yescharacteristic, complemented
350#103—151no—
351#102—32no—
352#102—152no—
353#102—152no—
354#102—151no—
355#102—152no—
356C22⋊C8—52no—
357C4×C8—51no—
358C2×C3×C5#54611yescharacteristic
359C2×C3×C5C22×SD1611yescharacteristic
360C2×C3×C5#57611yescharacteristic
361D15—82no—
362C3×D5—24no—
363C5×D3—42no—
364C23×C3—52no—
365C22×D3—21no—
366C22×D3—102no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×D4—54no—
371C2×C3×C4—52no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4D4×D511yescharacteristic
376C2×C3×C4C23×D511yescharacteristic
377#67—204no—
378C2×Dic3—22no—
379C2×Dic3—21no—
380C2×Dic3—101no—
381C2×Dic3—101no—
382C2×Dic3—402no—
383D12—21no—
384D12—102no—
385D12—102no—
386D12—204no—
387D12—202no—
388D12—401no—
389D12#71312yes—
390C4×D3—42no—
391Dic6—81no—
392Dic6—101no—
393Dic6—101no—
394C3×C8—22no—
395C3×C8—101no—
396C3×C8—101no—
397C22×C5—62no—
398C22×C5—121no—
399C22×C5—121no—
400C22×C5C22×D1211yescharacteristic
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—122no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—248no—
407C2×D5C2×#20414yes—
408C4×C5—21no—
409C4×C5—121no—
410C4×C5—122no—
411C4×C5C2×#20412yes—
412C4×C5#100411yescharacteristic
413C4×C5D3×#4111yescharacteristic
414Dic5—22no—
415Dic5—121no—
416Dic5—121no—
417C24—302no—
418C2×Q8—61no—
419C2×Q8—151no—
420C2×D4—31no—
421C2×D4—51no—
422C2×D4—152no—
423C2×D4—302no—
424C2×D4—302no—
425C2×D4—304no—
426C2×D4—301no—
427C2×D4—301no—
428C2×D4—602no—
429C2×D4—604no—
430C22×C4—52no—
431C22×C4—61no—
432C22×C4—302no—
433SD16—302no—
434SD16—602no—
435C2×C8—51no—
436C2×C8—51no—
437C2×C8—202no—
438C2×C8C2×D3×D512yes—
439C4⋊C4—32no—
440C4⋊C4—31no—
441C4⋊C4—51no—
442C4⋊C4—61no—
443C4⋊C4—151no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—301no—
447C22⋊C4—52no—
448C22⋊C4—61no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—301no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—54no—
455C22×C3—102no—
456C22×C3—102no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—22no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—202no—
462C2×D3—202no—
463C2×D3—202no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—102no—
467C3×C4D5×SD1612yes—
468C3×C4C2×#71311yescharacteristic
469C3×C4#414911yescharacteristic
470Dic3—41no—
471Dic3—42no—
472Dic3—201no—
473Dic3—201no—
474C2×C5—122no—
475C2×C5#555411yescharacteristic
476C2×C5C22×#20411yescharacteristic
477C2×C5#575211yescharacteristic
478D5—24no—
479D5—242no—
480C23—52no—
481C23—61no—
482C23—302no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—241no—
487Q8—301no—
488Q8—301no—
489D4—32no—
490D4—54no—
491D4—61no—
492D4—302no—
493D4—302no—
494D4—604no—
495D4—604no—
496D4—602no—
497D4—1201no—
498C2×C4—52no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—122no—
504C2×C4—301no—
505C2×C4—301no—
506C2×C4—1202no—
507C2×C4D5×D1211yescharacteristic
508C2×C4D5×D1211yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—22no—
511C8—101no—
512C8—101no—
513C2×C3—104no—
514C2×C3#6596411yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610811yescharacteristic
517D3—42no—
518D3—402no—
519C5#7943911yescharacteristic, complemented, Sylow
520C22—54no—
521C22—62no—
522C22—102no—
523C22—102no—
524C22—121no—
525C22—121no—
526C22—602no—
527C22—602no—
528C22—602no—
529C22—1208no—
530C22C2×D5×D1211yescharacteristic
531C4—21no—
532C4—102no—
533C4—122no—
534C4—121no—
535C4—601no—
536C4—601no—
537C4D5×#20412yes—
538C4#9202611yescharacteristic
539C4D3×#71311yescharacteristic
540C3#1061280611yescharacteristic, complemented, Sylow
541C2—104no—
542C2—122no—
543C2—1202no—
544C2#1175387611yescharacteristic
545C2C2×D5×#20411yescharacteristic
546C2#1175402411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalD12×D20C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3295
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
2. #11752648C2semidirect
3. #11750949C2semidirect
4. C5×#4842C2semidirect
5. C3×#65123C2semidirect
6. #11748115C2semidirect
7. D5×#821C2semidirect
8. #11747897C2semidirect
9. #11747614C2semidirect
10. C4×#6659C2semidirect
11. #11746912C2semidirect
15. C2×#6706C22semidirect
17. C4×Dic30C22semidirect
19. C5×#869C22semidirect
20. C2×C3×C8×D5C22semidirect
27. D5×C4⋊Dic3C22semidirect
29. #91360C22semidirect
31. C3×C5×C4⋊C8C22semidirect
32. #91105C22semidirect
34. C5×#817C22semidirect
35. C3×#3952C22semidirect
36. C3×C4×#168C22semidirect
37. #90985C22semidirect
38. #90975C22semidirect
39. #90969C22semidirect
40. #90969C22semidirect
51. #65123D3semidirect
96. #4842D5semidirect
109. C2×C8×D5C2×D3semidirect
120. C5×C4⋊C8C2×D3semidirect
124. #3952C2×D3semidirect
129. C4×#168C2×D3semidirect
155. C3×D20SD16semidirect
180. #869C2×D5semidirect
182. C3×C4⋊C8C2×D5semidirect
191. #817C2×D5semidirect
320. D20#204semidirect
349. C4⋊C8D3×D5semidirect
453. C3×C5#3295semidirect
519. C5#79439semidirect
540. C3#10612806semidirect

Maximal subgroups

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

subgroupindex
D12×D202
#117526482
#117509492
C5×#48422
C3×#651232
#117481152
D5×#8212
#117478972
#117476142
C4×#66592
#117469122
#106128063
#794395