Finite Group Databasebeta

← #14458513

Subgroups — #14458513

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
1D4×D60C211yesmaximal, characteristic
2C5×#5543C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748554C212yesmaximal, complemented
5#11748535C212yesmaximal, complemented
6C2×#90969C212yesmaximal, complemented
7#11748374C212yesmaximal, complemented
8#11747078C211yesmaximal, characteristic, complemented
9C4×#6660C211yesmaximal, characteristic, complemented
10#11746912C211yesmaximal, characteristic, complemented
11#11746885C211yesmaximal, characteristic, complemented
12#10615365—31nomaximal, Hall
13C2×D4×D15—21no—
14C22×D60C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16#91819C2212yes—
17#91784—21no—
18#91771—22no—
19#91763C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C5×D4×Dic3—21no—
22C2×C5×C4⋊Dic3C2212yescomplemented
23C5×#924C2212yescomplemented
24C5×#890—21no—
25C5×#878—22no—
26C5×#869C2211yescharacteristic, complemented
27C4×C5×Dic6C2211yescharacteristic, complemented
28C22×C3×#168C2212yescomplemented
29C2×#6660C2211yescharacteristic
30C2×#6660C2212yescomplemented
31C3×C22⋊#168C2212yescomplemented
32C3×C4⋊#168C2211yescharacteristic, complemented
33C3×C4×#168C2211yescharacteristic, complemented
34#90985C2211yescharacteristic, complemented
35#90985C2212yescomplemented
36#90973C2211yescharacteristic, complemented
37#90969C2211yescharacteristic
38#90969C2212yes—
39#90969C2212yescomplemented
40#90969C2212yescomplemented
41#90969C2212yescomplemented
42#79439—51nomaximal, Hall
43C5×#554—31no—
44D4×D20—31no—
45#65377—31no—
46#65373—31no—
47#65337—32no—
48#65335—32no—
49#65316—31no—
50C4×#688—31no—
51D4×#168D311yescharacteristic, complemented
52#65257—32no—
53C2×#3941—32no—
54C23×D15—22no—
55C2×C3×C5×D4D411yescharacteristic
56C22×C3×C4×C5C2312yes—
57C2×#1220—22no—
58D4×D15—44no—
59C2×D60—24no—
60C2×D60—21no—
61C2×D60—22no—
62C2×D60—21no—
63C2×D60—42no—
64C2×D60C2312yes—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C22×C5×Dic3—22no—
68C2×C5×Dic6—21no—
69C2×C5×Dic6C2311yescharacteristic
70C3×C5×C4⋊C4D411yescharacteristic
71C3×C5×C22⋊C4D412yes—
72C3×C42×C5C2311yescharacteristic
73#6714—21no—
74#6714—22no—
75C4⋊Dic15C2311yescharacteristic
76C5×#217—22no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3—22no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2312yes—
81C5×Dic3⋊C4—21no—
82C5×Dic3⋊C4—22no—
83C4×C5×Dic3—21no—
84C2×C3×#168—42no—
85C2×C3×#168C2311yescharacteristic
86C2×C3×#168C2312yes—
87C2×C3×#168C2311yescharacteristic
88#6660—22no—
89#6660—42no—
90D4×D12—51no—
91#5543D511yescharacteristic, complemented
92C3×C8×D4—51no—
93#5114—52no—
94C2×#821—52no—
95#4848—51no—
96#4842—51no—
97#4735—52no—
98#4731—52no—
99#4694—51no—
100C4×#204—51no—
101C2×D4×D5—61no—
102C22×D20—32no—
103C5×C4⋊Q8—31no—
104C5×#125—61no—
105C5×C22⋊Q8—32no—
106C5×C22⋊Q8—62no—
107C4×C5×Q8—31no—
108C4×C5×D4—61no—
109C4×C5×D4C2×D311yescharacteristic
110C2×C5×C4⋊C4—32no—
111C2×#688—31no—
112C2×#688—32no—
113#4076—32no—
114C22×#168C2×D312yescomplemented
115#4041—61no—
116#4028—62no—
117#4020—31no—
118C4×D20—31no—
119#3967—31no—
120C22⋊#168C2×D312yescomplemented
121#3941—31no—
122#3941—32no—
123#3941—32no—
124#3941—32no—
125#3941—32no—
126#3940—31no—
127#3940—32no—
128C4⋊#168C2×D311yescharacteristic, complemented
129C4×#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C23×C3×C5C2×D412yes—
132C22×D15—21no—
133C22×D15—22no—
134C22×D15—44no—
135C22×D15—44no—
136C22×D15—82no—
137C3×C5×D4SD1614yescomplemented
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144#1220—44no—
145C2×Dic15—21no—
146D60—22no—
147D60—21no—
148D60—22no—
149D60—44no—
150D60—42no—
151D60—81no—
152D60#4112yes—
153C4×D15—42no—
154C2×C5×Dic3—21no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—82no—
158C5×Dic6—21no—
159C5×Dic6—21no—
160C5×Dic6—81no—
161C3×#168—21no—
162C3×#168—22no—
163C3×#168—21no—
164C2×D3×D4—101no—
165C22×D12—52no—
166C22×C3×C8—52no—
167C3×C4×D4C2×D511yescharacteristic
168D4×Dic3—21no—
169#930—52no—
170C2×C4⋊Dic3C2×D512yescomplemented
171#924C2×D512yescomplemented
172C2×#204—51no—
173C2×#204—52no—
174#895—101no—
175#890—21no—
176#882—102no—
177#878—22no—
178#874—51no—
179C4×D12—51no—
180#869C2×D511yescharacteristic, complemented
181C4×Dic6C2×D511yescharacteristic, complemented
182C3×C4⋊C8—51no—
183C3×C22⋊C8—52no—
184C3×C4×C8—51no—
185#821—51no—
186#821—52no—
187#821—52no—
188#821—52no—
189#821—52no—
190#817—51no—
191#817—52no—
192#816—51no—
193C23×D5—62no—
194C2×C5×Q8—31no—
195C2×C5×Q8—61no—
196C2×C5×D4D1211yescharacteristic
197C22×C4×C5—62no—
198C22×C4×C5C22×D312yes—
199C2×C22⋊D5—62no—
200D4×D5—124no—
201C2×D20—31no—
202C2×D20—32no—
203C2×D20—64no—
204C2×D20—62no—
205C2×D20—61no—
206C2×D20—61no—
207C2×D20—122no—
208C2×C4×D5—61no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—32no—
211C5×C4⋊C4—62no—
212C5×C4⋊C4—61no—
213C5×C4⋊C4—61no—
214C5×C4⋊C4—62no—
215C5×C4⋊C4D1211yescharacteristic
216C5×C22⋊C4—62no—
217C5×C22⋊C4D1212yes—
218C42×C5—61no—
219C42×C5C22×D311yescharacteristic
220#688—62no—
221#688—122no—
222#685—61no—
223#685—62no—
224C4⋊Dic5—31no—
225C2×#168—42no—
226C2×#168C22×D311yescharacteristic
227C2×#168C22×D311yescharacteristic
228C2×#168C22×D312yes—
229#554—31no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—151no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—151no—
238C8×D4—51no—
239C2×#102—152no—
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5C2×SD1614yes—
243C22×C3×C5C22×D411yescharacteristic
244C2×D15—22no—
245C2×D15—41no—
246C2×D15—41no—
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—42no—
250C2×D15—88no—
251C3×C4×C5—22no—
252C3×C4×C5—21no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—41no—
257C5×Dic3—41no—
258C5×Dic3—42no—
259C5×Dic3—41no—
260C23×D3—102no—
261C2×C3×D4C22⋊D511yescharacteristic
262C22×C3×C4C22×D512yes—
263C2×#67—102no—
264C22×Dic3—22no—
265D3×D4—204no—
266C2×D12—51no—
267C2×D12—52no—
268C2×D12—104no—
269C2×D12—101no—
270C2×D12—102no—
271C2×D12—101no—
272C2×D12—202no—
273C2×C4×D3—101no—
274C2×Dic6—21no—
275C2×Dic6C22×D511yescharacteristic
276C2×C3×C8—51no—
277C2×C3×C8—51no—
278C2×C3×C8—52no—
279C2×C3×C8—202no—
280C3×C4⋊C4C22⋊D511yescharacteristic
281C3×C22⋊C4C22⋊D512yes—
282C3×C42C22×D511yescharacteristic
283#217—22no—
284(C2×D3)⋊C4—101no—
285(C2×D3)⋊C4—102no—
286C4⋊Dic3—21no—
287C4⋊Dic3—22no—
288C4⋊Dic3—51no—
289C4⋊Dic3C22×D511yescharacteristic
290C4⋊Dic3C22×D512yes—
291Dic3⋊C4—21no—
292Dic3⋊C4—22no—
293C4×Dic3—21no—
294#204—102no—
295#204—202no—
296C23×C5C2×D1212yes—
297C22×D5—61no—
298C22×D5—62no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—61no—
303C5×Q8—61no—
304C5×Q8—241no—
305C5×D4#20414yescomplemented
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—62no—
311C2×C4×C5—242no—
312C2×C4×C5C2×D1211yescharacteristic
313C2×C4×C5C2×D1212yes—
314C2×C4×C5C2×D1211yescharacteristic
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—124no—
317C2×Dic5—61no—
318D20—32no—
319D20—61no—
320D20—62no—
321D20—62no—
322D20—124no—
323D20—122no—
324D20—241no—
325C4×D5—122no—
326#168—21no—
327#168—22no—
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—61no—
337C22⋊Q8—32no—
338C22⋊Q8—62no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—31no—
343C4×D4—61no—
344C4×D4—151no—
345C4×D4D3×D511yescharacteristic
346C2×C4⋊C4—32no—
347#106—151no—
348#106—152no—
349C4⋊C8—51no—
350#103—151no—
351#102—151no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—52no—
357C4×C8—51no—
358C2×C3×C5—24no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362D15—42no—
363D15—82no—
364C23×C3C2×C22⋊D512yes—
365C22×D3—101no—
366C22×D3—102no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×D4#68814yescomplemented
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4C2×C22⋊D512yes—
374C2×C3×C4C2×C22⋊D511yescharacteristic
375C2×C3×C4C2×C22⋊D511yescharacteristic
376C2×C3×C4C23×D511yescharacteristic
377#67—204no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—82no—
382C2×Dic3—101no—
383D12—52no—
384D12—102no—
385D12—101no—
386D12—102no—
387D12—204no—
388D12—202no—
389D12—401no—
390C4×D3—202no—
391Dic6—21no—
392Dic6—21no—
393Dic6—81no—
394C3×C8—101no—
395C3×C8—102no—
396C3×C8—101no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5C2×#20414yes—
400C22×C5C22×D1211yescharacteristic
401C2×D5—62no—
402C2×D5—121no—
403C2×D5—121no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—122no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—22no—
410C4×C5—121no—
411C4×C5—122no—
412C4×C5—121no—
413C4×C5C2×#20412yes—
414C4×C5#100411yescharacteristic
415C4×C5D3×#4111yescharacteristic
416Dic5—121no—
417C24—302no—
418C2×Q8—31no—
419C2×Q8—61no—
420C2×D4—151no—
421C2×D4—152no—
422C2×D4—304no—
423C2×D4—302no—
424C2×D4—302no—
425C2×D4—301no—
426C2×D4—301no—
427C2×D4—602no—
428C2×D4—604no—
429C2×D4#120311yescharacteristic
430C22×C4—62no—
431C22×C4—301no—
432C22×C4C2×D3×D512yes—
433SD16—302no—
434SD16—602no—
435C2×C8—51no—
436C2×C8—51no—
437C2×C8—52no—
438C2×C8—202no—
439C4⋊C4—31no—
440C4⋊C4—32no—
441C4⋊C4—62no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—62no—
445C4⋊C4—151no—
446C4⋊C4#120311yescharacteristic
447C22⋊C4—62no—
448C22⋊C4—301no—
449C22⋊C4—302no—
450C22⋊C4#120312yes—
451C42—61no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—22no—
456C22×C3C2×#68814yes—
457C22×C3C22×C22⋊D511yescharacteristic
458C2×D3—102no—
459C2×D3—201no—
460C2×D3—201no—
461C2×D3—202no—
462C2×D3—202no—
463C2×D3—202no—
464C2×D3—408no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4C2×#68812yes—
468C3×C4D5×#4111yescharacteristic
469C3×C4#414911yescharacteristic
470Dic3—41no—
471Dic3—42no—
472Dic3—41no—
473Dic3—201no—
474C2×C5—24no—
475C2×C5#555411yescharacteristic
476C2×C5C22×#20411yescharacteristic
477C2×C5#575211yescharacteristic
478D5—122no—
479D5—242no—
480C23—301no—
481C23—302no—
482C23—604no—
483C23—604no—
484C23—1202no—
485C23C2×#120312yes—
486Q8—61no—
487Q8—61no—
488Q8—241no—
489D4—152no—
490D4—302no—
491D4—301no—
492D4—302no—
493D4—604no—
494D4—604no—
495D4—602no—
496D4—1201no—
497D4#666014yescomplemented
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—242no—
504C2×C4—301no—
505C2×C4—602no—
506C2×C4C2×#120311yescharacteristic
507C2×C4C2×#120312yes—
508C2×C4C2×#120311yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—101no—
511C8—101no—
512C8—102no—
513C2×C3—24no—
514C2×C3C22×#68811yescharacteristic
515C2×C3#6616311yescharacteristic
516C2×C3#6616911yescharacteristic
517D3—202no—
518D3—402no—
519C5#7943911yescharacteristic, complemented, Sylow
520C22—22no—
521C22—22no—
522C22—302no—
523C22—601no—
524C22—601no—
525C22—602no—
526C22—602no—
527C22—602no—
528C22—1208no—
529C22C2×#666014yes—
530C22C22×#120311yescharacteristic
531C4—21no—
532C4—22no—
533C4—121no—
534C4—122no—
535C4—121no—
536C4—601no—
537C4C2×#666012yes—
538C4#9202411yescharacteristic
539C4#9202611yescharacteristic
540C3#1061536511yescharacteristic, complemented, Sylow
541C2—24no—
542C2—602no—
543C2—1202no—
544C2C22×#666011yescharacteristic
545C2#1175498211yescharacteristic
546C2#1175530511yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalD4×D60C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5543C2semidirect
3. C3×D4×#168C2semidirect
4. #11748554C2semidirect
5. #11748535C2semidirect
6. C2×#90969C2semidirect
7. #11748374C2semidirect
8. #11747078C2semidirect
9. C4×#6660C2semidirect
10. #11746912C2semidirect
11. #11746885C2semidirect
22. C2×C5×C4⋊Dic3C22semidirect
23. C5×#924C22semidirect
26. C5×#869C22semidirect
27. C4×C5×Dic6C22semidirect
28. C22×C3×#168C22semidirect
30. C2×#6660C22semidirect
31. C3×C22⋊#168C22semidirect
32. C3×C4⋊#168C22semidirect
33. C3×C4×#168C22semidirect
34. #90985C22semidirect
35. #90985C22semidirect
36. #90973C22semidirect
39. #90969C22semidirect
40. #90969C22semidirect
41. #90969C22semidirect
51. D4×#168D3semidirect
91. #5543D5semidirect
114. C22×#168C2×D3semidirect
120. C22⋊#168C2×D3semidirect
128. C4⋊#168C2×D3semidirect
129. C4×#168C2×D3semidirect
137. C3×C5×D4SD16semidirect
170. C2×C4⋊Dic3C2×D5semidirect
171. #924C2×D5semidirect
180. #869C2×D5semidirect
181. C4×Dic6C2×D5semidirect
305. C5×D4#204semidirect
370. C3×D4#688semidirect
453. C3×C5#3295semidirect
497. D4#6660semidirect
519. C5#79439semidirect
540. C3#10615365semidirect

Maximal subgroups

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

subgroupindex
D4×D602
C5×#55432
C3×D4×#1682
#117485542
#117485352
C2×#909692
#117483742
#117470782
C4×#66602
#117469122
#117468852
#106153653
#794395