Finite Group Databasebeta

← #14458516

Subgroups — #14458516

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
2C3×#65877C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748551C212yesmaximal, complemented
5#11748541C212yesmaximal, complemented
6#11748454C212yesmaximal, complemented
7C2×#90968C212yesmaximal, complemented
8#11747064C211yesmaximal, characteristic, complemented
9C4×#6658C211yesmaximal, characteristic, complemented
10#11746942C211yesmaximal, characteristic, complemented
11#11746910C211yesmaximal, characteristic, complemented
12#10611170—31nomaximal, Hall
13C2×D4×D15—21no—
14C22×D60C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16#91819C2212yes—
17#91784—21no—
18#91771—22no—
19#91763C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C22×C5×C3⋊C8C2212yescomplemented
22C3×D4×Dic5—21no—
23C2×C3×C4⋊Dic5C2212yescomplemented
24C3×#4070C2212yescomplemented
25C3×#4036—21no—
26C3×#4024—22no—
27C3×#4015C2211yescharacteristic, complemented
28C3×C4×Dic10C2211yescharacteristic, complemented
29C2×#6658C2211yescharacteristic
30C2×#6658C2212yescomplemented
31C5×#830C2212yescomplemented
32C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
33C4×C5×C3⋊C8C2211yescharacteristic, complemented
34#90987C2211yescharacteristic, complemented
35#90987C2212yescomplemented
36#90971C2211yescharacteristic, complemented
37#90968C2211yescharacteristic
38#90968C2212yes—
39#90968C2212yescomplemented
40#90968C2212yescomplemented
41#90968C2212yescomplemented
42#83634—51nomaximal, Hall
43D4×D20—31no—
44#65877D311yescharacteristic, complemented
45C5×C8×D4—31no—
46#65403—32no—
47C2×#3953—32no—
48#65137—31no—
49#65131—31no—
50#65024—32no—
51#65020—32no—
52#64983—31no—
53C4×#677—31no—
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×C3×Dic5—22no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10C2311yescharacteristic
70C3×C5×C4⋊C4D411yescharacteristic
71C3×C5×C22⋊C4D412yes—
72C3×C42×C5C2311yescharacteristic
73#6714—21no—
74#6714—22no—
75C4⋊Dic15C2311yescharacteristic
76C2×C5×C3⋊C8—42no—
77C2×C5×C3⋊C8C2311yescharacteristic
78C2×C5×C3⋊C8C2312yes—
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×C22⋊Dic5—22no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5—22no—
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4⋊Dic5C2312yes—
85C3×#683—21no—
86C3×#683—22no—
87C3×C4×Dic5—21no—
88#6658—22no—
89#6658—42no—
90C3×#554—51no—
91D4×D12—51no—
92#5088—51no—
93#5084—51no—
94#5048—52no—
95#5046—52no—
96#5027—51no—
97C4×#215—51no—
98D4×C3⋊C8D511yescharacteristic, complemented
99#4968—52no—
100C2×#809—52no—
101C2×D4×D5—61no—
102C22×D20—32no—
103C22×C5×C8—32no—
104C4×C5×D4C2×D311yescharacteristic
105D4×Dic5—21no—
106#4076—32no—
107C2×C4⋊Dic5C2×D312yescomplemented
108#4070C2×D312yescomplemented
109C2×#677—31no—
110C2×#677—32no—
111#4041—61no—
112#4036—21no—
113#4028—62no—
114#4024—22no—
115#4020—31no—
116C4×D20—31no—
117#4015C2×D311yescharacteristic, complemented
118C4×Dic10C2×D311yescharacteristic, complemented
119C5×C4⋊C8—31no—
120C5×C22⋊C8—32no—
121C4×C5×C8—31no—
122#3953—32no—
123#3953—32no—
124#3953—32no—
125#3953—31no—
126#3953—32no—
127#3949—31no—
128#3949—32no—
129#3948—31no—
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×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—82no—
158C3×Dic10—21no—
159C3×Dic10—21no—
160C3×Dic10—81no—
161C5×C3⋊C8—21no—
162C5×C3⋊C8—22no—
163C5×C3⋊C8—21no—
164C2×D3×D4—101no—
165C22×D12—52no—
166C3×C4⋊Q8—51no—
167C3×#125—101no—
168C3×C22⋊Q8—52no—
169C3×C22⋊Q8—102no—
170C3×C4×Q8—51no—
171C3×C4×D4—101no—
172C3×C4×D4C2×D511yescharacteristic
173C2×C3×C4⋊C4—52no—
174C2×#215—51no—
175C2×#215—52no—
176#930—52no—
177C22×C3⋊C8C2×D512yescomplemented
178#895—101no—
179#882—102no—
180#874—51no—
181C4×D12—51no—
182#835—51no—
183#830C2×D512yescomplemented
184#809—51no—
185#809—52no—
186#809—52no—
187#809—52no—
188#809—52no—
189#808—51no—
190#808—52no—
191C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
192C4×C3⋊C8C2×D511yescharacteristic, complemented
193C23×D5—62no—
194C2×C5×D4#6711yescharacteristic
195C22×C4×C5C22×D312yes—
196C2×C22⋊D5—62no—
197C22×Dic5—22no—
198D4×D5—124no—
199C2×D20—31no—
200C2×D20—32no—
201C2×D20—64no—
202C2×D20—62no—
203C2×D20—61no—
204C2×D20—61no—
205C2×D20—122no—
206C2×C4×D5—61no—
207C2×Dic10—21no—
208C2×Dic10C22×D311yescharacteristic
209C2×C5×C8—31no—
210C2×C5×C8—32no—
211C2×C5×C8—31no—
212C2×C5×C8—122no—
213C5×C4⋊C4#6711yescharacteristic
214C5×C22⋊C4#6712yes—
215C42×C5C22×D311yescharacteristic
216C22⋊Dic5—22no—
217#685—61no—
218#685—62no—
219C4⋊Dic5—21no—
220C4⋊Dic5—22no—
221C4⋊Dic5—31no—
222C4⋊Dic5C22×D311yescharacteristic
223C4⋊Dic5C22×D312yes—
224#683—21no—
225#683—22no—
226C4×Dic5—21no—
227#677—62no—
228#677—122no—
229#554—51no—
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—31no—
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—
257C3×Dic5—41no—
258C3×Dic5—42no—
259C3×Dic5—41no—
260C23×D3—102no—
261C2×C3×Q8—51no—
262C2×C3×Q8—101no—
263C2×C3×D4D2011yescharacteristic
264C22×C3×C4—102no—
265C22×C3×C4C22×D512yes—
266C2×#67—102no—
267D3×D4—204no—
268C2×D12—51no—
269C2×D12—52no—
270C2×D12—104no—
271C2×D12—101no—
272C2×D12—102no—
273C2×D12—101no—
274C2×D12—202no—
275C2×C4×D3—101no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4—52no—
278C3×C4⋊C4—101no—
279C3×C4⋊C4—102no—
280C3×C4⋊C4—102no—
281C3×C4⋊C4—101no—
282C3×C4⋊C4D2011yescharacteristic
283C3×C22⋊C4—102no—
284C3×C22⋊C4D2012yes—
285C3×C42—101no—
286C3×C42C22×D511yescharacteristic
287#215—102no—
288#215—202no—
289(C2×D3)⋊C4—101no—
290(C2×D3)⋊C4—102no—
291C4⋊Dic3—51no—
292C2×C3⋊C8—42no—
293C2×C3⋊C8C22×D511yescharacteristic
294C2×C3⋊C8C22×D511yescharacteristic
295C2×C3⋊C8C22×D512yes—
296C23×C5C2×#6712yes—
297C22×D5—61no—
298C22×D5—62no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×D4#21514yescomplemented
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5C2×#6712yes—
306C2×C4×C5C2×#6711yescharacteristic
307C2×C4×C5C2×#6711yescharacteristic
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—124no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—22no—
313C2×Dic5—61no—
314C2×Dic5—82no—
315D20—32no—
316D20—62no—
317D20—61no—
318D20—62no—
319D20—124no—
320D20—122no—
321D20—241no—
322C4×D5—122no—
323Dic10—21no—
324Dic10—21no—
325Dic10—81no—
326C5×C8—61no—
327C5×C8—62no—
328C5×C8—61no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—151no—
332C2×SD16—152no—
333C22×C8—32no—
334C4⋊Q8—51no—
335#127—151no—
336#125—101no—
337C22⋊Q8—52no—
338C22⋊Q8—102no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—51no—
343C4×D4—101no—
344C4×D4—151no—
345C4×D4D3×D511yescharacteristic
346C2×C4⋊C4—52no—
347#106—151no—
348#106—152no—
349C4⋊C8—31no—
350#103—151no—
351#102—151no—
352#102—152no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—32no—
357C4×C8—31no—
358C2×C3×C5—24no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362D15—42no—
363D15—82no—
364C23×C3C2×D2012yes—
365C22×D3—101no—
366C22×D3—102no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—101no—
371C3×Q8—101no—
372C3×Q8—401no—
373C3×D4#67714yescomplemented
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—102no—
379C2×C3×C4—402no—
380C2×C3×C4C2×D2011yescharacteristic
381C2×C3×C4C2×D2012yes—
382C2×C3×C4C2×D2011yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—204no—
385C2×Dic3—101no—
386D12—52no—
387D12—101no—
388D12—102no—
389D12—102no—
390D12—204no—
391D12—202no—
392D12—401no—
393C4×D3—202no—
394C3⋊C8—21no—
395C3⋊C8—22no—
396C3⋊C8—21no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5C2×#21514yes—
400C22×C5C22×#6711yescharacteristic
401C2×D5—62no—
402C2×D5—121no—
403C2×D5—121no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—122no—
407C2×D5—248no—
408C4×C5—22no—
409C4×C5—21no—
410C4×C5C2×#21512yes—
411C4×C5D3×#4111yescharacteristic
412C4×C5#100911yescharacteristic
413Dic5—41no—
414Dic5—42no—
415Dic5—41no—
416Dic5—121no—
417C24—302no—
418C2×Q8—51no—
419C2×Q8—101no—
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#120211yescharacteristic
430C22×C4—102no—
431C22×C4—301no—
432C22×C4C2×D3×D512yes—
433SD16—302no—
434SD16—602no—
435C2×C8—31no—
436C2×C8—31no—
437C2×C8—32no—
438C2×C8—122no—
439C4⋊C4—51no—
440C4⋊C4—52no—
441C4⋊C4—102no—
442C4⋊C4—101no—
443C4⋊C4—101no—
444C4⋊C4—102no—
445C4⋊C4—151no—
446C4⋊C4#120211yescharacteristic
447C22⋊C4—102no—
448C22⋊C4—301no—
449C22⋊C4—302no—
450C22⋊C4#120212yes—
451C42—101no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—22no—
456C22×C3C2×#67714yes—
457C22×C3C22×D2011yescharacteristic
458C2×D3—102no—
459C2×D3—201no—
460C2×D3—201no—
461C2×D3—202no—
462C2×D3—202no—
463C2×D3—202no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—201no—
468C3×C4—202no—
469C3×C4—201no—
470C3×C4C2×#67712yes—
471C3×C4#414411yescharacteristic
472C3×C4D5×#4111yescharacteristic
473Dic3—201no—
474C2×C5—24no—
475C2×C5C22×#21511yescharacteristic
476C2×C5#582911yescharacteristic
477C2×C5#583511yescharacteristic
478D5—122no—
479D5—242no—
480C23—301no—
481C23—302no—
482C23—604no—
483C23—604no—
484C23—1202no—
485C23C2×#120212yes—
486Q8—101no—
487Q8—101no—
488Q8—401no—
489D4—152no—
490D4—302no—
491D4—301no—
492D4—302no—
493D4—604no—
494D4—604no—
495D4—602no—
496D4—1201no—
497D4#665814yescomplemented
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—101no—
501C2×C4—101no—
502C2×C4—102no—
503C2×C4—301no—
504C2×C4—402no—
505C2×C4—602no—
506C2×C4C2×#120211yescharacteristic
507C2×C4C2×#120212yes—
508C2×C4C2×#120211yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—61no—
511C8—61no—
512C8—62no—
513C2×C3—24no—
514C2×C3#6588811yescharacteristic
515C2×C3C22×#67711yescharacteristic
516C2×C3#6608611yescharacteristic
517D3—202no—
518D3—402no—
519C5#8363411yescharacteristic, complemented, Sylow
520C22—22no—
521C22—22no—
522C22—302no—
523C22—601no—
524C22—601no—
525C22—602no—
526C22—602no—
527C22—602no—
528C22—1208no—
529C22C2×#665814yes—
530C22C22×#120211yescharacteristic
531C4—21no—
532C4—22no—
533C4—201no—
534C4—202no—
535C4—201no—
536C4—601no—
537C4C2×#665812yes—
538C4#9202411yescharacteristic
539C4#9202711yescharacteristic
540C3#1061117011yescharacteristic, complemented, Sylow
541C2—24no—
542C2—602no—
543C2—1202no—
544C2C22×#665811yescharacteristic
545C2#1175498011yescharacteristic
546C2#1175531111yescharacteristic
subgroupG/H
centerC22C22×#1202
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. C3×#65877C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748551C2semidirect
5. #11748541C2semidirect
6. #11748454C2semidirect
7. C2×#90968C2semidirect
8. #11747064C2semidirect
9. C4×#6658C2semidirect
10. #11746942C2semidirect
11. #11746910C2semidirect
21. C22×C5×C3⋊C8C22semidirect
23. C2×C3×C4⋊Dic5C22semidirect
24. C3×#4070C22semidirect
27. C3×#4015C22semidirect
28. C3×C4×Dic10C22semidirect
30. C2×#6658C22semidirect
31. C5×#830C22semidirect
32. C5×C4⋊(C3⋊C8)C22semidirect
33. C4×C5×C3⋊C8C22semidirect
34. #90987C22semidirect
35. #90987C22semidirect
36. #90971C22semidirect
39. #90968C22semidirect
40. #90968C22semidirect
41. #90968C22semidirect
44. #65877D3semidirect
98. D4×C3⋊C8D5semidirect
107. C2×C4⋊Dic5C2×D3semidirect
108. #4070C2×D3semidirect
117. #4015C2×D3semidirect
118. C4×Dic10C2×D3semidirect
137. C3×C5×D4SD16semidirect
177. C22×C3⋊C8C2×D5semidirect
183. #830C2×D5semidirect
191. C4⋊(C3⋊C8)C2×D5semidirect
192. C4×C3⋊C8C2×D5semidirect
302. C5×D4#215semidirect
373. C3×D4#677semidirect
453. C3×C5#3295semidirect
497. D4#6658semidirect
519. C5#83634semidirect
540. C3#10611170semidirect

Maximal subgroups

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

subgroupindex
D4×D602
C3×#658772
C5×D4×C3⋊C82
#117485512
#117485412
#117484542
C2×#909682
#117470642
C4×#66582
#117469422
#117469102
#106111703
#836345