Finite Group Databasebeta

← #14458286

Subgroups — #14458286

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756485C211yesmaximal, characteristic, complemented
2D4×D60C211yesmaximal, characteristic, complemented
3C3×C5×#474C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic, complemented
5C4×#6715C211yesmaximal, characteristic, complemented
6#11750984C212yesmaximal, complemented
7#11750983C212yesmaximal, complemented
8#11750944C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750874C212yesmaximal, complemented
11D15×#102C212yesmaximal, complemented
12#10612711—31nomaximal, Hall
13C2×#6821—21no—
14C2×D4×D15C2212yes—
15C22×D60—21no—
16C3×C5×C4⋊Q8C2211yescharacteristic, complemented
17C3×C4×C5×D4C2211yescharacteristic
18#91835—21no—
19C2×#6715C2211yescharacteristic
20#91819—21no—
21C2×D120C2212yescomplemented
22C2×C8×D15C2212yescomplemented
23#91784C2212yes—
24#91784C2212yescomplemented
25#91783—22no—
26C4⋊C4×D15C2212yescomplemented
27#91771—22no—
28#91763C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C4×D60C2211yescharacteristic, complemented
31C3×C5×#107C2212yescomplemented
32C3×C5×C4⋊C8C2211yescharacteristic, complemented
33C3×C5×#102C2212yes—
34#91116C2211yescharacteristic
35#91105C2212yescomplemented
36#91104C2212yescomplemented
37#91093C2212yescomplemented
38#91093C2212yescomplemented
39#91093C2211yescharacteristic, complemented
40#91091C2211yescharacteristic, complemented
41C4×C3⋊#168C2211yescharacteristic, complemented
42#80980—51nomaximal, Hall
43#66060—31no—
44D4×D20—31no—
45C5×#474D311yescharacteristic, complemented
46#65377—31no—
47C4×#686—31no—
48#65172—32no—
49#65171—32no—
50#65132—31no—
51#65123—31no—
52#65062—32no—
53D5×#102—32no—
54C23×D15—22no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C2×#1220—22no—
59#6821—44no—
60D4×D15—24no—
61D4×D15—42no—
62C2×D60—22no—
63C2×D60—22no—
64C2×D60—21no—
65C2×D60—21no—
66C2×D60—44no—
67C2×D60D411yescharacteristic
68C2×D60C2311yescharacteristic
69C2×D60C2312yes—
70C2×C4×D15—22no—
71C2×C4×D15—21no—
72C2×C4×D15C2312yes—
73C2×C3×C5×C8C2312yes—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4C2312yes—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C3×C42×C5C2311yescharacteristic
79#6715—22no—
80#6714—21no—
81#6714—22no—
82#6714—22no—
83#6714D412yes—
84C4⋊Dic15D411yescharacteristic
85C4⋊Dic15C2311yescharacteristic
86#6712—22no—
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2311yescharacteristic
89D120—42no—
90C8×D15—42no—
91#5726—51no—
92D4×D12—51no—
93C3×#474D511yescharacteristic, complemented
94#5088—51no—
95C4×#213—51no—
96#4883—52no—
97#4882—52no—
98#4843—51no—
99#4834—51no—
100#4773—52no—
101D3×#102—52no—
102C2×#713—61no—
103C2×D4×D5—32no—
104C22×D20—61no—
105C5×C4⋊Q8C2×D311yescharacteristic, complemented
106C4×C5×D4C2×D311yescharacteristic
107#4092—61no—
108C2×#686—31no—
109#4076—61no—
110C2×D40—32no—
111C2×C8×D5—32no—
112#4041—32no—
113#4041—32no—
114#4040—62no—
115D5×C4⋊C4—32no—
116#4028—62no—
117#4020—31no—
118C4×D20—31no—
119C4×D20—31no—
120C5×#107C2×D312yescomplemented
121C5×C4⋊C8C2×D311yescharacteristic, complemented
122C5×#102C2×D312yes—
123#3964—31no—
124#3953—32no—
125#3952—32no—
126#3941—31no—
127#3941—32no—
128#3941—32no—
129#3939—31no—
130C4×#168—31no—
131#3294—151noSylow
132C23×C3×C5—21no—
133C22×D15—21no—
134C22×D15—22no—
135C22×D15—44no—
136C22×D15—44no—
137C22×D15—82no—
138C22×D15C2×D412yes—
139C3×C5×Q8—42no—
140C3×C5×D4—21no—
141C3×C5×D4#4112yescomplemented
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—42no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148#1220—44no—
149C2×Dic15—21no—
150C2×Dic15C2×D412yes—
151D60—21no—
152D60—22no—
153D60—21no—
154D60—22no—
155D60—44no—
156D60—44no—
157D60—42no—
158D60—81no—
159D60D814yescomplemented
160C4×D15—22no—
161C4×D15—22no—
162C4×D15—44no—
163C4×D15—42no—
164C3×C5×C8—22no—
165C3⋊#168—21no—
166C3⋊#168—21no—
167C2×#239—101no—
168C2×D3×D4—52no—
169C22×D12—101no—
170C3×C4⋊Q8C2×D511yescharacteristic, complemented
171C3×C4×D4C2×D511yescharacteristic
172#946—101no—
173C2×#213—51no—
174#930—101no—
175C2×D24—52no—
176C2×D3×C8—52no—
177#895—52no—
178#895—52no—
179#894—102no—
180D3×C4⋊C4—52no—
181#882—102no—
182#874—51no—
183C4×D12—51no—
184C4×D12—51no—
185C3×#107C2×D512yescomplemented
186C3×C4⋊C8C2×D511yescharacteristic, complemented
187C3×#102C2×D512yes—
188#832—51no—
189#821—52no—
190(C2×D3)⋊C8—52no—
191#809—52no—
192#809—51no—
193#809—52no—
194#807—51no—
195C4×C3⋊C8—51no—
196C23×D5—62no—
197C2×C5×Q8—21no—
198C2×C5×D4C22×D311yescharacteristic
199C22×C4×C5—21no—
200C2×C22⋊D5—62no—
201#713—124no—
202D4×D5—64no—
203D4×D5—122no—
204C2×D20—31no—
205C2×D20—32no—
206C2×D20—31no—
207C2×D20—62no—
208C2×D20—62no—
209C2×D20—61no—
210C2×D20—61no—
211C2×D20—124no—
212C2×C4×D5—32no—
213C2×C4×D5—62no—
214C2×C4×D5—61no—
215C2×C5×C8C22×D312yes—
216C5×C4⋊C4—21no—
217C5×C4⋊C4C22×D311yescharacteristic
218C5×C4⋊C4C22×D312yes—
219C5×C22⋊C4—21no—
220C42×C5C22×D311yescharacteristic
221#686—62no—
222#685—32no—
223#685—62no—
224#685—62no—
225#685—61no—
226C4⋊Dic5—31no—
227C4⋊Dic5—31no—
228#683—62no—
229C2×#168—31no—
230C2×#168—31no—
231D40—122no—
232C8×D5—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474D1511yescharacteristic, complemented
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—151no—
242C8×D4—151no—
243C2×#102—152no—
244C22×C3×C5—22no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—22no—
249C2×D15—22no—
250C2×D15—42no—
251C2×D15—41no—
252C2×D15—41no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15—41no—
256C2×D15—88no—
257C2×D15C2×D814yes—
258C3×C4×C5—21no—
259C3×C4×C5—42no—
260C3×C4×C5—41no—
261C3×C4×C5C2×D812yes—
262C3×C4×C5C2×#4111yescharacteristic
263C3×C4×C5H(5,𝔽2)11yescharacteristic
264Dic15—22no—
265Dic15—41no—
266C23×D3—102no—
267C2×C3×Q8—21no—
268C2×C3×D4C22×D511yescharacteristic
269C22×C3×C4—21no—
270C2×#67—102no—
271#239—204no—
272D3×D4—104no—
273D3×D4—202no—
274C2×D12—51no—
275C2×D12—52no—
276C2×D12—51no—
277C2×D12—102no—
278C2×D12—102no—
279C2×D12—101no—
280C2×D12—101no—
281C2×D12—204no—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×C4×D3—101no—
285C2×C3×C8C22×D512yes—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C4⋊C4C22×D512yes—
289C3×C22⋊C4—21no—
290C3×C42C22×D511yescharacteristic
291#213—102no—
292(C2×D3)⋊C4—52no—
293(C2×D3)⋊C4—102no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—101no—
296C4⋊Dic3—51no—
297C4⋊Dic3—51no—
298Dic3⋊C4—102no—
299C2×C3⋊C8—51no—
300C2×C3⋊C8—51no—
301D24—202no—
302D3×C8—202no—
303C23×C5—21no—
304C22×D5—32no—
305C22×D5—61no—
306C22×D5—62no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×Q8—42no—
311C5×D4—21no—
312C5×D4#23912yescomplemented
313C2×C4×C5—22no—
314C2×C4×C5—21no—
315C2×C4×C5—42no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5C23×D311yescharacteristic
319C22⋊D5—124no—
320C2×Dic5—32no—
321C2×Dic5—61no—
322D20—34no—
323D20—61no—
324D20—62no—
325D20—61no—
326D20—62no—
327D20—124no—
328D20—124no—
329D20—122no—
330D20—241no—
331C4×D5—62no—
332C4×D5—62no—
333C4×D5—124no—
334C4×D5—122no—
335C5×C8—22no—
336#168—61no—
337#168—61no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—151no—
342C2×D8—152no—
343C22×C8—152no—
344C4⋊Q8C2×D1511yescharacteristic, complemented
345#127—151no—
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—151no—
353C4×D4—151no—
354C4×D4C2×D1511yescharacteristic
355C2×C4⋊C4—152no—
356#107—151no—
357#107C2×D1512yescomplemented
358C4⋊C8C2×D1511yescharacteristic, complemented
359#102—151no—
360#102—152no—
361#102—152no—
362#102—151no—
363#102—152no—
364#102C2×D1512yes—
365C22⋊C8—152no—
366C4×C8—151no—
367C2×C3×C5—42no—
368C2×C3×C5#54611yescharacteristic
369C2×C3×C5C22×D811yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—24no—
372D15—81no—
373D15—82no—
374C23×C3—21no—
375C22×D3—52no—
376C22×D3—101no—
377C22×D3—102no—
378C22×D3—204no—
379C22×D3—204no—
380C22×D3—402no—
381C3×Q8—42no—
382C3×D4—21no—
383C3×D4#71312yescomplemented
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—42no—
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4D4×D511yescharacteristic
389C2×C3×C4C23×D511yescharacteristic
390#67—204no—
391C2×Dic3—52no—
392C2×Dic3—101no—
393D12—54no—
394D12—101no—
395D12—102no—
396D12—101no—
397D12—102no—
398D12—204no—
399D12—204no—
400D12—202no—
401D12—401no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—204no—
405C4×D3—202no—
406C3×C8—22no—
407C3⋊C8—101no—
408C3⋊C8—101no—
409C22×C5—22no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5C2×D3×D411yescharacteristic
413C2×D5—34no—
414C2×D5—62no—
415C2×D5—62no—
416C2×D5—121no—
417C2×D5—122no—
418C2×D5—122no—
419C2×D5—121no—
420C2×D5—122no—
421C2×D5—121no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—42no—
425C4×C5—41no—
426C4×C5D3×D812yes—
427C4×C5C2×#23911yescharacteristic
428C4×C5#100911yescharacteristic
429Dic5—62no—
430Dic5—121no—
431C24—302no—
432#41—604no—
433C2×Q8—21no—
434C2×D4—151no—
435C2×D4—152no—
436C2×D4—151no—
437C2×D4—302no—
438C2×D4—302no—
439C2×D4—302no—
440C2×D4—304no—
441C2×D4—301no—
442C2×D4—301no—
443C2×D4—604no—
444C2×D4—602no—
445C2×D4C22×D1511yescharacteristic
446C22×C4—21no—
447C22×C4—152no—
448C22×C4—302no—
449C22×C4—301no—
450D8—302no—
451D8—602no—
452C2×C8—151no—
453C2×C8—151no—
454C2×C8—602no—
455C2×C8C22×D1512yes—
456C4⋊C4—21no—
457C4⋊C4—151no—
458C4⋊C4—151no—
459C4⋊C4—302no—
460C4⋊C4C22×D1512yes—
461C4⋊C4C22×D1511yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—152no—
464C22⋊C4—302no—
465C22⋊C4—302no—
466C22⋊C4—301no—
467C42C22×D1511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—22no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3C2×D4×D511yescharacteristic
473C2×D3—54no—
474C2×D3—102no—
475C2×D3—102no—
476C2×D3—201no—
477C2×D3—202no—
478C2×D3—202no—
479C2×D3—201no—
480C2×D3—202no—
481C2×D3—201no—
482C2×D3—408no—
483C3×C4—21no—
484C3×C4—42no—
485C3×C4—41no—
486C3×C4D5×D812yes—
487C3×C4C2×#71311yescharacteristic
488C3×C4#414911yescharacteristic
489Dic3—102no—
490Dic3—201no—
491C2×C5—42no—
492C2×C5#563011yescharacteristic
493C2×C5C2×D3×D811yescharacteristic
494C2×C5#577811yescharacteristic
495D5—64no—
496D5—242no—
497D5—241no—
498C23—21no—
499C23—152no—
500C23—301no—
501C23—302no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—42no—
506D4—21no—
507D4—154no—
508D4—301no—
509D4—302no—
510D4—301no—
511D4—302no—
512D4—604no—
513D4—604no—
514D4—604no—
515D4—602no—
516D4—1201no—
517D4#682112yescomplemented
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—42no—
521C2×C4—152no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—301no—
525C2×C4—604no—
526C2×C4—602no—
527C2×C4D4×D1511yescharacteristic
528C2×C4D4×D1511yescharacteristic
529C2×C4C23×D1511yescharacteristic
530C8—22no—
531C8—301no—
532C8—301no—
533C2×C3—42no—
534C2×C3#6596411yescharacteristic
535C2×C3C2×D5×D811yescharacteristic
536C2×C3#6611211yescharacteristic
537D3—104no—
538D3—402no—
539D3—401no—
540C5#8098011yescharacteristic, complemented, Sylow
541C22—22no—
542C22—41no—
543C22—41no—
544C22—154no—
545C22—302no—
546C22—302no—
547C22—602no—
548C22—601no—
549C22—601no—
550C22—602no—
551C22—602no—
552C22—601no—
553C22—1208no—
554C22C2×D4×D1511yescharacteristic
555C4—21no—
556C4—41no—
557C4—42no—
558C4—302no—
559C4—601no—
560C4D8×D1512yes—
561C4C2×#682111yescharacteristic
562C4#9210011yescharacteristic
563C3#1061271111yescharacteristic, complemented, Sylow
564C2—42no—
565C2—304no—
566C2—1202no—
567C2—1201no—
568C2#1175638911yescharacteristic
569C2C2×D8×D1511yescharacteristic
570C2#1175653711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#474C2
socleC22×C3×C5C22×D4
hypercenter#474D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11756485C2semidirect
2. D4×D60C2semidirect
3. C3×C5×#474C2semidirect
4. #11751189C2semidirect
5. C4×#6715C2semidirect
6. #11750984C2semidirect
7. #11750983C2semidirect
8. #11750944C2semidirect
9. #11750935C2semidirect
10. #11750874C2semidirect
11. D15×#102C2semidirect
16. C3×C5×C4⋊Q8C22semidirect
21. C2×D120C22semidirect
22. C2×C8×D15C22semidirect
24. #91784C22semidirect
26. C4⋊C4×D15C22semidirect
30. C4×D60C22semidirect
31. C3×C5×#107C22semidirect
32. C3×C5×C4⋊C8C22semidirect
35. #91105C22semidirect
36. #91104C22semidirect
37. #91093C22semidirect
38. #91093C22semidirect
39. #91093C22semidirect
40. #91091C22semidirect
41. C4×C3⋊#168C22semidirect
45. C5×#474D3semidirect
93. C3×#474D5semidirect
105. C5×C4⋊Q8C2×D3semidirect
120. C5×#107C2×D3semidirect
121. C5×C4⋊C8C2×D3semidirect
141. C3×C5×D4#41semidirect
159. D60D8semidirect
170. C3×C4⋊Q8C2×D5semidirect
185. C3×#107C2×D5semidirect
186. C3×C4⋊C8C2×D5semidirect
237. #474D15semidirect
312. C5×D4#239semidirect
344. C4⋊Q8C2×D15semidirect
357. #107C2×D15semidirect
358. C4⋊C8C2×D15semidirect
383. C3×D4#713semidirect
468. C3×C5#3294semidirect
517. D4#6821semidirect
540. C5#80980semidirect
563. C3#10612711semidirect

Maximal subgroups

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

subgroupindex
#117564852
D4×D602
C3×C5×#4742
#117511892
C4×#67152
#117509842
#117509832
#117509442
#117509352
#117508742
D15×#1022
#106127113
#809805