Finite Group Databasebeta

← #14478521

Subgroups — #14478521

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66103C211yesmaximal, characteristic, complemented
2#11753961C211yesmaximal, characteristic, complemented
3#11751295C211yesmaximal, characteristic, complemented
4C5×#5193C211yesmaximal, characteristic, complemented
5#11748301C212yesmaximal, complemented
6#11748289C212yesmaximal, complemented
7#11748276C212yesmaximal, complemented
8D5×#826C212yesmaximal, complemented
9#11747543C211yesmaximal, characteristic, complemented
10C2×#90937C211yesmaximal, characteristic, complemented
11#11747525C211yesmaximal, characteristic, complemented
12#10613767—31nomaximal, Hall
13C3×#4149—21no—
14#92018—21no—
15C3×C5×#135C2211yescharacteristic, complemented
16#91793C2211yescharacteristic, complemented
17C2×C5×D24C2211yescharacteristic, complemented
18C3×#4095—21no—
19C3×#4065C2212yescomplemented
20C3×#4060—22no—
21C3×D5×D8C2212yescomplemented
22C2×C3×D40C2211yescharacteristic, complemented
23C3×#4047C2211yescharacteristic
24#91304—21no—
25#91270C2212yescomplemented
26#91250—22no—
27D5×D24C2212yescomplemented
28#91113C2211yescharacteristic, complemented
29#91112C2211yescharacteristic, complemented
30#91111C2211yescharacteristic, complemented
31#91110C2211yescharacteristic, complemented
32C2×C3⋊#672C2211yescharacteristic, complemented
33C5×#828C2212yescomplemented
34C5×#826C2212yescomplemented
35C5×#812C2211yescharacteristic, complemented
36#90942C2212yescomplemented
37#90938C2212yescomplemented
38#90937C2212yescomplemented
39#90937C2212yescomplemented
40#90934C2212yescomplemented
41D5×C3⋊C16C2212yescomplemented
42#84007—51nomaximal, Hall
43#66103D311yescharacteristic, complemented
44#66091—31no—
45C5×#509—31no—
46#65483—31no—
47C2×#3958—31no—
48#65205—32no—
49#65203—32no—
50#65200—32no—
51D5×D16—32no—
52#65197—31no—
53#65196—31no—
54C3×C5×#41—21no—
55#6817—21no—
56C2×C5×D12—21no—
57C3×#713—22no—
58C3×D4×D5—22no—
59C3×D4×D5—42no—
60C3×#709—41no—
61C3×#709D411yescharacteristic
62C2×C3×D20—21no—
63C2×C3×D20—41no—
64D3×C22⋊D5—42no—
65#6777—41no—
66D5×D12—22no—
67#6772—22no—
68#6768—41no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8C2311yescharacteristic
72C2×C3×C5×C8C2311yescharacteristic
73Dic60C2311yescharacteristic
74D120C2311yescharacteristic
75#6706—21no—
76C5×D24—21no—
77C5×D24C2312yes—
78C3×#688—22no—
79C3×#686—22no—
80C3×#681D411yescharacteristic
81C3×D40—21no—
82C3×D40C2312yes—
83C3×#676D412yes—
84C3×C8×D5C2312yes—
85#6659—22no—
86#6654—22no—
87C3⋊#672C2311yescharacteristic
88C3⋊#672C2311yescharacteristic
89C5×C3⋊C16C2312yes—
90C3×#576—51no—
91#5752—51no—
92#5194—51no—
93#5194—52no—
94#5193—52no—
95#5193D511yescharacteristic, complemented
96#5147—52no—
97#5147—51no—
98C2×#826—51no—
99C2×#826—52no—
100#5140—51no—
101#4149—21no—
102#4144—61no—
103C5×#135C2×D311yescharacteristic, complemented
104C2×C5×D8—31no—
105#4095—21no—
106#4078—61no—
107#4065C2×D312yescomplemented
108#4060—22no—
109#4058—32no—
110#4057—62no—
111D5×D8—32no—
112D5×D8C2×D312yescomplemented
113#4050—31no—
114C2×D40C2×D311yescharacteristic, complemented
115#4047C2×D311yescharacteristic
116C5×SD32—32no—
117C5×D16—32no—
118C5×M32—31no—
119#3961—31no—
120#3960—31no—
121#3959—31no—
122#3958—31no—
123#3958—32no—
124#3958—32no—
125C2×#672—31no—
126#3932—32no—
127D80—32no—
128#3930—32no—
129D5×C16—32no—
130#3415—151noSylow
131C22×C5×D3—41no—
132C22×C3×D5—41no—
133C22×C3×D5—42no—
134C2×D3×D5—42no—
135C3×C5×Q8—21no—
136C3×C5×D4—21no—
137C3×C5×D4—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5C2×D411yescharacteristic
140#1220—41no—
141D60—21no—
142C4×D15—41no—
143Dic30—21no—
144C5×D12—22no—
145C5×D12—41no—
146C3×C22⋊D5—42no—
147C3×C22⋊D5D812yes—
148C3×D20—22no—
149C3×D20—42no—
150C3×D20—41no—
151C3×D20D811yescharacteristic
152C3×C4×D5—42no—
153C3×C4×D5C2×D412yes—
154C3×Dic10D811yescharacteristic
155#1203—42no—
156#1201—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3×#168C2×D412yes—
161C3×H(5,𝔽2)—101no—
162#1009—101no—
163C3×AGL(1,ℤ/8)—102no—
164C3×AGL(1,ℤ/8)—101no—
165C3×#135—52no—
166C3×#135C2×D511yescharacteristic, complemented
167C2×C3×D8—52no—
168C2×C3×D8—51no—
169C3×#131—51no—
170#908—102no—
171#908—101no—
172#904—51no—
173#904—52no—
174C2×D24—52no—
175C2×D24C2×D511yescharacteristic, complemented
176#829—51no—
177#828—51no—
178#828C2×D512yescomplemented
179#827—51no—
180#827—52no—
181#826—51no—
182#826—52no—
183#826—52no—
184#826—52no—
185#826C2×D512yescomplemented
186#812—52no—
187#812C2×D511yescharacteristic, complemented
188C2×C3⋊C16—51no—
189C2×C3⋊C16—52no—
190C5×#41—21no—
191C2×C5×D4—61no—
192C2×C22⋊D5—122no—
193#713—22no—
194#711—62no—
195#711—121no—
196D4×D5—22no—
197D4×D5—42no—
198D4×D5—62no—
199D4×D5—121no—
200#709—41no—
201#709—61no—
202#709#6711yescharacteristic
203C2×D20—21no—
204C2×D20—41no—
205C5×Q16C22×D311yescharacteristic
206C5×SD16—21no—
207C5×D8—32no—
208C5×D8—61no—
209C5×D8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211#688—22no—
212#687—62no—
213#686—22no—
214#686—62no—
215#681#6711yescharacteristic
216Dic20—31no—
217D40—21no—
218D40—31no—
219D40C22×D312yes—
220#677—61no—
221#676#6712yes—
222C8×D5C22×D312yes—
223C5×C16—32no—
224#672—31no—
225#672—31no—
226#576—51no—
227#576—151no—
228#509—31no—
229#509—151no—
230#509—152no—
231#509—152no—
232#508—152no—
233#508—151no—
234C2×D16—152no—
235C2×D16—151no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×D15—41no—
240C2×C5×D3—42no—
241C2×C5×D3—161no—
242C2×C3×D5—42no—
243C2×C3×D5—162no—
244C2×C3×D5—161no—
245C2×C3×D5C2×D812yes—
246D3×D5—162no—
247C3×C4×C5—41no—
248C3×C4×C5C2×D811yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—41no—
251C3×Dic5C2×D812yes—
252C3×#41—21no—
253C3×#41—51no—
254C3×#41—102no—
255C3×#41—201no—
256C2×C3×D4—102no—
257C2×C3×D4—101no—
258C2×C3×D4—201no—
259C2×C3×D4—202no—
260#239—201no—
261D3×D4—201no—
262D3×D4—202no—
263#235—102no—
264#235—101no—
265C2×D12—21no—
266C2×D12—102no—
267C3×Q16C22×D511yescharacteristic
268C3×SD16—21no—
269C3×SD16—102no—
270C3×D8—52no—
271C3×D8—102no—
272C3×D8—101no—
273C3×D8C22×D511yescharacteristic
274C3×M16—51no—
275C3×M16—52no—
276C2×C3×C8—52no—
277C2×C3×C8C22×D511yescharacteristic
278Dic12—51no—
279D24—21no—
280D24—51no—
281D24—102no—
282D24C22×D512yes—
283#204—102no—
284#204—101no—
285C3⋊C16—51no—
286C3⋊C16—51no—
287C3⋊C16C22×D512yes—
288C23×C5—121no—
289C22×D5—41no—
290C22×D5—42no—
291C22×D5—122no—
292C5×Q8—21no—
293C5×D4—21no—
294C5×D4—41no—
295C5×D4—62no—
296C5×D4—121no—
297C2×C4×C5—41no—
298C2×C4×C5C2×#6711yescharacteristic
299C22⋊D5—42no—
300C22⋊D5—121no—
301C22⋊D5—122no—
302C22⋊D5—122no—
303C22⋊D5#21312yes—
304C2×Dic5—122no—
305D20—22no—
306D20—42no—
307D20—41no—
308D20—61no—
309D20#21311yescharacteristic
310C4×D5—42no—
311C4×D5—121no—
312C4×D5C2×#6712yes—
313Dic10—61no—
314Dic10#21311yescharacteristic
315C5×C8C2×#6711yescharacteristic
316C5×C8C23×D311yescharacteristic
317#168C2×#6712yes—
318H(5,𝔽2)—101no—
319H(5,𝔽2)—301no—
320AGL(1,ℤ/8)—102no—
321AGL(1,ℤ/8)—101no—
322AGL(1,ℤ/8)—302no—
323AGL(1,ℤ/8)—301no—
324#135—52no—
325#135—152no—
326#135—151no—
327#135D3×D511yescharacteristic, complemented
328C2×D8—31no—
329C2×D8—52no—
330C2×D8—51no—
331C2×D8—152no—
332#131—51no—
333Q32—151no—
334SD32—32no—
335SD32—152no—
336SD32—151no—
337SD32—151no—
338D16—32no—
339D16—152no—
340D16—152no—
341D16—152no—
342D16—151no—
343M32—31no—
344M32—152no—
345C2×C16—152no—
346C2×C16—151no—
347C2×C3×C5—21no—
348C2×C3×C5—81no—
349C2×C3×C5C22×D811yescharacteristic
350D15—81no—
351C3×D5—22no—
352C3×D5—82no—
353C5×D3—82no—
354C23×C3—202no—
355C23×C3—201no—
356C22×D3—41no—
357C22×D3—202no—
358C3×Q8—21no—
359C3×Q8—51no—
360C3×D4—21no—
361C3×D4—41no—
362C3×D4—52no—
363C3×D4—51no—
364C3×D4—102no—
365C3×D4—202no—
366C3×D4—202no—
367C3×D4—201no—
368C2×C3×C4—41no—
369C2×C3×C4—52no—
370C2×C3×C4—202no—
371C2×C3×C4D4×D511yescharacteristic
372#67—202no—
373#67—201no—
374D12—22no—
375D12—41no—
376D12—101no—
377D12—202no—
378C4×D3—202no—
379C4×D3—201no—
380Dic6—101no—
381C3×C8—52no—
382C3×C8D4×D511yescharacteristic
383C3×C8C23×D511yescharacteristic
384C22×C5—41no—
385C22×C5—122no—
386C22×C5—481no—
387C22×C5C2×#21311yescharacteristic
388C2×D5—42no—
389C2×D5—121no—
390C2×D5—162no—
391C2×D5—161no—
392C2×D5—482no—
393C2×D5C2×#21312yes—
394C4×C5—41no—
395C4×C5C2×#21311yescharacteristic
396C4×C5C22×#6711yescharacteristic
397Dic5—121no—
398Dic5C2×#21312yes—
399#41—21no—
400#41—51no—
401#41—102no—
402#41—201no—
403#41—302no—
404#41—301no—
405#41—601no—
406C2×D4—61no—
407C2×D4—102no—
408C2×D4—101no—
409C2×D4—201no—
410C2×D4—202no—
411C2×D4—302no—
412C2×D4—601no—
413C2×D4—602no—
414Q16—151no—
415Q16C2×D3×D511yescharacteristic
416SD16—21no—
417SD16—102no—
418SD16—302no—
419SD16—301no—
420D8—32no—
421D8—52no—
422D8—61no—
423D8—102no—
424D8—101no—
425D8—151no—
426D8—302no—
427D8C2×D3×D511yescharacteristic
428M16—51no—
429M16—52no—
430C2×C8—52no—
431C2×C8C2×D3×D511yescharacteristic
432C16—32no—
433C16—151no—
434C16—151no—
435C3×C5#341511yescharacteristic, complemented, Hall
436C22×C3—41no—
437C22×C3—52no—
438C22×C3—202no—
439C22×C3—801no—
440C22×C3—802no—
441C22×C3D5×D811yescharacteristic
442C2×D3—42no—
443C2×D3—161no—
444C2×D3—201no—
445C2×D3—802no—
446C3×C4—41no—
447C3×C4—52no—
448C3×C4D5×D811yescharacteristic
449C3×C4C2×D4×D511yescharacteristic
450Dic3—201no—
451C2×C5—21no—
452C2×C5—81no—
453C2×C5—242no—
454C2×C5C22×#21311yescharacteristic
455D5—22no—
456D5—82no—
457D5—241no—
458C23—121no—
459C23—202no—
460C23—201no—
461C23—602no—
462Q8—21no—
463Q8—51no—
464Q8—301no—
465D4—21no—
466D4—41no—
467D4—52no—
468D4—51no—
469D4—62no—
470D4—102no—
471D4—121no—
472D4—202no—
473D4—202no—
474D4—201no—
475D4—301no—
476D4—602no—
477D4—602no—
478D4—601no—
479C2×C4—41no—
480C2×C4—52no—
481C2×C4—202no—
482C2×C4—602no—
483C2×C4—601no—
484C2×C4D5×#6711yescharacteristic
485C8—52no—
486C8D5×#6711yescharacteristic
487C8C22×D3×D511yescharacteristic
488C2×C3—21no—
489C2×C3—81no—
490C2×C3—102no—
491C2×C3—402no—
492C2×C3C2×D5×D811yescharacteristic
493D3—82no—
494D3—401no—
495C5#8400711yescharacteristic, complemented, Sylow
496C22—41no—
497C22—52no—
498C22—122no—
499C22—202no—
500C22—481no—
501C22—601no—
502C22—801no—
503C22—802no—
504C22—2402no—
505C22D5×#21311yescharacteristic
506C4—41no—
507C4—52no—
508C4—601no—
509C4D5×#21311yescharacteristic
510C4C2×D5×#6711yescharacteristic
511C3#1061376711yescharacteristic, complemented, Sylow
512C2—21no—
513C2—81no—
514C2—102no—
515C2—242no—
516C2—402no—
517C2—1201no—
518C2C2×D5×#21311yescharacteristic
subgroupG/H
centerC2C2×D5×#213
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C22×D8
hypercenter#135D3×D5
hypocenterC3×C5#3415
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#66103C2semidirect
2. #11753961C2semidirect
3. #11751295C2semidirect
4. C5×#5193C2semidirect
5. #11748301C2semidirect
6. #11748289C2semidirect
7. #11748276C2semidirect
8. D5×#826C2semidirect
9. #11747543C2semidirect
10. C2×#90937C2semidirect
11. #11747525C2semidirect
15. C3×C5×#135C22semidirect
16. #91793C22semidirect
17. C2×C5×D24C22semidirect
19. C3×#4065C22semidirect
21. C3×D5×D8C22semidirect
22. C2×C3×D40C22semidirect
25. #91270C22semidirect
27. D5×D24C22semidirect
28. #91113C22semidirect
29. #91112C22semidirect
30. #91111C22semidirect
31. #91110C22semidirect
32. C2×C3⋊#672C22semidirect
33. C5×#828C22semidirect
34. C5×#826C22semidirect
35. C5×#812C22semidirect
36. #90942C22semidirect
37. #90938C22semidirect
38. #90937C22semidirect
39. #90937C22semidirect
40. #90934C22semidirect
41. D5×C3⋊C16C22semidirect
43. #66103D3semidirect
95. #5193D5semidirect
103. C5×#135C2×D3semidirect
107. #4065C2×D3semidirect
112. D5×D8C2×D3semidirect
114. C2×D40C2×D3semidirect
166. C3×#135C2×D5semidirect
175. C2×D24C2×D5semidirect
178. #828C2×D5semidirect
185. #826C2×D5semidirect
187. #812C2×D5semidirect
327. #135D3×D5semidirect
435. C3×C5#3415semidirect
495. C5#84007semidirect
511. C3#10613767semidirect

Maximal subgroups

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

subgroupindex
C3×#661032
#117539612
#117512952
C5×#51932
#117483012
#117482892
#117482762
D5×#8262
#117475432
C2×#909372
#117475252
#106137673
#840075