Finite Group Databasebeta

← #14418045

Subgroups — #14418045

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11753959C211yesmaximal, characteristic
2D5×#901C212yesmaximal, complemented
3#11750801C211yesmaximal, characteristic, complemented
4C5×#4700C211yesmaximal, characteristic, complemented
5C3×#64978C211yesmaximal, characteristic, complemented
6#11748078C212yesmaximal, complemented
7#11748065C211yesmaximal, characteristic, complemented
8#11748063C211yesmaximal, characteristic, complemented
9#11748057C211yesmaximal, characteristic, complemented
10#11747109C212yesmaximal, complemented
11#11747019C212yesmaximal, complemented
12#10611619—31nomaximal, Hall
13D5×#235C2212yes—
14#91793C2211yescharacteristic
15#91790C2212yescomplemented
16C5×#904C2211yescharacteristic
17C5×#901C2212yescomplemented
18C2×C3×#676C2211yescharacteristic
19C2×C3×C8×D5C2211yescharacteristic
20C3×#4018C2211yescharacteristic
21#91303C2212yes—
22#91290C2212yescomplemented
23#91286C2212yescomplemented
24D5×#208C2212yes—
25#91266—22no—
26#91265—22no—
27#91261C412yescomplemented
28#91260C412yescomplemented
29#91250C412yescomplemented
30#91249C412yescomplemented
31D5×ΓL(1,𝔽25)—22no—
32D3×C8×D5—22no—
33C3×C4×C5×C8C2211yescharacteristic, complemented
34#91103C2211yescharacteristic, complemented
35#91089C2212yescomplemented
36C5×#819C2211yescharacteristic, complemented
37C5×#805C2212yescomplemented
38C3×#3947C2211yescharacteristic, complemented
39C3×C8×Dic5C2211yescharacteristic, complemented
40C3×#3935C2211yescharacteristic, complemented
41#90991C2212yescomplemented
42#90981C2212yescomplemented
43#90979C2212yescomplemented
44#78579—51nomaximal, Hall
45#66102—31no—
46D5×#131—32no—
47C5×#443—31no—
48#65486—31no—
49#65433—32no—
50#65183—31no—
51#65182—31no—
52#65112—32no—
53#65110—32no—
54#64989—31no—
55#64978D311yescharacteristic, complemented
56#6817C2312yes—
57C5×#235C2312yes—
58C2×C3×C4×D5C2311yescharacteristic
59D5×#67—22no—
60#6782—22no—
61D5×D12C2×C412yes—
62C4×D3×D5—22no—
63#6773C2×C412yes—
64#6772C2×C412yes—
65#6771—22no—
66D5×Dic6C2×C412yes—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70#6710C2312yes—
71Dic60C2×C411yescharacteristic
72D120C2×C411yescharacteristic
73#6706C2×C412yes—
74#6705—22no—
75C8×D15—22no—
76C5×#208C2312yes—
77C5×Dic12C2×C411yescharacteristic
78C5×D24C2×C411yescharacteristic
79C5×#204C2×C412yes—
80C5×ΓL(1,𝔽25)—22no—
81C5×D3×C8—22no—
82C3×#685—21no—
83C3×#683—21no—
84C3×C4×Dic5C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
86C2×C3×#168C2311yescharacteristic
87C3×#676C2×C412yes—
88C3×#676C2×C412yes—
89C3×C8×D5D412yes—
90C3×C8×D5D412yes—
91#6663C2×C412yes—
92#6660C2×C412yes—
93#6659C2×C412yes—
94#6654C2×C412yes—
95#6651—22no—
96#6650—22no—
97#6649—22no—
98#6648—22no—
99D3×#168—22no—
100D5×C3⋊C8—22no—
101#5748—51no—
102C2×#901—52no—
103C3×#405—51no—
104#5125—51no—
105#5005—52no—
106#4717—51no—
107#4717—51no—
108#4717—52no—
109#4700—52no—
110#4700—51no—
111#4700D511yescharacteristic, complemented
112D5×#41—32no—
113C5×#135—31no—
114C5×#131—32no—
115#4096—32no—
116#4094—32no—
117#4064—32no—
118#4061—32no—
119#4060—32no—
120#4057—32no—
121#4053—32no—
122#4053—62no—
123D5×M16—32no—
124D5×M16—62no—
125#4050—31no—
126#4047—32no—
127#4047—62no—
128C2×#676C2×D311yescharacteristic
129C2×C8×D5—62no—
130C2×C8×D5C2×D311yescharacteristic
131#4018C2×D311yescharacteristic
132C5×#108—31no—
133C5×#104—32no—
134C4×C5×C8C2×D311yescharacteristic, complemented
135#3969—32no—
136#3957—32no—
137#3954—32no—
138#3951—31no—
139#3947C2×D311yescharacteristic, complemented
140C8×Dic5C2×D311yescharacteristic, complemented
141#3937—32no—
142#3935C2×D311yescharacteristic, complemented
143#2955—151noSylow
144C22×C3×D5#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C2411yescharacteristic
148#1220—22no—
149D60C22×C412yes—
150C4×D15—22no—
151Dic30C22×C412yes—
152C5×#67—22no—
153C5×D12C22×C412yes—
154C4×C5×D3—22no—
155C5×Dic6C22×C412yes—
156C2×C3×Dic5—21no—
157C2×C3×Dic5#4111yescharacteristic
158C3×C4×D5C22×C412yes—
159C3×C4×D5C2×D412yes—
160#1204—22no—
161#1203—22no—
162#1202—22no—
163#1201—22no—
164#1200—22no—
165D3×Dic5—22no—
166D5×Dic3—22no—
167C3×C5×C8C22×C411yescharacteristic
168C3×C5×C8C22×C411yescharacteristic
169C3×C5×C8C2×D411yescharacteristic
170C3×C5×C8C2×D411yescharacteristic
171C3⋊#168—22no—
172C3×#168C22×C412yes—
173C3×#168C2×D412yes—
174C5×C3⋊C8—22no—
175C2×#235—52no—
176C2×C3×M16—51no—
177C22×C3×C8—51no—
178C3×#117—51no—
179C2×#208—52no—
180#909—52no—
181#909—52no—
182#908—52no—
183#908—52no—
184#904—52no—
185#904—51no—
186#904C2×D511yescharacteristic
187#901—52no—
188#901—52no—
189#901—52no—
190#901—102no—
191#901—102no—
192#901C2×D512yescomplemented
193C2×ΓL(1,𝔽25)—102no—
194C2×D3×C8—102no—
195C3×#97—51no—
196C3×#97—51no—
197C3×C4×C8—51no—
198C3×C4×C8C2×D511yescharacteristic, complemented
199#819—51no—
200#819—52no—
201#819C2×D511yescharacteristic, complemented
202#805—52no—
203#805—52no—
204#805—52no—
205#805C2×D512yescomplemented
206C5×#41—32no—
207#713—32no—
208Q8×D5—32no—
209#711—32no—
210#711—62no—
211D4×D5—32no—
212D4×D5—62no—
213#709—32no—
214#709—62no—
215C2×C4×D5—62no—
216C2×C4×D5C22×D311yescharacteristic
217C5×Q16—31no—
218C5×SD16—32no—
219C5×D8—31no—
220C5×M16—32no—
221C5×M16—62no—
222C2×C5×C8—62no—
223C2×C5×C8C22×D311yescharacteristic
224C2×C5×C8C22×D311yescharacteristic
225C42×C5C22×D311yescharacteristic
226#689—32no—
227#688—32no—
228#687—32no—
229#686—32no—
230#685—21no—
231#683—21no—
232C4×Dic5C22×D311yescharacteristic
233#681—32no—
234#681—62no—
235C2×#168—62no—
236C2×#168C22×D311yescharacteristic
237C2×#168C22×D311yescharacteristic
238Dic20—31no—
239D40—31no—
240#677—32no—
241#676—62no—
242#676—62no—
243#676—62no—
244#676C4×D312yes—
245#676C4×D312yes—
246C8×D5—62no—
247C8×D5—62no—
248C8×D5—62no—
249C8×D5D1212yes—
250C8×D5D1212yes—
251#575—151no—
252C2×#131—152no—
253#444—152no—
254#444—151no—
255#444—151no—
256#443—31no—
257#443—152no—
258#443—151no—
259#430—151no—
260#421—152no—
261#405—51no—
262C22×C3×C5C2×#4111yescharacteristic
263C2×D15—22no—
264C2×C5×D3—22no—
265C2×C3×D5—41no—
266C2×C3×D5C4×D412yes—
267D3×D5—44no—
268C3×C4×C5—41no—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272C3×Dic5—41no—
273C3×Dic5C4×D412yes—
274C5×Dic3—22no—
275C22×C3×C4—51no—
276C2×#67—102no—
277#235—52no—
278#235—52no—
279#235—52no—
280#235—102no—
281#235—102no—
282#235C22×D512yes—
283C2×D12—52no—
284C2×C4×D3—102no—
285C2×Dic6—52no—
286C3×M16—52no—
287C3×M16—52no—
288C2×C3×C8—51no—
289C2×C3×C8—51no—
290C2×C3×C8—52no—
291C2×C3×C8—52no—
292C2×C3×C8C22×D511yescharacteristic
293C2×C3×C8C22×D511yescharacteristic
294C3×C4⋊C4—101no—
295C3×C22⋊C4—101no—
296C3×C42—51no—
297C3×C42C22×D511yescharacteristic
298#208—52no—
299#208—102no—
300#208C22×D512yes—
301C2×C3⋊C8—102no—
302Dic12—52no—
303Dic12—51no—
304Dic12C4×D511yescharacteristic
305D24—52no—
306D24—51no—
307D24C4×D511yescharacteristic
308#204—52no—
309#204—52no—
310#204—52no—
311#204C4×D512yes—
312ΓL(1,𝔽25)—22no—
313ΓL(1,𝔽25)—102no—
314ΓL(1,𝔽25)—102no—
315ΓL(1,𝔽25)—102no—
316D3×C8—22no—
317D3×C8—102no—
318D3×C8—102no—
319D3×C8—102no—
320C22×D5—62no—
321C22×D5#23511yescharacteristic
322C5×Q8—32no—
323C5×D4—32no—
324C5×D4—62no—
325C2×C4×C5—21no—
326C2×C4×C5—62no—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—62no—
329C22⋊D5—62no—
330C22⋊D5—62no—
331C2×Dic5—21no—
332C2×Dic5—62no—
333C2×Dic5#23511yescharacteristic
334D20—32no—
335D20—62no—
336C4×D5—62no—
337C4×D5—62no—
338C4×D5—62no—
339C4×D5C2×C4×D312yes—
340C4×D5C2×D1212yes—
341Dic10—32no—
342Dic10—62no—
343C5×C8—62no—
344C5×C8C2×C4×D311yescharacteristic
345C5×C8C2×C4×D311yescharacteristic
346C5×C8C2×D1211yescharacteristic
347C5×C8C2×D1211yescharacteristic
348#168—62no—
349#168C2×C4×D312yes—
350#168C2×D1212yes—
351C2×#41—152no—
352#137—152no—
353#137—152no—
354AGL(1,ℤ/8)—152no—
355AGL(1,ℤ/8)—152no—
356#135—31no—
357#135—152no—
358#135—151no—
359#131—32no—
360#131—152no—
361#131—152no—
362#131—152no—
363#131—302no—
364#131—302no—
365C2×M16—51no—
366C2×M16—152no—
367C2×M16—302no—
368C22×C8—51no—
369C22×C8—302no—
370#117—51no—
371#108—31no—
372#108—152no—
373#108—151no—
374#104—32no—
375#104—152no—
376#104—152no—
377#104—152no—
378#97—51no—
379#97—51no—
380C4×C8—51no—
381C4×C8D3×D511yescharacteristic, complemented
382C2×C3×C5—21no—
383C2×C3×C5C2×C4×D411yescharacteristic
384D15—42no—
385C3×D5—22no—
386C5×D3—42no—
387C23×C3—51no—
388C22×D3—102no—
389C2×C3×C4—21no—
390C2×C3×C4—51no—
391C2×C3×C4—52no—
392C2×C3×C4—52no—
393C2×C3×C4—101no—
394C2×C3×C4C23×D511yescharacteristic
395#67—22no—
396#67—102no—
397#67—102no—
398#67—102no—
399C2×Dic3—102no—
400D12—52no—
401D12—102no—
402D12C2×C4×D512yes—
403C4×D3—22no—
404C4×D3—102no—
405C4×D3—102no—
406C4×D3—102no—
407Dic6—52no—
408Dic6—102no—
409Dic6C2×C4×D512yes—
410C3×C8—52no—
411C3×C8—52no—
412C3×C8C2×C4×D511yescharacteristic
413C3×C8C2×C4×D511yescharacteristic
414C3×C8D4×D511yescharacteristic
415C3×C8D4×D511yescharacteristic
416C3⋊C8—22no—
417C3⋊C8—102no—
418C22×C5—62no—
419C22×C5C2×#23511yescharacteristic
420C2×D5—41no—
421C2×D5—62no—
422C2×D5—124no—
423C2×D5C4×D1212yes—
424C4×C5—41no—
425C4×C5—62no—
426C4×C5C22×C4×D311yescharacteristic
427C4×C5C22×D1211yescharacteristic
428Dic5—41no—
429Dic5—62no—
430Dic5C4×D1212yes—
431#41—32no—
432#41—152no—
433#41—152no—
434#41—152no—
435#41—302no—
436#41—302no—
437C2×Q8—152no—
438C2×D4—152no—
439C2×D4—302no—
440C22×C4—51no—
441C22×C4—302no—
442Q16—31no—
443Q16—152no—
444Q16—151no—
445SD16—32no—
446SD16—152no—
447SD16—152no—
448SD16—152no—
449D8—31no—
450D8—152no—
451D8—151no—
452M16—32no—
453M16—52no—
454M16—52no—
455M16—62no—
456M16—152no—
457M16—302no—
458M16—302no—
459M16—302no—
460M16—302no—
461C2×C8—51no—
462C2×C8—51no—
463C2×C8—52no—
464C2×C8—52no—
465C2×C8—62no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8—302no—
470C2×C8C2×D3×D511yescharacteristic
471C2×C8C2×D3×D511yescharacteristic
472C4⋊C4—101no—
473C22⋊C4—101no—
474C42—51no—
475C42C2×D3×D511yescharacteristic
476C3×C5#295511yescharacteristic, complemented, Hall
477C22×C3—52no—
478C22×C3—201no—
479C22×C3D5×#4111yescharacteristic
480C2×D3—22no—
481C2×D3—102no—
482C2×D3—204no—
483C3×C4—41no—
484C3×C4—52no—
485C3×C4—201no—
486C3×C4C22×C4×D511yescharacteristic
487C3×C4C2×D4×D511yescharacteristic
488Dic3—22no—
489Dic3—102no—
490C2×C5—21no—
491C2×C5—122no—
492C2×C5C2×C4×D1211yescharacteristic
493D5—22no—
494D5—122no—
495C23—51no—
496C23—302no—
497Q8—32no—
498Q8—152no—
499Q8—302no—
500D4—32no—
501D4—62no—
502D4—152no—
503D4—302no—
504D4—302no—
505D4—302no—
506D4—302no—
507C2×C4—21no—
508C2×C4—51no—
509C2×C4—52no—
510C2×C4—52no—
511C2×C4—62no—
512C2×C4—101no—
513C2×C4—302no—
514C2×C4—302no—
515C2×C4—302no—
516C2×C4—302no—
517C2×C4C22×D3×D511yescharacteristic
518C8—52no—
519C8—52no—
520C8—62no—
521C8—302no—
522C8C4×D3×D511yescharacteristic
523C8C4×D3×D511yescharacteristic
524C8D5×D1211yescharacteristic
525C8D5×D1211yescharacteristic
526C2×C3—21no—
527C2×C3—102no—
528C2×C3C4×D4×D511yescharacteristic
529D3—42no—
530D3—202no—
531C5#7857911yescharacteristic, complemented, Sylow
532C22—52no—
533C22—62no—
534C22—201no—
535C22—302no—
536C22—604no—
537C22D5×#23511yescharacteristic
538C4—41no—
539C4—52no—
540C4—62no—
541C4—201no—
542C4—302no—
543C4C2×C4×D3×D511yescharacteristic
544C4C2×D5×D1211yescharacteristic
545C3#1061161911yescharacteristic, complemented, Sylow
546C2—21no—
547C2—102no—
548C2—122no—
549C2—602no—
550C2C4×D5×D1211yescharacteristic
subgroupG/H
centerC8D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC2×C3×C5C2×C4×D4
prime radical#11753959C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2955
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. D5×#901C2semidirect
3. #11750801C2semidirect
4. C5×#4700C2semidirect
5. C3×#64978C2semidirect
6. #11748078C2semidirect
7. #11748065C2semidirect
8. #11748063C2semidirect
9. #11748057C2semidirect
10. #11747109C2semidirect
11. #11747019C2semidirect
15. #91790C22semidirect
17. C5×#901C22semidirect
22. #91290C22semidirect
23. #91286C22semidirect
27. #91261C4semidirect
28. #91260C4semidirect
29. #91250C4semidirect
30. #91249C4semidirect
33. C3×C4×C5×C8C22semidirect
34. #91103C22semidirect
35. #91089C22semidirect
36. C5×#819C22semidirect
37. C5×#805C22semidirect
38. C3×#3947C22semidirect
39. C3×C8×Dic5C22semidirect
40. C3×#3935C22semidirect
41. #90991C22semidirect
42. #90981C22semidirect
43. #90979C22semidirect
55. #64978D3semidirect
111. #4700D5semidirect
134. C4×C5×C8C2×D3semidirect
139. #3947C2×D3semidirect
140. C8×Dic5C2×D3semidirect
142. #3935C2×D3semidirect
192. #901C2×D5semidirect
198. C3×C4×C8C2×D5semidirect
201. #819C2×D5semidirect
205. #805C2×D5semidirect
381. C4×C8D3×D5semidirect
476. C3×C5#2955semidirect
531. C5#78579semidirect
545. C3#10611619semidirect

Maximal subgroups

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

subgroupindex
#117539592
D5×#9012
#117508012
C5×#47002
C3×#649782
#117480782
#117480652
#117480632
#117480572
#117471092
#117470192
#106116193
#785795