Finite Group Databasebeta

← #14418047

Subgroups — #14418047

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#11753969C211yesmaximal, characteristic
2D3×#4047C212yesmaximal, complemented
3#11750801C211yesmaximal, characteristic, complemented
4C5×#4689C211yesmaximal, characteristic, complemented
5C3×#64989C211yesmaximal, characteristic, complemented
6#11748076C212yesmaximal, complemented
7#11748069C211yesmaximal, characteristic, complemented
8#11748067C211yesmaximal, characteristic, complemented
9#11748059C211yesmaximal, characteristic, complemented
10#11747111C212yesmaximal, complemented
11#11747017C212yesmaximal, complemented
12#10610310—31nomaximal, Hall
13D3×#709C2212yes—
14#91793C2211yescharacteristic
15#91790C2212yescomplemented
16C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
17C2×C5×D3×C8C2211yescharacteristic
18C5×#872C2211yescharacteristic
19C3×#4050C2211yescharacteristic
20C3×#4047C2212yescomplemented
21#91311C2212yes—
22#91291C2212yescomplemented
23D3×#681C2212yes—
24#91283C2212yescomplemented
25#91274C412yescomplemented
26#91267—22no—
27#91265—22no—
28#91263C412yescomplemented
29#91254C412yescomplemented
30#91253C412yescomplemented
31D3×#676—22no—
32D3×C8×D5—22no—
33C3×C4×C5×C8C2211yescharacteristic, complemented
34#91103C2211yescharacteristic, complemented
35#91089C2212yescomplemented
36C5×#815C2211yescharacteristic, complemented
37C5×C8×Dic3C2211yescharacteristic, complemented
38C5×#803C2211yescharacteristic, complemented
39C3×#3951C2211yescharacteristic, complemented
40C3×#3937C2212yescomplemented
41#90993C2212yescomplemented
42#90980C2212yescomplemented
43#90977C2212yescomplemented
44#79888—51nomaximal, Hall
45#66082—31no—
46C2×#4047—32no—
47C5×#405—31no—
48#65414—31no—
49#65294—32no—
50#65006—31no—
51#65006—31no—
52#65006—32no—
53#64989—32no—
54#64989—31no—
55#64989D311yescharacteristic, complemented
56#6817C2312yes—
57C2×C4×C5×D3C2311yescharacteristic
58C3×#709C2312yes—
59D3×C22⋊D5—22no—
60#6779—22no—
61D3×D20C2×C412yes—
62C4×D3×D5—22no—
63#6771—22no—
64#6769C2×C412yes—
65D3×Dic10C2×C412yes—
66#6765C2×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×(C2×D3)⋊C4—21no—
77C5×Dic3⋊C4—21no—
78C4×C5×Dic3C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C5×ΓL(1,𝔽25)C2×C412yes—
82C5×ΓL(1,𝔽25)C2×C412yes—
83C5×D3×C8D412yes—
84C5×D3×C8D412yes—
85C3×#681C2312yes—
86C3×Dic20C2×C411yescharacteristic
87C3×D40C2×C411yescharacteristic
88C3×#677C2×C412yes—
89C3×#676—22no—
90C3×C8×D5—22no—
91#6662C2×C412yes—
92#6658C2×C412yes—
93#6657C2×C412yes—
94#6653C2×C412yes—
95#6651—22no—
96#6650—22no—
97#6649—22no—
98#6648—22no—
99D3×#168—22no—
100D5×C3⋊C8—22no—
101#5768—51no—
102D3×#131—52no—
103C3×#443—51no—
104#5197—51no—
105#5144—52no—
106#4894—51no—
107#4893—51no—
108#4823—52no—
109#4821—52no—
110#4700—51no—
111#4689D511yescharacteristic, complemented
112C2×#709—32no—
113C2×C5×M16—31no—
114C22×C5×C8—31no—
115C5×#117—31no—
116C2×#681—32no—
117#4055—32no—
118#4055—32no—
119#4054—32no—
120#4054—32no—
121#4050—32no—
122#4050—31no—
123#4050C2×D311yescharacteristic
124#4047—32no—
125#4047—32no—
126#4047—32no—
127#4047—62no—
128#4047—62no—
129#4047C2×D312yescomplemented
130C2×#676—62no—
131C2×C8×D5—62no—
132C5×#97—31no—
133C5×#97—31no—
134C4×C5×C8—31no—
135C4×C5×C8C2×D311yescharacteristic, complemented
136#3951—31no—
137#3951—32no—
138#3951C2×D311yescharacteristic, complemented
139#3937—32no—
140#3937—32no—
141#3937—32no—
142#3937C2×D312yescomplemented
143#2955—151noSylow
144C22×C5×D3#4111yescharacteristic
145C2×D3×D5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C2411yescharacteristic
148#1220—22no—
149D60C22×C412yes—
150C4×D15—22no—
151Dic30C22×C412yes—
152C2×C5×Dic3—21no—
153C2×C5×Dic3#4111yescharacteristic
154C4×C5×D3C22×C412yes—
155C4×C5×D3C2×D412yes—
156C3×C22⋊D5—22no—
157C3×D20C22×C412yes—
158C3×C4×D5—22no—
159C3×Dic10C22×C412yes—
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×#168—22no—
173C5×C3⋊C8C22×C412yes—
174C5×C3⋊C8C2×D412yes—
175D3×#41—52no—
176C3×#135—51no—
177C3×#131—52no—
178#950—52no—
179#948—52no—
180#918—52no—
181#915—52no—
182#914—52no—
183#911—52no—
184#907—52no—
185#907—102no—
186D3×M16—52no—
187D3×M16—102no—
188#904—51no—
189#901—52no—
190#901—102no—
191C2×ΓL(1,𝔽25)C2×D511yescharacteristic
192C2×D3×C8—102no—
193C2×D3×C8C2×D511yescharacteristic
194#872C2×D511yescharacteristic
195C3×#108—51no—
196C3×#104—52no—
197C3×C4×C8C2×D511yescharacteristic, complemented
198#837—52no—
199#825—52no—
200#822—52no—
201#819—51no—
202#815C2×D511yescharacteristic, complemented
203C8×Dic3C2×D511yescharacteristic, complemented
204#805—52no—
205#803C2×D511yescharacteristic, complemented
206C22×C4×C5—31no—
207C2×C22⋊D5—62no—
208#709—32no—
209#709—32no—
210#709—32no—
211#709—62no—
212#709—62no—
213#709C22×D312yes—
214C2×D20—32no—
215C2×C4×D5—62no—
216C2×Dic10—32no—
217C5×M16—32no—
218C5×M16—32no—
219C2×C5×C8—31no—
220C2×C5×C8—31no—
221C2×C5×C8—32no—
222C2×C5×C8—32no—
223C2×C5×C8C22×D311yescharacteristic
224C2×C5×C8C22×D311yescharacteristic
225C5×C4⋊C4—61no—
226C5×C22⋊C4—61no—
227C42×C5—31no—
228C42×C5C22×D311yescharacteristic
229#681—32no—
230#681—62no—
231#681C22×D312yes—
232C2×#168—62no—
233Dic20—32no—
234Dic20—31no—
235Dic20C4×D311yescharacteristic
236D40—32no—
237D40—31no—
238D40C4×D311yescharacteristic
239#677—32no—
240#677—32no—
241#677—32no—
242#677C4×D312yes—
243#676—22no—
244#676—62no—
245#676—62no—
246#676—62no—
247C8×D5—22no—
248C8×D5—62no—
249C8×D5—62no—
250C8×D5—62no—
251#575—151no—
252C2×#131—152no—
253#444—152no—
254#444—151no—
255#444—151no—
256#443—51no—
257#443—152no—
258#443—151no—
259#430—151no—
260#421—152no—
261#405—31no—
262C22×C3×C5C2×#4111yescharacteristic
263C2×D15—22no—
264C2×C5×D3—41no—
265C2×C5×D3C4×D412yes—
266C2×C3×D5—22no—
267D3×D5—44no—
268C3×C4×C5—41no—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×D411yescharacteristic
271Dic15—22no—
272C3×Dic5—22no—
273C5×Dic3—41no—
274C5×Dic3C4×D412yes—
275C3×#41—52no—
276#239—52no—
277D3×Q8—52no—
278#237—52no—
279#237—102no—
280D3×D4—52no—
281D3×D4—102no—
282#235—52no—
283#235—102no—
284C2×C4×D3—102no—
285C2×C4×D3C22×D511yescharacteristic
286C3×Q16—51no—
287C3×SD16—52no—
288C3×D8—51no—
289C3×M16—52no—
290C3×M16—102no—
291C2×C3×C8—102no—
292C2×C3×C8C22×D511yescharacteristic
293C2×C3×C8C22×D511yescharacteristic
294C3×C42C22×D511yescharacteristic
295#216—52no—
296#215—52no—
297#214—52no—
298#213—52no—
299(C2×D3)⋊C4—21no—
300Dic3⋊C4—21no—
301C4×Dic3C22×D511yescharacteristic
302#208—52no—
303#208—102no—
304C2×C3⋊C8—102no—
305C2×C3⋊C8C22×D511yescharacteristic
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12—51no—
308D24—51no—
309#204—52no—
310ΓL(1,𝔽25)—102no—
311ΓL(1,𝔽25)—102no—
312ΓL(1,𝔽25)—102no—
313ΓL(1,𝔽25)C4×D512yes—
314ΓL(1,𝔽25)C4×D512yes—
315D3×C8—102no—
316D3×C8—102no—
317D3×C8—102no—
318D3×C8D2012yes—
319D3×C8D2012yes—
320C23×C5—31no—
321C22×D5—62no—
322C2×C4×C5—21no—
323C2×C4×C5—31no—
324C2×C4×C5—32no—
325C2×C4×C5—32no—
326C2×C4×C5—61no—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—22no—
329C22⋊D5—62no—
330C22⋊D5—62no—
331C22⋊D5—62no—
332C2×Dic5—62no—
333D20—32no—
334D20—62no—
335D20C2×C4×D312yes—
336C4×D5—22no—
337C4×D5—62no—
338C4×D5—62no—
339C4×D5—62no—
340Dic10—32no—
341Dic10—62no—
342Dic10C2×C4×D312yes—
343C5×C8—32no—
344C5×C8—32no—
345C5×C8C2×C4×D311yescharacteristic
346C5×C8C2×C4×D311yescharacteristic
347C5×C8D3×D411yescharacteristic
348C5×C8D3×D411yescharacteristic
349#168—22no—
350#168—62no—
351C2×#41—152no—
352#137—152no—
353#137—152no—
354AGL(1,ℤ/8)—152no—
355AGL(1,ℤ/8)—152no—
356#135—51no—
357#135—152no—
358#135—151no—
359#131—52no—
360#131—152no—
361#131—152no—
362#131—152no—
363#131—302no—
364#131—302no—
365C2×M16—31no—
366C2×M16—152no—
367C2×M16—302no—
368C22×C8—31no—
369C22×C8—302no—
370#117—31no—
371#108—51no—
372#108—152no—
373#108—151no—
374#104—52no—
375#104—152no—
376#104—152no—
377#104—152no—
378#97—31no—
379#97—31no—
380C4×C8—31no—
381C4×C8D3×D511yescharacteristic, complemented
382C2×C3×C5—21no—
383C2×C3×C5C2×C4×D411yescharacteristic
384D15—42no—
385C3×D5—42no—
386C5×D3—22no—
387C22×D3—102no—
388C22×D3#70911yescharacteristic
389C3×Q8—52no—
390C3×D4—52no—
391C3×D4—102no—
392C2×C3×C4—21no—
393C2×C3×C4—102no—
394C2×C3×C4C23×D511yescharacteristic
395#67—102no—
396#67—102no—
397#67—102no—
398C2×Dic3—21no—
399C2×Dic3—102no—
400C2×Dic3#70911yescharacteristic
401D12—52no—
402D12—102no—
403C4×D3—102no—
404C4×D3—102no—
405C4×D3—102no—
406C4×D3C2×C4×D512yes—
407C4×D3C2×D2012yes—
408Dic6—52no—
409Dic6—102no—
410C3×C8—102no—
411C3×C8C2×C4×D511yescharacteristic
412C3×C8C2×C4×D511yescharacteristic
413C3×C8C2×D2011yescharacteristic
414C3×C8C2×D2011yescharacteristic
415C3⋊C8—102no—
416C3⋊C8C2×C4×D512yes—
417C3⋊C8C2×D2012yes—
418C22×C5—32no—
419C22×C5—121no—
420C22×C5D3×#4111yescharacteristic
421C2×D5—22no—
422C2×D5—62no—
423C2×D5—124no—
424C4×C5—32no—
425C4×C5—41no—
426C4×C5—121no—
427C4×C5C22×C4×D311yescharacteristic
428C4×C5C2×D3×D411yescharacteristic
429Dic5—22no—
430Dic5—62no—
431#41—52no—
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—31no—
441C22×C4—302no—
442Q16—51no—
443Q16—152no—
444Q16—151no—
445SD16—52no—
446SD16—152no—
447SD16—152no—
448SD16—152no—
449D8—51no—
450D8—152no—
451D8—151no—
452M16—32no—
453M16—32no—
454M16—52no—
455M16—102no—
456M16—152no—
457M16—302no—
458M16—302no—
459M16—302no—
460M16—302no—
461C2×C8—31no—
462C2×C8—31no—
463C2×C8—32no—
464C2×C8—32no—
465C2×C8—102no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8—302no—
470C2×C8C2×D3×D511yescharacteristic
471C2×C8C2×D3×D511yescharacteristic
472C4⋊C4—61no—
473C22⋊C4—61no—
474C42—31no—
475C42C2×D3×D511yescharacteristic
476C3×C5#295511yescharacteristic, complemented, Hall
477C22×C3—102no—
478C22×C3C2×#70911yescharacteristic
479C2×D3—41no—
480C2×D3—102no—
481C2×D3—204no—
482C2×D3C4×D2012yes—
483C3×C4—41no—
484C3×C4—102no—
485C3×C4C22×C4×D511yescharacteristic
486C3×C4C22×D2011yescharacteristic
487Dic3—41no—
488Dic3—102no—
489Dic3C4×D2012yes—
490C2×C5—21no—
491C2×C5—62no—
492C2×C5C4×D3×D411yescharacteristic
493D5—42no—
494D5—122no—
495C23—31no—
496C23—302no—
497Q8—52no—
498Q8—152no—
499Q8—302no—
500D4—52no—
501D4—102no—
502D4—152no—
503D4—302no—
504D4—302no—
505D4—302no—
506D4—302no—
507C2×C4—21no—
508C2×C4—31no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—61no—
512C2×C4—102no—
513C2×C4—302no—
514C2×C4—302no—
515C2×C4—302no—
516C2×C4—302no—
517C2×C4C22×D3×D511yescharacteristic
518C8—32no—
519C8—32no—
520C8—102no—
521C8—302no—
522C8C4×D3×D511yescharacteristic
523C8C4×D3×D511yescharacteristic
524C8D3×D2011yescharacteristic
525C8D3×D2011yescharacteristic
526C2×C3—21no—
527C2×C3—202no—
528C2×C3C2×C4×D2011yescharacteristic
529D3—22no—
530D3—202no—
531C5#7988811yescharacteristic, complemented, Sylow
532C22—32no—
533C22—102no—
534C22—121no—
535C22—302no—
536C22—604no—
537C22D3×#70911yescharacteristic
538C4—32no—
539C4—41no—
540C4—102no—
541C4—121no—
542C4—302no—
543C4C2×C4×D3×D511yescharacteristic
544C4C2×D3×D2011yescharacteristic
545C3#1061031011yescharacteristic, complemented, Sylow
546C2—21no—
547C2—62no—
548C2—202no—
549C2—602no—
550C2C4×D3×D2011yescharacteristic
subgroupG/H
centerC8D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC2×C3×C5C2×C4×D4
prime radical#11753969C2
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. D3×#4047C2semidirect
3. #11750801C2semidirect
4. C5×#4689C2semidirect
5. C3×#64989C2semidirect
6. #11748076C2semidirect
7. #11748069C2semidirect
8. #11748067C2semidirect
9. #11748059C2semidirect
10. #11747111C2semidirect
11. #11747017C2semidirect
15. #91790C22semidirect
20. C3×#4047C22semidirect
22. #91291C22semidirect
24. #91283C22semidirect
25. #91274C4semidirect
28. #91263C4semidirect
29. #91254C4semidirect
30. #91253C4semidirect
33. C3×C4×C5×C8C22semidirect
34. #91103C22semidirect
35. #91089C22semidirect
36. C5×#815C22semidirect
37. C5×C8×Dic3C22semidirect
38. C5×#803C22semidirect
39. C3×#3951C22semidirect
40. C3×#3937C22semidirect
41. #90993C22semidirect
42. #90980C22semidirect
43. #90977C22semidirect
55. #64989D3semidirect
111. #4689D5semidirect
129. #4047C2×D3semidirect
135. C4×C5×C8C2×D3semidirect
138. #3951C2×D3semidirect
142. #3937C2×D3semidirect
197. C3×C4×C8C2×D5semidirect
202. #815C2×D5semidirect
203. C8×Dic3C2×D5semidirect
205. #803C2×D5semidirect
381. C4×C8D3×D5semidirect
476. C3×C5#2955semidirect
531. C5#79888semidirect
545. C3#10610310semidirect

Maximal subgroups

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

subgroupindex
#117539692
D3×#40472
#117508012
C5×#46892
C3×#649892
#117480762
#117480692
#117480672
#117480592
#117471112
#117470172
#106103103
#798885