Finite Group Databasebeta

← #14478575

Subgroups — #14478575

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5757C211yesmaximal, characteristic, complemented
2#11753991C211yesmaximal, characteristic, complemented
3#11751248C211yesmaximal, characteristic, complemented
4C2×C3×#3959C211yesmaximal, characteristic, complemented
5#11748283C212yesmaximal, complemented
6#11748282C212yesmaximal, complemented
7#11748273C212yesmaximal, complemented
8D3×#3959C212yesmaximal, complemented
9#11747552C211yesmaximal, characteristic, complemented
10#11747546C211yesmaximal, characteristic, complemented
11#11747527C211yesmaximal, characteristic, complemented
12#10615739—31nomaximal, Hall
13C5×#1004—21no—
14#92004—21no—
15C2×C3×C5×D8C2211yescharacteristic
16#91793C2211yescharacteristic, complemented
17C5×#932—21no—
18C5×#912C2212yes—
19C5×#911—22no—
20C5×D3×D8C2212yes—
21C5×#904C2211yescharacteristic
22C5×#901C2211yescharacteristic
23C2×C3×Dic20C2211yescharacteristic, complemented
24#91315—21no—
25#91275C2212yescomplemented
26#91263—22no—
27D3×Dic20C2212yescomplemented
28#91111C2212yescomplemented
29#91110C2212yescomplemented
30#91096C2211yescharacteristic, complemented
31C3×#3959C2212yescomplemented
32C3×#3959C2212yescomplemented
33C2×C3×#672C2211yescharacteristic, complemented
34#90948C2211yescharacteristic, complemented
35#90946C2212yescomplemented
36#90945C2211yescharacteristic, complemented
37#90944C2211yescharacteristic, complemented
38#90941C2212yescomplemented
39#90939C2211yescharacteristic, complemented
40#90935C2212yescomplemented
41D3×#672C2212yescomplemented
42#82024—51nomaximal, Hall
43C5×#576—31no—
44#66087—31no—
45#65484—31no—
46#65484—32no—
47#65483—32no—
48#65483—31no—
49C2×#3959—32no—
50C2×#3959D311yescharacteristic, complemented
51#65436—32no—
52#65436—31no—
53#65429—31no—
54C2×C3×C5×D4—21no—
55#6817—21no—
56C2×C5×#67—42no—
57C5×#237—22no—
58C5×#237—41no—
59C5×D3×D4—22no—
60C5×D3×D4—41no—
61C5×#235—21no—
62C5×#235D411yescharacteristic
63C2×C3×Dic10—21no—
64#6782—42no—
65D15⋊Q8—41no—
66#6769—22no—
67#6768—41no—
68D3×Dic10—22no—
69C3×C5×D8—21no—
70C3×C5×D8C2312yes—
71C2×C3×C5×C8C2311yescharacteristic
72Dic60C2311yescharacteristic
73D120C2311yescharacteristic
74#6706—21no—
75C5×#214—22no—
76C5×#213—22no—
77C5×#208D411yescharacteristic
78C5×Dic12C2311yescharacteristic
79C5×D24C2311yescharacteristic
80C5×#204—21no—
81C5×ΓL(1,𝔽25)D412yes—
82C5×D3×C8C2312yes—
83C3×Dic20—21no—
84C3×Dic20C2312yes—
85#6662—22no—
86#6658—22no—
87C3⋊#672C2312yes—
88C3×#672C2311yescharacteristic
89C3×#672C2311yescharacteristic
90#5766—51no—
91#5757D511yescharacteristic, complemented
92C2×C3×SD32—51no—
93#5179—51no—
94#5147—51no—
95#4916—52no—
96#4915—52no—
97#4914—52no—
98D3×SD32—52no—
99#4904—51no—
100#4901—51no—
101C5×H(5,𝔽2)—61no—
102#4150—61no—
103C5×AGL(1,ℤ/8)—62no—
104C5×AGL(1,ℤ/8)—61no—
105C5×#135—32no—
106C5×#135—31no—
107C2×C5×D8—32no—
108C2×C5×D8C2×D311yescharacteristic
109C5×#131—31no—
110#4055—62no—
111#4055—61no—
112C2×Dic20—32no—
113C2×Dic20C2×D311yescharacteristic, complemented
114#4050—31no—
115#4050—32no—
116#3961—32no—
117#3961—31no—
118#3960—31no—
119#3959—32no—
120#3959—32no—
121#3959—31no—
122#3959C2×D312yescomplemented
123#3959C2×D312yescomplemented
124#3958—32no—
125#3958—31no—
126#3944—31no—
127#3944—32no—
128C2×#672—32no—
129C2×#672C2×D311yescharacteristic, complemented
130#3416—151noSylow
131C23×C3×C5—41no—
132C22×C5×D3—42no—
133C3×C5×D4—22no—
134C3×C5×D4—41no—
135C2×C3×C4×C5C2×D411yescharacteristic
136#1220—41no—
137D60—21no—
138C4×D15—41no—
139Dic30—21no—
140C5×#67—41no—
141C5×#67—42no—
142C5×#67—42no—
143C5×#67D812yes—
144C2×C5×Dic3—42no—
145C5×D12—21no—
146C5×D12D811yescharacteristic
147C4×C5×D3—41no—
148C4×C5×D3C2×D412yes—
149C5×Dic6—21no—
150C5×Dic6D811yescharacteristic
151C2×C3×Dic5—41no—
152C3×Dic10—22no—
153C3×Dic10—41no—
154#1204—42no—
155#1203—42no—
156#1200—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C5×C3⋊C8C2×D412yes—
161#1007—101no—
162#1004—21no—
163C2×C3×Q16—51no—
164C2×C3×D8C2×D511yescharacteristic
165#942—101no—
166#932—21no—
167#919—52no—
168#918—102no—
169D3×Q16—52no—
170#912C2×D512yes—
171#911—22no—
172D3×D8C2×D512yes—
173#904—51no—
174#904C2×D511yescharacteristic
175#901C2×D511yescharacteristic
176C3×SD32—52no—
177C3×SD32—52no—
178C2×C3×C16—51no—
179#829—52no—
180#828—52no—
181#827—52no—
182#826—52no—
183#812—51no—
184Dic24—51no—
185#800—51no—
186#800—51no—
187D48—51no—
188#798—52no—
189D3×C16—52no—
190C5×#41—31no—
191C5×#41—62no—
192C5×#41—61no—
193C5×#41—121no—
194C2×C5×D4—21no—
195C2×C5×D4—62no—
196C2×C5×D4—121no—
197C2×C5×D4—122no—
198Q8×D5—121no—
199#711—121no—
200#711—122no—
201#709—62no—
202#709—61no—
203C2×Dic10—21no—
204C2×Dic10—62no—
205C5×Q16—31no—
206C5×SD16—62no—
207C5×SD16—61no—
208C5×D8—21no—
209C5×D8—31no—
210C5×D8—62no—
211C5×D8C22×D312yes—
212C5×M16—31no—
213C5×M16—32no—
214C2×C5×C8—32no—
215C2×C5×C8C22×D311yescharacteristic
216Dic20—21no—
217Dic20—31no—
218Dic20—62no—
219Dic20C22×D312yes—
220D40—31no—
221#677—62no—
222#677—61no—
223#672—32no—
224#672C22×D311yescharacteristic
225#672C22×D311yescharacteristic
226#578—151no—
227#576—31no—
228#510—152no—
229#510—151no—
230#509—152no—
231#509—151no—
232#508—151no—
233#508—152no—
234C2×SD32—51no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5—42no—
238C22×C3×C5—161no—
239C22×C3×C5C2×D811yescharacteristic
240C2×D15—41no—
241C2×C5×D3—41no—
242C2×C5×D3—162no—
243C2×C5×D3C2×D812yes—
244C3×C4×C5C2×D811yescharacteristic
245C3×C4×C5C22×D411yescharacteristic
246Dic15—41no—
247C3×Dic5—42no—
248C5×Dic3—41no—
249C5×Dic3C2×D812yes—
250C2×C3×Q8—101no—
251C2×C3×D4—21no—
252C2×#67—42no—
253#239—102no—
254#239—201no—
255D3×Q8—102no—
256D3×Q8—201no—
257#237—22no—
258#237—41no—
259D3×D4—22no—
260D3×D4—41no—
261#235—21no—
262#235—101no—
263#235—202no—
264#235C22⋊D511yescharacteristic
265C3×Q16—52no—
266C3×Q16—101no—
267C3×D8—21no—
268C3×D8C22×D512yes—
269C2×C3×C8C22×D511yescharacteristic
270#216—102no—
271#215—102no—
272#214—22no—
273#213—22no—
274#208C22⋊D511yescharacteristic
275Dic12—51no—
276Dic12C22×D511yescharacteristic
277D24—51no—
278D24C22×D511yescharacteristic
279#204—21no—
280#204—101no—
281ΓL(1,𝔽25)C22⋊D512yes—
282D3×C8C22×D512yes—
283C3×C16—51no—
284C3×C16—51no—
285C3⋊C16—52no—
286C23×C5—41no—
287C23×C5—122no—
288C5×Q8—31no—
289C5×Q8—61no—
290C5×D4—22no—
291C5×D4—32no—
292C5×D4—31no—
293C5×D4—41no—
294C5×D4—61no—
295C5×D4—122no—
296C5×D4—122no—
297C5×D4—121no—
298C2×C4×C5—32no—
299C2×C4×C5—122no—
300C2×C4×C5—121no—
301C2×C4×C5D3×D411yescharacteristic
302C22⋊D5—122no—
303C22⋊D5—121no—
304C2×Dic5—41no—
305C2×Dic5—122no—
306D20—61no—
307C4×D5—122no—
308C4×D5—121no—
309Dic10—22no—
310Dic10—41no—
311Dic10—61no—
312Dic10—122no—
313C5×C8—32no—
314C5×C8D3×D411yescharacteristic
315C5×C8C23×D311yescharacteristic
3162−1+4—301no—
317H(5,𝔽2)—61no—
318#137—302no—
319#137—301no—
320AGL(1,ℤ/8)—62no—
321AGL(1,ℤ/8)—61no—
322#135—32no—
323#135—31no—
324#135—152no—
325#135—151no—
326C2×Q16—51no—
327C2×Q16—152no—
328C2×D8—32no—
329C2×D8D3×D511yescharacteristic
330#131—31no—
331Q32—151no—
332Q32—152no—
333SD32—52no—
334SD32—52no—
335SD32—151no—
336SD32—151no—
337SD32—152no—
338SD32—152no—
339D16—151no—
340D16—152no—
341M32—152no—
342M32—151no—
343C2×C16—51no—
344C2×C16—152no—
345C2×C3×C5—21no—
346C2×C3×C5—82no—
347C2×C3×C5C22×D811yescharacteristic
348D15—81no—
349C5×D3—22no—
350C5×D3—81no—
351C23×C3—41no—
352C22×D3—42no—
353C3×Q8—102no—
354C3×Q8—201no—
355C3×D4—22no—
356C3×D4—41no—
357C2×C3×C4—201no—
358C2×C3×C4C2×C22⋊D511yescharacteristic
359#67—41no—
360#67—42no—
361#67—42no—
362#67—201no—
363#67#68612yes—
364C2×Dic3—42no—
365D12—21no—
366D12—101no—
367D12—202no—
368D12#68611yescharacteristic
369C4×D3—41no—
370C4×D3—202no—
371C4×D3—201no—
372C4×D3—202no—
373C4×D3C2×C22⋊D512yes—
374Dic6—21no—
375Dic6—101no—
376Dic6—202no—
377Dic6#68611yescharacteristic
378C3×C8C2×C22⋊D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8C2×C22⋊D512yes—
381C22×C5—32no—
382C22×C5—42no—
383C22×C5—121no—
384C22×C5—161no—
385C22×C5—482no—
386C22×C5D3×D811yescharacteristic
387C2×D5—121no—
388C4×C5—32no—
389C4×C5—121no—
390C4×C5D3×D811yescharacteristic
391C4×C5C2×D3×D411yescharacteristic
392Dic5—42no—
393Dic5—121no—
394#41—31no—
395#41—62no—
396#41—61no—
397#41—121no—
398#41—302no—
399#41—301no—
400#41—602no—
401#41—601no—
402C2×Q8—101no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—21no—
406C2×D4—62no—
407C2×D4—121no—
408C2×D4—122no—
409Q16—31no—
410Q16—52no—
411Q16—101no—
412Q16—151no—
413Q16—302no—
414SD16—62no—
415SD16—61no—
416SD16—302no—
417SD16—301no—
418D8—21no—
419D8—31no—
420D8—62no—
421D8—151no—
422D8C2×D3×D512yes—
423M16—31no—
424M16—32no—
425C2×C8—32no—
426C2×C8C2×D3×D511yescharacteristic
427C16—51no—
428C16—51no—
429C16—152no—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—42no—
432C22×C3—161no—
433C22×C3C2×#68611yescharacteristic
434C2×D3—41no—
435C2×D3—162no—
436C2×D3—201no—
437C2×D3C2×#68612yes—
438C3×C4—202no—
439C3×C4C2×#68611yescharacteristic
440C3×C4C22×C22⋊D511yescharacteristic
441Dic3—41no—
442Dic3—201no—
443Dic3C2×#68612yes—
444C2×C5—21no—
445C2×C5—62no—
446C2×C5—82no—
447C2×C5—241no—
448C2×C5C2×D3×D811yescharacteristic
449D5—241no—
450C23—41no—
451C23—122no—
452Q8—31no—
453Q8—61no—
454Q8—102no—
455Q8—201no—
456Q8—301no—
457Q8—602no—
458D4—22no—
459D4—32no—
460D4—31no—
461D4—41no—
462D4—61no—
463D4—122no—
464D4—122no—
465D4—121no—
466D4—301no—
467D4—602no—
468D4—601no—
469C2×C4—32no—
470C2×C4—122no—
471C2×C4—121no—
472C2×C4—201no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—601no—
476C2×C4D3×C22⋊D511yescharacteristic
477C8—32no—
478C8D3×C22⋊D511yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—82no—
482C2×C3C22×#68611yescharacteristic
483D3—22no—
484D3—81no—
485D3—401no—
486C5#8202411yescharacteristic, complemented, Sylow
487C22—32no—
488C22—42no—
489C22—121no—
490C22—161no—
491C22—482no—
492C22—601no—
493C22D3×#68611yescharacteristic
494C4—32no—
495C4—121no—
496C4—202no—
497C4—601no—
498C4D3×#68611yescharacteristic
499C4C2×D3×C22⋊D511yescharacteristic
500C3#1061573911yescharacteristic, complemented, Sylow
501C2—21no—
502C2—62no—
503C2—82no—
504C2—241no—
505C2—1201no—
506C2C2×D3×#68611yescharacteristic
subgroupG/H
centerC2C2×D3×#686
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×D8C22
socleC2×C3×C5C22×D8
hypercenterC2×D8D3×D5
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C5×#5757C2semidirect
2. #11753991C2semidirect
3. #11751248C2semidirect
4. C2×C3×#3959C2semidirect
5. #11748283C2semidirect
6. #11748282C2semidirect
7. #11748273C2semidirect
8. D3×#3959C2semidirect
9. #11747552C2semidirect
10. #11747546C2semidirect
11. #11747527C2semidirect
16. #91793C22semidirect
23. C2×C3×Dic20C22semidirect
25. #91275C22semidirect
27. D3×Dic20C22semidirect
28. #91111C22semidirect
29. #91110C22semidirect
30. #91096C22semidirect
31. C3×#3959C22semidirect
32. C3×#3959C22semidirect
33. C2×C3×#672C22semidirect
34. #90948C22semidirect
35. #90946C22semidirect
36. #90945C22semidirect
37. #90944C22semidirect
38. #90941C22semidirect
39. #90939C22semidirect
40. #90935C22semidirect
41. D3×#672C22semidirect
50. C2×#3959D3semidirect
91. #5757D5semidirect
113. C2×Dic20C2×D3semidirect
122. #3959C2×D3semidirect
123. #3959C2×D3semidirect
129. C2×#672C2×D3semidirect
430. C3×C5#3416semidirect
486. C5#82024semidirect
500. C3#10615739semidirect

Maximal subgroups

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

subgroupindex
C5×#57572
#117539912
#117512482
C2×C3×#39592
#117482832
#117482822
#117482732
D3×#39592
#117475522
#117475462
#117475272
#106157393
#820245