Finite Group Databasebeta

← #14478583

Subgroups — #14478583

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
1#11754011C211yesmaximal, characteristic, complemented
2#11753981C211yesmaximal, characteristic, complemented
3#11751002C211yesmaximal, characteristic, complemented
4C5×#4904C211yesmaximal, characteristic, complemented
5C2×C3×#3932C211yesmaximal, characteristic, complemented
6#11747552C211yesmaximal, characteristic, complemented
7#11747539C211yesmaximal, characteristic, complemented
8#11746841C212yesmaximal, complemented
9#11746840C212yesmaximal, complemented
10#11746825C212yesmaximal, complemented
11#11746823C212yesmaximal, complemented
12#10613763—31nomaximal, Hall
13#92017—21no—
14#92004—21no—
15#91790C2211yescharacteristic
16C5×#904C2211yescharacteristic
17C5×#904C2211yescharacteristic, complemented
18C2×C3×Dic20C2211yescharacteristic, complemented
19C2×C3×D40C2211yescharacteristic
20#91309—21no—
21#91298—21no—
22#91280—22no—
23#91279C2212yescomplemented
24#91277C2212yes—
25#91264C2212yescomplemented
26#91258—22no—
27#91256C2212yes—
28C2×C3×C5×C16C2211yescharacteristic, complemented
29#91096C2211yescharacteristic, complemented
30#91082C2212yescomplemented
31C16×D15C2212yescomplemented
32C5×Dic24C2211yescharacteristic, complemented
33C5×#800C2211yescharacteristic, complemented
34C5×#800C2211yescharacteristic, complemented
35C5×D48C2211yescharacteristic, complemented
36C3×#3932C2212yescomplemented
37C3×#3932C2212yescomplemented
38#90946C2212yescomplemented
39#90941C2212yescomplemented
40#90940C2212yescomplemented
41#90937C2212yescomplemented
42#82024—51nomaximal, Hall
43#66105—31no—
44#66103—31no—
45C5×#508—31no—
46#65484—31no—
47#65482—31no—
48#65207—32no—
49#65205—32no—
50D5×SD32—32no—
51#65200—32no—
52C2×#3932D311yescharacteristic, complemented
53#65190—31no—
54#6817D411yescharacteristic
55C5×#235—21no—
56C5×#235—21no—
57C2×C3×D20—21no—
58C2×C3×Dic10—21no—
59D5×#67—42no—
60#6782—42no—
61#6777—22no—
62D3×D20—41no—
63D15⋊Q8—22no—
64#6769—41no—
65#6768—22no—
66D3×Dic10—41no—
67#6766—22no—
68#6765—41no—
69C2×C3×C5×C8C2311yescharacteristic
70#6710D411yescharacteristic
71#6705D412yes—
72C8×D15C2312yes—
73C5×Dic12C2311yescharacteristic
74C5×Dic12C2311yescharacteristic
75C5×D24C2311yescharacteristic
76C5×D24C2311yescharacteristic
77C5×#204—21no—
78C5×#204—21no—
79C3×Dic20—21no—
80C3×Dic20C2312yes—
81C3×D40—21no—
82C3×D40C2312yes—
83#6661—22no—
84#6656—22no—
85#6655—22no—
86#6652—22no—
87C3×C5×C16C2311yescharacteristic
88C3×C5×C16C2311yescharacteristic
89C3⋊#672C2312yes—
90#5766—51no—
91#5757—51no—
92C2×C3×SD32—51no—
93#5179—51no—
94#5147—51no—
95#4916—52no—
96#4915—52no—
97#4914—52no—
98D3×SD32—52no—
99#4904D511yescharacteristic, complemented
100#4901—51no—
101#4150—61no—
102#4149—61no—
103C5×#135—31no—
104C5×#135—31no—
105#4097—61no—
106#4095—61no—
107#4065—32no—
108D5×Q16—32no—
109#4061—62no—
110#4060—62no—
111#4058—32no—
112D5×D8—32no—
113C2×Dic20C2×D311yescharacteristic, complemented
114C2×D40C2×D311yescharacteristic
115#4047—31no—
116C5×Q32—31no—
117C5×SD32—31no—
118C5×SD32—31no—
119C5×D16—31no—
120C2×C5×C16C2×D311yescharacteristic, complemented
121#3961—32no—
122#3960—32no—
123#3959—32no—
124#3958—32no—
125#3944—31no—
126#3932C2×D312yescomplemented
127#3932C2×D312yescomplemented
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×C3×D5—41no—
132C2×D3×D5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134#1220D812yes—
135D60D811yescharacteristic
136C4×D15C2×D412yes—
137Dic30D811yescharacteristic
138C5×#67—41no—
139C5×#67—41no—
140C5×D12—21no—
141C5×D12—21no—
142C4×C5×D3—41no—
143C4×C5×D3—41no—
144C5×Dic6—21no—
145C5×Dic6—21no—
146C2×C3×Dic5—41no—
147C3×D20—22no—
148C3×D20—41no—
149C3×Dic10—22no—
150C3×Dic10—41no—
151#1204—42no—
152#1203—42no—
153#1202—42no—
154#1201—42no—
155#1200—42no—
156D3×Dic5—42no—
157D5×Dic3—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1007—101no—
162#1004—101no—
163C2×C3×Q16—51no—
164C2×C3×D8—51no—
165#942—101no—
166#932—101no—
167#919—52no—
168#918—102no—
169D3×Q16—52no—
170#912—52no—
171#911—102no—
172D3×D8—52no—
173#904C2×D511yescharacteristic
174#904C2×D511yescharacteristic, complemented
175#901—51no—
176C3×SD32—52no—
177C3×SD32—52no—
178C2×C3×C16C2×D511yescharacteristic, complemented
179#829—52no—
180#828—52no—
181#827—52no—
182#826—52no—
183#812—51no—
184Dic24C2×D511yescharacteristic, complemented
185#800C2×D511yescharacteristic, complemented
186#800C2×D511yescharacteristic, complemented
187D48C2×D511yescharacteristic, complemented
188#798—52no—
189D3×C16—52no—
190C5×#41—61no—
191C5×#41—61no—
192#713—62no—
193Q8×D5—62no—
194#711—62no—
195#711—122no—
196D4×D5—62no—
197D4×D5—122no—
198#709—31no—
199#709—121no—
200#709—121no—
201C2×D20—21no—
202C2×D20—121no—
203C2×Dic10—21no—
204C2×Dic10—121no—
205C5×Q16—31no—
206C5×Q16—31no—
207C5×SD16—61no—
208C5×SD16—61no—
209C5×D8—31no—
210C5×D8—31no—
211C2×C5×C8C22×D311yescharacteristic
212#689—62no—
213#688—62no—
214#687—62no—
215#686—62no—
216#681—31no—
217Dic20—21no—
218Dic20C22×D312yes—
219D40—21no—
220D40C22×D312yes—
221#676—32no—
222C8×D5—32no—
223C5×C16C22×D311yescharacteristic
224C5×C16C22×D311yescharacteristic
225#672—32no—
226#578—151no—
227#576—151no—
228#510—152no—
229#510—151no—
230#509—152no—
231#509—151no—
232#508—31no—
233#508—152no—
234C2×SD32—51no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5C2×D811yescharacteristic
238C2×D15C2×D812yes—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C3×D5—42no—
242C2×C3×D5—161no—
243D3×D5—162no—
244C3×C4×C5C2×D811yescharacteristic
245C3×C4×C5C22×D411yescharacteristic
246Dic15C2×D812yes—
247C3×Dic5—42no—
248C5×Dic3—41no—
249C5×Dic3—41no—
250C2×C3×Q8—101no—
251C2×C3×D4—101no—
252C2×#67—202no—
253#239—102no—
254#239—201no—
255D3×Q8—102no—
256D3×Q8—201no—
257#237—102no—
258#237—201no—
259D3×D4—102no—
260D3×D4—201no—
261#235—21no—
262#235—21no—
263#235—51no—
264#235—202no—
265C3×Q16—52no—
266C3×Q16—101no—
267C3×D8—52no—
268C3×D8—101no—
269C2×C3×C8C22×D511yescharacteristic
270#216—102no—
271#215—102no—
272#214—102no—
273#213—102no—
274#208—51no—
275Dic12C22×D511yescharacteristic
276Dic12C22×D511yescharacteristic
277D24C22×D511yescharacteristic
278D24C22×D511yescharacteristic
279#204—21no—
280#204—21no—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16C22×D511yescharacteristic
284C3×C16C22×D511yescharacteristic
285C3⋊C16—52no—
286C22×D5—41no—
287C22×D5—122no—
288C5×Q8—61no—
289C5×Q8—61no—
290C5×D4—61no—
291C5×D4—61no—
292C5×D4—121no—
293C5×D4—121no—
294C2×C4×C5—121no—
295C2×C4×C5—121no—
296C2×C4×C5D3×D411yescharacteristic
297C22⋊D5—32no—
298C22⋊D5—122no—
299C22⋊D5—122no—
300C2×Dic5—41no—
301C2×Dic5—122no—
302D20—22no—
303D20—31no—
304D20—41no—
305D20—122no—
306C4×D5—32no—
307C4×D5—122no—
308C4×D5—122no—
309Dic10—22no—
310Dic10—31no—
311Dic10—41no—
312Dic10—122no—
313C5×C8D3×D411yescharacteristic
314C5×C8C23×D311yescharacteristic
315#168—32no—
3162−1+4—301no—
317H(5,𝔽2)—301no—
318#137—302no—
319#137—301no—
320AGL(1,ℤ/8)—302no—
321AGL(1,ℤ/8)—301no—
322#135—31no—
323#135—31no—
324#135—152no—
325#135—152no—
326C2×Q16—51no—
327C2×Q16—152no—
328C2×D8—51no—
329C2×D8—152no—
330#131—151no—
331Q32—31no—
332Q32—152no—
333SD32—31no—
334SD32—31no—
335SD32—52no—
336SD32—52no—
337SD32—152no—
338SD32—152no—
339D16—31no—
340D16—152no—
341M32—151no—
342M32—152no—
343C2×C16—152no—
344C2×C16D3×D511yescharacteristic, complemented
345C2×C3×C5—21no—
346C2×C3×C5C22×D811yescharacteristic
347D15—22no—
348C3×D5—82no—
349C5×D3—81no—
350C5×D3—81no—
351C23×C3—201no—
352C22×D3—202no—
353C3×Q8—102no—
354C3×Q8—201no—
355C3×D4—102no—
356C3×D4—201no—
357C2×C3×C4—201no—
358C2×C3×C4D4×D511yescharacteristic
359#67—41no—
360#67—41no—
361#67—52no—
362#67—202no—
363#67—202no—
364C2×Dic3—202no—
365D12—21no—
366D12—21no—
367D12—51no—
368D12—202no—
369C4×D3—41no—
370C4×D3—41no—
371C4×D3—52no—
372C4×D3—202no—
373C4×D3—202no—
374Dic6—21no—
375Dic6—21no—
376Dic6—51no—
377Dic6—202no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—121no—
382C22×C5—121no—
383C22×C5D3×D811yescharacteristic
384C2×D5—32no—
385C2×D5—42no—
386C2×D5—161no—
387C2×D5—482no—
388C4×C5—121no—
389C4×C5—121no—
390C4×C5D3×D811yescharacteristic
391C4×C5C2×D3×D411yescharacteristic
392Dic5—32no—
393Dic5—42no—
394#41—61no—
395#41—61no—
396#41—151no—
397#41—302no—
398#41—302no—
399#41—601no—
400#41—601no—
401#41—602no—
402C2×Q8—101no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—101no—
406C2×D4—302no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—31no—
410Q16—31no—
411Q16—52no—
412Q16—101no—
413Q16—302no—
414SD16—61no—
415SD16—61no—
416SD16—302no—
417SD16—302no—
418D8—31no—
419D8—31no—
420D8—52no—
421D8—101no—
422D8—302no—
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C2×D3×D511yescharacteristic
427C16—152no—
428C16C2×D3×D511yescharacteristic
429C16C2×D3×D511yescharacteristic
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—202no—
432C22×C3—801no—
433C22×C3D5×D811yescharacteristic
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—52no—
437C2×D3—802no—
438C3×C4—202no—
439C3×C4D5×D811yescharacteristic
440C3×C4C2×D4×D511yescharacteristic
441Dic3—41no—
442Dic3—41no—
443Dic3—52no—
444C2×C5—21no—
445C2×C5—241no—
446C2×C5—241no—
447C2×C5C2×D3×D811yescharacteristic
448D5—62no—
449D5—82no—
450C23—201no—
451C23—602no—
452Q8—61no—
453Q8—61no—
454Q8—102no—
455Q8—151no—
456Q8—201no—
457Q8—602no—
458D4—61no—
459D4—61no—
460D4—102no—
461D4—121no—
462D4—121no—
463D4—152no—
464D4—151no—
465D4—201no—
466D4—602no—
467D4—602no—
468D4—602no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—152no—
472C2×C4—201no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—602no—
476C2×C4#677711yescharacteristic
477C8—152no—
478C8#677711yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—402no—
482C2×C3C2×D5×D811yescharacteristic
483D3—81no—
484D3—81no—
485D3—102no—
486C5#8202411yescharacteristic, complemented, Sylow
487C22—121no—
488C22—121no—
489C22—152no—
490C22—202no—
491C22—801no—
492C22—2402no—
493C22#9125611yescharacteristic
494C4—121no—
495C4—121no—
496C4—152no—
497C4—202no—
498C4#9125611yescharacteristic
499C4C2×#677711yescharacteristic
500C3#1061376311yescharacteristic, complemented, Sylow
501C2—21no—
502C2—241no—
503C2—241no—
504C2—302no—
505C2—402no—
506C2C2×#9125611yescharacteristic
subgroupG/H
centerC2C2×#91256
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC2×C3×C5C22×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #11754011C2semidirect
2. #11753981C2semidirect
3. #11751002C2semidirect
4. C5×#4904C2semidirect
5. C2×C3×#3932C2semidirect
6. #11747552C2semidirect
7. #11747539C2semidirect
8. #11746841C2semidirect
9. #11746840C2semidirect
10. #11746825C2semidirect
11. #11746823C2semidirect
17. C5×#904C22semidirect
18. C2×C3×Dic20C22semidirect
23. #91279C22semidirect
25. #91264C22semidirect
28. C2×C3×C5×C16C22semidirect
29. #91096C22semidirect
30. #91082C22semidirect
31. C16×D15C22semidirect
32. C5×Dic24C22semidirect
33. C5×#800C22semidirect
34. C5×#800C22semidirect
35. C5×D48C22semidirect
36. C3×#3932C22semidirect
37. C3×#3932C22semidirect
38. #90946C22semidirect
39. #90941C22semidirect
40. #90940C22semidirect
41. #90937C22semidirect
52. C2×#3932D3semidirect
99. #4904D5semidirect
113. C2×Dic20C2×D3semidirect
120. C2×C5×C16C2×D3semidirect
126. #3932C2×D3semidirect
127. #3932C2×D3semidirect
174. #904C2×D5semidirect
178. C2×C3×C16C2×D5semidirect
184. Dic24C2×D5semidirect
185. #800C2×D5semidirect
186. #800C2×D5semidirect
187. D48C2×D5semidirect
344. C2×C16D3×D5semidirect
430. C3×C5#3416semidirect
486. C5#82024semidirect
500. C3#10613763semidirect

Maximal subgroups

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

subgroupindex
#117540112
#117539812
#117510022
C5×#49042
C2×C3×#39322
#117475522
#117475392
#117468412
#117468402
#117468252
#117468232
#106137633
#820245