Finite Group Databasebeta

← #14478586

Subgroups — #14478586

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#11756530C211yesmaximal, characteristic, complemented
2#11753983C211yesmaximal, characteristic, complemented
3C5×#5193C211yesmaximal, characteristic, complemented
4C3×#65483C211yesmaximal, characteristic, complemented
5#11748311C212yesmaximal, complemented
6#11748292C212yesmaximal, complemented
7#11748286C212yesmaximal, complemented
8#11748269C212yesmaximal, complemented
9C2×#90944C211yesmaximal, characteristic, complemented
10#11747554C211yesmaximal, characteristic, complemented
11#11747531C211yesmaximal, characteristic, complemented
12#10613768—31nomaximal, Hall
13#92101—21no—
14#92018—21no—
15C3×C5×#135C2211yescharacteristic, complemented
16#91840—21no—
17Q16×D15C2212yescomplemented
18#91804—22no—
19#91801C2212yescomplemented
20C2×Dic60C2211yescharacteristic, complemented
21#91790C2211yescharacteristic
22C2×C5×D24C2211yescharacteristic
23C3×#4050C2211yescharacteristic
24#91299—21no—
25#91279C2212yes—
26#91257—22no—
27#91256C2212yes—
28C5×#828C2212yescomplemented
29C5×#826C2212yescomplemented
30C5×#812C2211yescharacteristic, complemented
31C3×#3961C2211yescharacteristic, complemented
32C3×#3960C2211yescharacteristic, complemented
33C3×#3959C2211yescharacteristic, complemented
34C3×#3958C2211yescharacteristic, complemented
35C2×C3×#672C2211yescharacteristic, complemented
36#90947C2212yescomplemented
37#90944C2212yescomplemented
38#90944C2212yescomplemented
39#90942C2212yescomplemented
40#90936C2212yescomplemented
41#90933C2212yescomplemented
42#82032—51nomaximal, Hall
43#66105—31no—
44#66091—31no—
45C5×#509—31no—
46#65483D311yescharacteristic, complemented
47C2×#3959—31no—
48#65204—32no—
49D5×SD32—32no—
50#65201—32no—
51#65200—32no—
52#65198—31no—
53#65196—31no—
54C3×C5×#41—21no—
55Q8×D15—22no—
56#6819—22no—
57#6819—42no—
58#6817—41no—
59#6817D411yescharacteristic
60C2×Dic30—21no—
61C2×Dic30—41no—
62C2×C5×D12—21no—
63C3×#709—21no—
64D3×C22⋊D5—42no—
65#6777—22no—
66D5×D12—41no—
67#6772—41no—
68#6768—22no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8C2311yescharacteristic
72C2×C3×C5×C8C2311yescharacteristic
73#6718—22no—
74#6716—22no—
75#6710D411yescharacteristic
76Dic60—21no—
77Dic60C2312yes—
78#6705D412yes—
79C8×D15C2312yes—
80C5×D24—21no—
81C5×D24C2312yes—
82C3×Dic20C2311yescharacteristic
83C3×D40C2311yescharacteristic
84C3×#677—21no—
85#6656—22no—
86#6652—22no—
87C3×#672C2311yescharacteristic
88C3×#672C2311yescharacteristic
89C5×C3⋊C16C2312yes—
90#5771—51no—
91#5769—51no—
92C3×#508—51no—
93#5195—51no—
94#5193D511yescharacteristic, complemented
95#4918—52no—
96#4916—52no—
97D3×SD32—52no—
98#4911—52no—
99C2×#800—51no—
100#4901—51no—
101#4150—61no—
102#4144—61no—
103C5×#135C2×D311yescharacteristic, complemented
104C2×C5×D8—31no—
105#4097—61no—
106#4078—61no—
107D5×Q16—32no—
108#4061—62no—
109#4058—32no—
110#4058—32no—
111#4057—62no—
112D5×D8—32no—
113C2×Dic20—31no—
114#4050C2×D311yescharacteristic
115#4047—31no—
116C5×SD32—32no—
117C5×D16—32no—
118C5×M32—31no—
119#3961C2×D311yescharacteristic, complemented
120#3960C2×D311yescharacteristic, complemented
121#3959—32no—
122#3959—32no—
123#3959C2×D311yescharacteristic, complemented
124#3958C2×D311yescharacteristic, complemented
125C2×#672C2×D311yescharacteristic, complemented
126Dic40—32no—
127#3932—32no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×C5×D3—41no—
132C2×D3×D5—42no—
133C3×C5×Q8—21no—
134C3×C5×D4—21no—
135C3×C5×D4—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5C2×D411yescharacteristic
138#1220—42no—
139#1220D812yes—
140C2×Dic15—41no—
141C2×Dic15—42no—
142D60D811yescharacteristic
143C4×D15—42no—
144C4×D15C2×D412yes—
145Dic30—22no—
146Dic30—41no—
147Dic30—42no—
148Dic30D811yescharacteristic
149C5×D12—22no—
150C5×D12—41no—
151C3×C22⋊D5—41no—
152C3×D20—21no—
153C3×C4×D5—41no—
154C3×Dic10—21no—
155#1203—42no—
156#1201—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1010—101no—
162#1009—101no—
163C3×#135—51no—
164C3×#135C2×D511yescharacteristic, complemented
165#951—101no—
166#949—101no—
167#919—52no—
168D3×Q16—52no—
169#915—102no—
170#914—102no—
171#912—52no—
172D3×D8—52no—
173C2×Dic12—51no—
174C2×D24C2×D511yescharacteristic
175#901—51no—
176C3×Q32—51no—
177C3×SD32—51no—
178C3×SD32—51no—
179C3×D16—51no—
180C2×C3×C16—51no—
181#829—52no—
182#828C2×D512yescomplemented
183#827—52no—
184#826C2×D512yescomplemented
185#812C2×D511yescharacteristic, complemented
186#800—52no—
187#800—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C2×C5×D4—61no—
192C2×C22⋊D5—122no—
193Q8×D5—62no—
194#711—62no—
195#711—62no—
196#711—121no—
197#711—122no—
198D4×D5—62no—
199D4×D5—121no—
200#709—21no—
201#709—31no—
202#709—121no—
203C2×Dic10—61no—
204C2×Dic10—121no—
205C5×Q16C22×D311yescharacteristic
206C5×SD16—21no—
207C5×D8—32no—
208C5×D8—61no—
209C5×D8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211#689—62no—
212#687—62no—
213#687—62no—
214#686—62no—
215#681—31no—
216Dic20—32no—
217Dic20—61no—
218Dic20C22×D311yescharacteristic
219D40C22×D311yescharacteristic
220#677—21no—
221#676—32no—
222C8×D5—32no—
223C5×C16—32no—
224#672C22×D311yescharacteristic
225#672C22×D311yescharacteristic
226#578—151no—
227#576—151no—
228#510—151no—
229#510—152no—
230#509—31no—
231#509—152no—
232#508—51no—
233#508—152no—
234C2×SD32—151no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×D15C2×D812yes—
240C2×C5×D3—42no—
241C2×C5×D3—161no—
242C2×C3×D5—41no—
243D3×D5—162no—
244C3×C4×C5—41no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247Dic15—42no—
248Dic15C2×D812yes—
249C3×Dic5—41no—
250C3×#41—21no—
251C3×#41—101no—
252#239—102no—
253D3×Q8—102no—
254#237—102no—
255#237—202no—
256D3×D4—102no—
257D3×D4—202no—
258#235—51no—
259#235—201no—
260#235—201no—
261C2×D12—21no—
262C2×D12—201no—
263C2×Dic6—101no—
264C2×Dic6—201no—
265C3×Q16—51no—
266C3×Q16C22×D511yescharacteristic
267C3×SD16—21no—
268C3×SD16—101no—
269C3×D8—51no—
270C3×D8C22×D511yescharacteristic
271C2×C3×C8C22×D511yescharacteristic
272#216—102no—
273#215—102no—
274#214—102no—
275#213—102no—
276#208—51no—
277Dic12—52no—
278Dic12—101no—
279D24—21no—
280D24C22×D512yes—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16—51no—
284C3×C16—51no—
285C3⋊C16C22×D512yes—
286C23×C5—121no—
287C22×D5—122no—
288C5×Q8—21no—
289C5×D4—21no—
290C5×D4—41no—
291C5×D4—62no—
292C5×D4—121no—
293C2×C4×C5—41no—
294C2×C4×C5D3×D411yescharacteristic
295C22⋊D5—32no—
296C22⋊D5—41no—
297C22⋊D5—122no—
298C22⋊D5—122no—
299C22⋊D5—122no—
300C2×Dic5—122no—
301C2×Dic5—122no—
302C2×Dic5—121no—
303D20—21no—
304D20—31no—
305C4×D5—32no—
306C4×D5—41no—
307C4×D5—122no—
308Dic10—21no—
309Dic10—31no—
310Dic10—62no—
311Dic10—122no—
312Dic10—121no—
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—51no—
323#135—152no—
324#135—152no—
325#135D3×D511yescharacteristic, complemented
326C2×Q16—152no—
327C2×Q16—151no—
328C2×D8—31no—
329C2×D8—152no—
330#131—151no—
331Q32—51no—
332Q32—152no—
333SD32—32no—
334SD32—51no—
335SD32—51no—
336SD32—152no—
337SD32—152no—
338SD32—152no—
339D16—32no—
340D16—51no—
341M32—31no—
342M32—152no—
343C2×C16—51no—
344C2×C16—152no—
345C2×C3×C5—21no—
346C2×C3×C5—81no—
347C2×C3×C5C22×D811yescharacteristic
348D15—22no—
349C3×D5—81no—
350C5×D3—82no—
351C22×D3—41no—
352C22×D3—202no—
353C3×Q8—21no—
354C3×Q8—101no—
355C3×D4—21no—
356C3×D4—41no—
357C3×D4—101no—
358C3×D4—201no—
359C2×C3×C4—41no—
360C2×C3×C4—201no—
361C2×C3×C4D4×D511yescharacteristic
362#67—52no—
363#67—202no—
364#67—202no—
365C2×Dic3—202no—
366C2×Dic3—201no—
367D12—22no—
368D12—41no—
369D12—51no—
370D12—202no—
371C4×D3—52no—
372C4×D3—202no—
373C4×D3—202no—
374Dic6—51no—
375Dic6—102no—
376Dic6—202no—
377Dic6—201no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—41no—
382C22×C5—122no—
383C22×C5—481no—
384C22×C5D3×D811yescharacteristic
385C2×D5—32no—
386C2×D5—41no—
387C2×D5—482no—
388C4×C5—41no—
389C4×C5D3×D811yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—32no—
392Dic5—41no—
393Dic5—122no—
394#41—21no—
395#41—101no—
396#41—151no—
397#41—302no—
398#41—302no—
399#41—601no—
400#41—601no—
401#41—602no—
402C2×Q8—302no—
403C2×Q8—301no—
404C2×Q8—601no—
405C2×D4—61no—
406C2×D4—302no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—51no—
410Q16—152no—
411Q16—302no—
412Q16—301no—
413Q16C2×D3×D511yescharacteristic
414SD16—21no—
415SD16—101no—
416SD16—302no—
417SD16—302no—
418D8—32no—
419D8—51no—
420D8—61no—
421D8—302no—
422D8C2×D3×D511yescharacteristic
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C2×D3×D511yescharacteristic
427C16—32no—
428C16—51no—
429C16—51no—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—41no—
432C22×C3—201no—
433C22×C3D5×D811yescharacteristic
434C2×D3—42no—
435C2×D3—52no—
436C2×D3—161no—
437C2×D3—802no—
438C3×C4—41no—
439C3×C4—201no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—52no—
443Dic3—202no—
444C2×C5—21no—
445C2×C5—81no—
446C2×C5—242no—
447C2×C5C2×D3×D811yescharacteristic
448D5—62no—
449D5—81no—
450C23—121no—
451C23—602no—
452Q8—21no—
453Q8—101no—
454Q8—151no—
455Q8—302no—
456Q8—602no—
457Q8—601no—
458D4—21no—
459D4—41no—
460D4—62no—
461D4—101no—
462D4—121no—
463D4—152no—
464D4—151no—
465D4—201no—
466D4—602no—
467D4—602no—
468D4—602no—
469C2×C4—41no—
470C2×C4—152no—
471C2×C4—201no—
472C2×C4—602no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—601no—
476C2×C4#679011yescharacteristic
477C8—152no—
478C8#679011yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—81no—
482C2×C3—401no—
483C2×C3C2×D5×D811yescharacteristic
484D3—82no—
485D3—102no—
486C5#8203211yescharacteristic, complemented, Sylow
487C22—41no—
488C22—122no—
489C22—152no—
490C22—201no—
491C22—481no—
492C22—2402no—
493C22#9148111yescharacteristic
494C4—41no—
495C4—152no—
496C4—201no—
497C4—602no—
498C4#9148111yescharacteristic
499C4C2×#679011yescharacteristic
500C3#1061376811yescharacteristic, complemented, Sylow
501C2—21no—
502C2—81no—
503C2—242no—
504C2—302no—
505C2—401no—
506C2C2×#9148111yescharacteristic
subgroupG/H
centerC2C2×#91481
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C22×D8
hypercenter#135D3×D5
hypocenterC3×C5#3416
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. #11756530C2semidirect
2. #11753983C2semidirect
3. C5×#5193C2semidirect
4. C3×#65483C2semidirect
5. #11748311C2semidirect
6. #11748292C2semidirect
7. #11748286C2semidirect
8. #11748269C2semidirect
9. C2×#90944C2semidirect
10. #11747554C2semidirect
11. #11747531C2semidirect
15. C3×C5×#135C22semidirect
17. Q16×D15C22semidirect
19. #91801C22semidirect
20. C2×Dic60C22semidirect
28. C5×#828C22semidirect
29. C5×#826C22semidirect
30. C5×#812C22semidirect
31. C3×#3961C22semidirect
32. C3×#3960C22semidirect
33. C3×#3959C22semidirect
34. C3×#3958C22semidirect
35. C2×C3×#672C22semidirect
36. #90947C22semidirect
37. #90944C22semidirect
38. #90944C22semidirect
39. #90942C22semidirect
40. #90936C22semidirect
41. #90933C22semidirect
46. #65483D3semidirect
94. #5193D5semidirect
103. C5×#135C2×D3semidirect
119. #3961C2×D3semidirect
120. #3960C2×D3semidirect
123. #3959C2×D3semidirect
124. #3958C2×D3semidirect
125. C2×#672C2×D3semidirect
164. C3×#135C2×D5semidirect
182. #828C2×D5semidirect
184. #826C2×D5semidirect
185. #812C2×D5semidirect
325. #135D3×D5semidirect
430. C3×C5#3416semidirect
486. C5#82032semidirect
500. C3#10613768semidirect

Maximal subgroups

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

subgroupindex
#117565302
#117539832
C5×#51932
C3×#654832
#117483112
#117482922
#117482862
#117482692
C2×#909442
#117475542
#117475312
#106137683
#820325