Finite Group Databasebeta

← #14478591

Subgroups — #14478591

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
1C3×#66103C211yesmaximal, characteristic, complemented
2#11753987C211yesmaximal, characteristic, complemented
3#11751295C211yesmaximal, characteristic, complemented
4C5×#5195C211yesmaximal, characteristic, complemented
5#11748303C212yesmaximal, complemented
6#11748295C212yesmaximal, complemented
7#11748278C212yesmaximal, complemented
8D5×#827C212yesmaximal, complemented
9C2×#90940C211yesmaximal, characteristic, complemented
10#11747543C211yesmaximal, characteristic, complemented
11#11747525C211yesmaximal, characteristic, complemented
12#10613771—31nomaximal, Hall
13C3×#4149—21no—
14#92000—21no—
15C3×C5×#135C2211yescharacteristic
16#91793C2211yescharacteristic, complemented
17C2×C5×Dic12C2211yescharacteristic, complemented
18C3×#4095—21no—
19C3×#4065C2212yes—
20C3×#4060—22no—
21C3×D5×D8C2212yes—
22C2×C3×D40C2211yescharacteristic
23C3×#4047C2211yescharacteristic
24#91321—21no—
25#91271C2212yescomplemented
26#91261—22no—
27D5×Dic12C2212yescomplemented
28#91113C2211yescharacteristic, complemented
29#91112C2211yescharacteristic, complemented
30#91111C2211yescharacteristic, complemented
31#91110C2211yescharacteristic, complemented
32C2×C3⋊#672C2211yescharacteristic, complemented
33C5×#829C2212yescomplemented
34C5×#827C2212yescomplemented
35C5×#812C2211yescharacteristic, complemented
36#90942C2212yescomplemented
37#90940C2212yescomplemented
38#90940C2212yescomplemented
39#90938C2212yescomplemented
40#90934C2212yescomplemented
41D5×C3⋊C16C2212yescomplemented
42#84008—51nomaximal, Hall
43#66103D311yescharacteristic, complemented
44#66100—31no—
45C5×#510—31no—
46#65483—31no—
47C2×#3960—31no—
48#65208—32no—
49#65207—32no—
50#65203—32no—
51D5×SD32—32no—
52#65197—31no—
53#65196—31no—
54C3×C5×#41—21no—
55#6817—21no—
56C2×C5×Dic6—21no—
57C3×#713—22no—
58C3×D4×D5—22no—
59C3×D4×D5—42no—
60C3×#709—41no—
61C3×#709D411yescharacteristic
62C2×C3×D20—21no—
63C2×C3×D20—41no—
64#6779—42no—
65#6773—22no—
66D15⋊Q8—41no—
67#6766—41no—
68D5×Dic6—22no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8C2311yescharacteristic
72C2×C3×C5×C8C2311yescharacteristic
73Dic60C2311yescharacteristic
74D120C2311yescharacteristic
75#6706—21no—
76C5×Dic12—21no—
77C5×Dic12C2312yes—
78C3×#688—22no—
79C3×#686—22no—
80C3×#681D411yescharacteristic
81C3×D40—21no—
82C3×D40C2312yes—
83C3×#676D412yes—
84C3×C8×D5C2312yes—
85#6663—22no—
86#6660—22no—
87C3⋊#672C2311yescharacteristic
88C3⋊#672C2311yescharacteristic
89C5×C3⋊C16C2312yes—
90C3×#576—51no—
91#5753—51no—
92#5195—52no—
93#5195D511yescharacteristic, complemented
94#5194—51no—
95#5194—52no—
96C2×#827—51no—
97C2×#827—52no—
98#5147—52no—
99#5147—51no—
100#5140—51no—
101#4149—21no—
102#4147—61no—
103C5×#135C2×D311yescharacteristic
104C2×C5×Q16—31no—
105#4095—21no—
106#4088—61no—
107#4065—32no—
108#4065C2×D312yes—
109#4064—62no—
110D5×Q16—32no—
111#4060—22no—
112D5×D8C2×D312yes—
113#4050—31no—
114C2×D40C2×D311yescharacteristic
115#4047C2×D311yescharacteristic
116C5×Q32—32no—
117C5×SD32—32no—
118C5×M32—31no—
119#3961—31no—
120#3960—31no—
121#3960—32no—
122#3960—32no—
123#3959—31no—
124#3958—31no—
125C2×#672—31no—
126#3932—32no—
127D80—32no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×C3×D5—41no—
132C22×C3×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—41no—
139D60—21no—
140C4×D15—41no—
141Dic30—21no—
142C2×C5×Dic3—41no—
143C5×Dic6—22no—
144C5×Dic6—41no—
145C3×C22⋊D5—42no—
146C3×C22⋊D5D812yes—
147C3×D20—22no—
148C3×D20—42no—
149C3×D20—41no—
150C3×D20D811yescharacteristic
151C3×C4×D5—42no—
152C3×C4×D5C2×D412yes—
153C3×Dic10D811yescharacteristic
154#1204—42no—
155#1202—42no—
156#1200—42no—
157D5×Dic3—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3×#168C2×D412yes—
161C3×H(5,𝔽2)—101no—
162#1010—101no—
163C3×AGL(1,ℤ/8)—102no—
164C3×AGL(1,ℤ/8)—101no—
165C3×#135—52no—
166C3×#135C2×D511yescharacteristic
167C2×C3×D8—52no—
168C2×C3×D8—51no—
169C3×#131—51no—
170#909—102no—
171#909—101no—
172C2×Dic12—52no—
173C2×Dic12C2×D511yescharacteristic, complemented
174#904—51no—
175#904—52no—
176#829—51no—
177#829C2×D512yescomplemented
178#828—51no—
179#827—51no—
180#827—52no—
181#827—52no—
182#827—52no—
183#827C2×D512yescomplemented
184#826—51no—
185#826—52no—
186#812—52no—
187#812C2×D511yescharacteristic, complemented
188C2×C3⋊C16—51no—
189C2×C3⋊C16—52no—
190C5×#41—21no—
191C2×C5×Q8—61no—
192#713—22no—
193#713—62no—
194#713—121no—
195Q8×D5—62no—
196Q8×D5—121no—
197D4×D5—22no—
198D4×D5—42no—
199#709—41no—
200#709—61no—
201#709—122no—
202#709#6711yescharacteristic
203C2×D20—21no—
204C2×D20—41no—
205C5×Q16—32no—
206C5×Q16—61no—
207C5×Q16C22×D311yescharacteristic
208C5×SD16—21no—
209C5×D8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211#689—62no—
212#688—22no—
213#688—62no—
214#686—22no—
215#681#6711yescharacteristic
216Dic20—31no—
217D40—21no—
218D40—31no—
219D40C22×D312yes—
220#677—61no—
221#676#6712yes—
222C8×D5C22×D312yes—
223C5×C16—32no—
224#672—31no—
225#672—31no—
226#578—151no—
227#576—51no—
228#510—31no—
229#510—152no—
230#509—151no—
231#509—152no—
232#508—152no—
233#508—151no—
234C2×SD32—152no—
235C2×SD32—151no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×D15—41no—
240C2×C3×D5—42no—
241C2×C3×D5—162no—
242C2×C3×D5—161no—
243C2×C3×D5C2×D812yes—
244C3×C4×C5—41no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247Dic15—41no—
248C3×Dic5C2×D812yes—
249C5×Dic3—42no—
250C3×#41—21no—
251C3×#41—51no—
252C3×#41—102no—
253C3×#41—201no—
254C2×C3×D4—102no—
255C2×C3×D4—101no—
256C2×C3×D4—201no—
257C2×C3×D4—202no—
258D3×Q8—201no—
259#237—201no—
260#237—202no—
261#235—102no—
262#235—101no—
263C2×Dic6—21no—
264C2×Dic6—102no—
265C3×Q16C22×D511yescharacteristic
266C3×SD16—21no—
267C3×SD16—102no—
268C3×D8—52no—
269C3×D8—102no—
270C3×D8—101no—
271C3×D8C22×D511yescharacteristic
272C3×M16—51no—
273C3×M16—52no—
274C2×C3×C8—52no—
275C2×C3×C8C22×D511yescharacteristic
276Dic12—21no—
277Dic12—51no—
278Dic12—102no—
279Dic12C22×D512yes—
280D24—51no—
281#204—102no—
282#204—101no—
283C3⋊C16—51no—
284C3⋊C16—51no—
285C3⋊C16C22×D512yes—
286C22×D5—41no—
287C22×D5—42no—
288C5×Q8—21no—
289C5×Q8—62no—
290C5×Q8—121no—
291C5×D4—21no—
292C5×D4—41no—
293C2×C4×C5—41no—
294C2×C4×C5—121no—
295C2×C4×C5C2×#6711yescharacteristic
296C22⋊D5—42no—
297C22⋊D5—121no—
298C22⋊D5#21312yes—
299D20—22no—
300D20—42no—
301D20—41no—
302D20—61no—
303D20—122no—
304D20#21311yescharacteristic
305C4×D5—42no—
306C4×D5—122no—
307C4×D5—121no—
308C4×D5—122no—
309C4×D5C2×#6712yes—
310Dic10—61no—
311Dic10—122no—
312Dic10#21311yescharacteristic
313C5×C8C2×#6711yescharacteristic
314C5×C8C23×D311yescharacteristic
315#168C2×#6712yes—
3162−1+4—301no—
317H(5,𝔽2)—101no—
318#137—302no—
319#137—301no—
320AGL(1,ℤ/8)—102no—
321AGL(1,ℤ/8)—101no—
322#135—52no—
323#135—152no—
324#135—151no—
325#135D3×D511yescharacteristic
326C2×Q16—31no—
327C2×Q16—152no—
328C2×D8—52no—
329C2×D8—51no—
330#131—51no—
331Q32—32no—
332Q32—151no—
333SD32—32no—
334SD32—152no—
335SD32—152no—
336SD32—152no—
337SD32—151no—
338SD32—151no—
339D16—152no—
340D16—151no—
341M32—31no—
342M32—152no—
343C2×C16—152no—
344C2×C16—151no—
345C2×C3×C5—21no—
346C2×C3×C5—81no—
347C2×C3×C5C22×D811yescharacteristic
348D15—81no—
349C3×D5—22no—
350C3×D5—82no—
351C23×C3—202no—
352C23×C3—201no—
353C3×Q8—21no—
354C3×Q8—51no—
355C3×D4—21no—
356C3×D4—41no—
357C3×D4—52no—
358C3×D4—51no—
359C3×D4—102no—
360C3×D4—202no—
361C3×D4—202no—
362C3×D4—201no—
363C2×C3×C4—41no—
364C2×C3×C4—52no—
365C2×C3×C4—202no—
366C2×C3×C4D4×D511yescharacteristic
367#67—202no—
368#67—201no—
369C2×Dic3—41no—
370C2×Dic3—202no—
371D12—101no—
372C4×D3—202no—
373C4×D3—201no—
374Dic6—22no—
375Dic6—41no—
376Dic6—101no—
377Dic6—202no—
378C3×C8—52no—
379C3×C8D4×D511yescharacteristic
380C3×C8C23×D511yescharacteristic
381C22×C5—41no—
382C22×C5C2×#21311yescharacteristic
383C2×D5—42no—
384C2×D5—121no—
385C2×D5—162no—
386C2×D5—161no—
387C2×D5C2×#21312yes—
388C4×C5—41no—
389C4×C5—122no—
390C4×C5C2×#21311yescharacteristic
391C4×C5C22×#6711yescharacteristic
392Dic5—121no—
393Dic5C2×#21312yes—
394#41—21no—
395#41—51no—
396#41—102no—
397#41—201no—
398#41—302no—
399#41—301no—
400#41—602no—
401#41—601no—
402C2×Q8—61no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—102no—
406C2×D4—101no—
407C2×D4—201no—
408C2×D4—202no—
409Q16—32no—
410Q16—61no—
411Q16—151no—
412Q16—302no—
413Q16C2×D3×D511yescharacteristic
414SD16—21no—
415SD16—102no—
416SD16—302no—
417SD16—301no—
418D8—52no—
419D8—102no—
420D8—101no—
421D8—151no—
422D8C2×D3×D511yescharacteristic
423M16—51no—
424M16—52no—
425C2×C8—52no—
426C2×C8C2×D3×D511yescharacteristic
427C16—32no—
428C16—151no—
429C16—151no—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—41no—
432C22×C3—52no—
433C22×C3—202no—
434C22×C3—801no—
435C22×C3—802no—
436C22×C3D5×D811yescharacteristic
437C2×D3—201no—
438C3×C4—41no—
439C3×C4—52no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—42no—
443Dic3—201no—
444C2×C5—21no—
445C2×C5—81no—
446C2×C5C22×#21311yescharacteristic
447D5—22no—
448D5—82no—
449D5—241no—
450C23—202no—
451C23—201no—
452Q8—21no—
453Q8—51no—
454Q8—62no—
455Q8—121no—
456Q8—301no—
457Q8—602no—
458D4—21no—
459D4—41no—
460D4—52no—
461D4—51no—
462D4—102no—
463D4—202no—
464D4—202no—
465D4—201no—
466D4—301no—
467D4—602no—
468D4—601no—
469C2×C4—41no—
470C2×C4—52no—
471C2×C4—121no—
472C2×C4—202no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—601no—
476C2×C4D5×#6711yescharacteristic
477C8—52no—
478C8D5×#6711yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—81no—
482C2×C3—102no—
483C2×C3—402no—
484C2×C3C2×D5×D811yescharacteristic
485D3—401no—
486C5#8400811yescharacteristic, complemented, Sylow
487C22—41no—
488C22—52no—
489C22—202no—
490C22—601no—
491C22—801no—
492C22—802no—
493C22D5×#21311yescharacteristic
494C4—41no—
495C4—52no—
496C4—122no—
497C4—601no—
498C4D5×#21311yescharacteristic
499C4C2×D5×#6711yescharacteristic
500C3#1061377111yescharacteristic, complemented, Sylow
501C2—21no—
502C2—81no—
503C2—102no—
504C2—402no—
505C2—1201no—
506C2C2×D5×#21311yescharacteristic
subgroupG/H
centerC2C2×D5×#213
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. C3×#66103C2semidirect
2. #11753987C2semidirect
3. #11751295C2semidirect
4. C5×#5195C2semidirect
5. #11748303C2semidirect
6. #11748295C2semidirect
7. #11748278C2semidirect
8. D5×#827C2semidirect
9. C2×#90940C2semidirect
10. #11747543C2semidirect
11. #11747525C2semidirect
16. #91793C22semidirect
17. C2×C5×Dic12C22semidirect
25. #91271C22semidirect
27. D5×Dic12C22semidirect
28. #91113C22semidirect
29. #91112C22semidirect
30. #91111C22semidirect
31. #91110C22semidirect
32. C2×C3⋊#672C22semidirect
33. C5×#829C22semidirect
34. C5×#827C22semidirect
35. C5×#812C22semidirect
36. #90942C22semidirect
37. #90940C22semidirect
38. #90940C22semidirect
39. #90938C22semidirect
40. #90934C22semidirect
41. D5×C3⋊C16C22semidirect
43. #66103D3semidirect
93. #5195D5semidirect
173. C2×Dic12C2×D5semidirect
177. #829C2×D5semidirect
183. #827C2×D5semidirect
187. #812C2×D5semidirect
430. C3×C5#3416semidirect
486. C5#84008semidirect
500. C3#10613771semidirect

Maximal subgroups

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

subgroupindex
C3×#661032
#117539872
#117512952
C5×#51952
#117483032
#117482952
#117482782
D5×#8272
C2×#909402
#117475432
#117475252
#106137713
#840085