Finite Group Databasebeta

← #14478548

Subgroups — #14478548

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#11756516C211yesmaximal, characteristic, complemented
3C3×C5×#509C211yesmaximal, characteristic, complemented
4#11751295C211yesmaximal, characteristic, complemented
5C2×#91111C211yesmaximal, characteristic, complemented
6#11751016C212yesmaximal, complemented
7D15×SD32C212yesmaximal, complemented
8#11751013C212yesmaximal, complemented
9#11751012C212yesmaximal, complemented
10#11751010C211yesmaximal, characteristic, complemented
11#11751008C211yesmaximal, characteristic, complemented
12#10613768—31nomaximal, Hall
13#92101—21no—
14#92095—21no—
15C3×C5×#135C2211yescharacteristic, complemented
16C2×C3×C5×D8C2211yescharacteristic
17#91840—21no—
18#91821—21no—
19Q16×D15C2212yescomplemented
20#91804—22no—
21#91801C2212yes—
22#91801C2212yescomplemented
23#91800—22no—
24D8×D15C2212yes—
25C2×Dic60C2211yescharacteristic, complemented
26#91793C2211yescharacteristic
27#91790C2211yescharacteristic
28C3×C5×SD32C2212yescomplemented
29C3×C5×D16C2212yescomplemented
30C3×C5×M32C2211yescharacteristic, complemented
31#91113C2211yescharacteristic, complemented
32#91112C2211yescharacteristic, complemented
33#91111C2212yescomplemented
34#91111C2212yescomplemented
35#91111C2211yescharacteristic, complemented
36#91110C2211yescharacteristic, complemented
37C2×C3⋊#672C2211yescharacteristic, complemented
38Dic120C2212yescomplemented
39#91084C2212yescomplemented
40#91082C2212yescomplemented
41C16×D15C2212yescomplemented
42#82037—51nomaximal, Hall
43#66105—31no—
44#66091—31no—
45C5×#509D311yescharacteristic, complemented
46#65483—31no—
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—
55C2×C3×C5×D4—21no—
56C2×#1220—42no—
57Q8×D15—22no—
58#6819—22no—
59#6819—22no—
60#6819—42no—
61#6819—41no—
62D4×D15—22no—
63D4×D15—41no—
64#6817—21no—
65#6817—41no—
66#6817D411yescharacteristic
67C2×Dic30—21no—
68C2×Dic30—41no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8—21no—
72C3×C5×D8C2311yescharacteristic
73C3×C5×D8C2312yes—
74C2×C3×C5×C8C2311yescharacteristic
75#6718—22no—
76#6716—22no—
77#6716—22no—
78#6715—22no—
79#6710D411yescharacteristic
80Dic60—21no—
81Dic60C2311yescharacteristic
82Dic60C2312yes—
83D120C2311yescharacteristic
84#6706—21no—
85#6705D412yes—
86C8×D15C2312yes—
87C3×C5×C16C2312yes—
88C3⋊#672C2311yescharacteristic
89C3⋊#672C2311yescharacteristic
90#5771—51no—
91#5757—51no—
92C3×#509D511yescharacteristic, complemented
93#5194—51no—
94C2×#827—51no—
95#4915—52no—
96D3×SD32—52no—
97#4912—52no—
98#4911—52no—
99#4909—51no—
100#4907—51no—
101#4150—61no—
102#4144—61no—
103C5×#135C2×D311yescharacteristic, complemented
104C2×C5×D8C2×D311yescharacteristic
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#4050—31no—
115#4047—31no—
116C5×SD32C2×D312yescomplemented
117C5×D16C2×D312yescomplemented
118C5×M32C2×D311yescharacteristic, complemented
119#3961—31no—
120#3960—31no—
121#3959—32no—
122#3959—32no—
123#3959—31no—
124#3958—31no—
125C2×#672—31no—
126Dic40—32no—
127#3932—32no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C23×C3×C5—41no—
132C22×D15—42no—
133C3×C5×Q8—21no—
134C3×C5×D4—22no—
135C3×C5×D4—21no—
136C3×C5×D4—41no—
137C3×C5×D4—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5C2×D411yescharacteristic
140#1220—41no—
141#1220—42no—
142#1220—42no—
143#1220—42no—
144#1220D812yes—
145C2×Dic15—41no—
146C2×Dic15—42no—
147C2×Dic15—42no—
148D60—21no—
149D60D811yescharacteristic
150C4×D15—42no—
151C4×D15—41no—
152C4×D15C2×D412yes—
153Dic30—21no—
154Dic30—22no—
155Dic30—41no—
156Dic30—42no—
157Dic30D811yescharacteristic
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1010—101no—
162#1004—101no—
163C3×#135C2×D511yescharacteristic, complemented
164C2×C3×D8C2×D511yescharacteristic
165#951—101no—
166#932—101no—
167D3×Q16—52no—
168#915—102no—
169#912—52no—
170#912—52no—
171#911—102no—
172D3×D8—52no—
173C2×Dic12—51no—
174#904—51no—
175#901—51no—
176C3×SD32C2×D512yescomplemented
177C3×D16C2×D512yescomplemented
178C3×M32C2×D511yescharacteristic, complemented
179#829—51no—
180#828—51no—
181#827—52no—
182#827—52no—
183#827—51no—
184#826—51no—
185C2×C3⋊C16—51no—
186Dic24—52no—
187#800—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C2×C5×D4—21no—
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—31no—
201#709—61no—
202#709—121no—
203C2×Dic10—61no—
204C2×Dic10—121no—
205C5×Q16C22×D311yescharacteristic
206C5×SD16—21no—
207C5×D8—21no—
208C5×D8C22×D312yes—
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—31no—
218Dic20—61no—
219D40—31no—
220#677—61no—
221#676—32no—
222C8×D5—32no—
223C5×C16C22×D312yes—
224#672—31no—
225#672—31no—
226#578—151no—
227#576—151no—
228#510—152no—
229#510—151no—
230#509—152no—
231#509D1511yescharacteristic, complemented
232#508—151no—
233#508—152no—
234C2×SD32—151no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5—42no—
239C22×C3×C5—161no—
240C22×C3×C5C2×D811yescharacteristic
241C2×D15—41no—
242C2×D15—162no—
243C2×D15C2×D812yes—
244C3×C4×C5—41no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247Dic15—42no—
248Dic15—41no—
249Dic15C2×D812yes—
250C3×#41—21no—
251C2×C3×D4—21no—
252C2×#67—202no—
253D3×Q8—102no—
254#237—102no—
255#237—102no—
256#237—201no—
257#237—202no—
258D3×D4—102no—
259D3×D4—201no—
260#235—51no—
261#235—101no—
262#235—201no—
263C2×Dic6—101no—
264C2×Dic6—201no—
265C3×Q16C22×D511yescharacteristic
266C3×SD16—21no—
267C3×D8—21no—
268C3×D8C22×D511yescharacteristic
269C3×D8C22×D512yes—
270C2×C3×C8C22×D511yescharacteristic
271#216—102no—
272#214—102no—
273#214—102no—
274#213—102no—
275#208—51no—
276Dic12—52no—
277Dic12—51no—
278Dic12—101no—
279D24—51no—
280#204—101no—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16C22×D512yes—
284C3⋊C16—51no—
285C3⋊C16—51no—
286C23×C5—41no—
287C22×D5—122no—
288C5×Q8—21no—
289C5×D4—22no—
290C5×D4—21no—
291C5×D4—41no—
292C5×D4—41no—
293C2×C4×C5—41no—
294C2×C4×C5D3×D411yescharacteristic
295C22⋊D5—32no—
296C22⋊D5—122no—
297C22⋊D5—122no—
298C22⋊D5—122no—
299C22⋊D5—121no—
300C2×Dic5—122no—
301C2×Dic5—122no—
302C2×Dic5—121no—
303D20—31no—
304D20—61no—
305C4×D5—32no—
306C4×D5—122no—
307C4×D5—121no—
308Dic10—31no—
309Dic10—61no—
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—152no—
323#135—152no—
324#135—151no—
325#135C2×D1511yescharacteristic, complemented
326C2×Q16—152no—
327C2×Q16—151no—
328C2×D8—152no—
329C2×D8C2×D1511yescharacteristic
330#131—151no—
331Q32—151no—
332Q32—152no—
333SD32—151no—
334SD32—152no—
335SD32—152no—
336SD32—151no—
337SD32—152no—
338SD32C2×D1512yescomplemented
339D16—151no—
340D16C2×D1512yescomplemented
341M32—152no—
342M32C2×D1511yescharacteristic, complemented
343C2×C16—151no—
344C2×C16—152no—
345C2×C3×C5—21no—
346C2×C3×C5—82no—
347C2×C3×C5—81no—
348C2×C3×C5C22×D811yescharacteristic
349D15—22no—
350D15—81no—
351C23×C3—41no—
352C22×D3—202no—
353C3×Q8—21no—
354C3×D4—22no—
355C3×D4—21no—
356C3×D4—41no—
357C3×D4—41no—
358C2×C3×C4—41no—
359C2×C3×C4D4×D511yescharacteristic
360#67—52no—
361#67—202no—
362#67—202no—
363#67—202no—
364#67—201no—
365C2×Dic3—202no—
366C2×Dic3—202no—
367C2×Dic3—201no—
368D12—51no—
369D12—101no—
370C4×D3—52no—
371C4×D3—202no—
372C4×D3—201no—
373Dic6—51no—
374Dic6—101no—
375Dic6—102no—
376Dic6—202no—
377Dic6—201no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—41no—
382C22×C5—42no—
383C22×C5—161no—
384C22×C5D3×D811yescharacteristic
385C2×D5—32no—
386C2×D5—121no—
387C2×D5—482no—
388C4×C5—41no—
389C4×C5D3×D811yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—32no—
392Dic5—122no—
393Dic5—121no—
394#41—21no—
395#41—151no—
396#41—302no—
397#41—302no—
398#41—301no—
399#41—601no—
400#41—602no—
401#41—601no—
402C2×Q8—302no—
403C2×Q8—301no—
404C2×Q8—601no—
405C2×D4—21no—
406C2×D4—302no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—152no—
410Q16—151no—
411Q16—302no—
412Q16—301no—
413Q16C22×D1511yescharacteristic
414SD16—21no—
415SD16—302no—
416SD16—302no—
417SD16—301no—
418D8—21no—
419D8—151no—
420D8—302no—
421D8C22×D1511yescharacteristic
422D8C22×D1512yes—
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C22×D1511yescharacteristic
427C16—151no—
428C16—151no—
429C16C22×D1512yes—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—41no—
432C22×C3—42no—
433C22×C3—161no—
434C22×C3D5×D811yescharacteristic
435C2×D3—52no—
436C2×D3—201no—
437C2×D3—802no—
438C3×C4—41no—
439C3×C4D5×D811yescharacteristic
440C3×C4C2×D4×D511yescharacteristic
441Dic3—52no—
442Dic3—202no—
443Dic3—201no—
444C2×C5—21no—
445C2×C5—82no—
446C2×C5—81no—
447C2×C5C2×D3×D811yescharacteristic
448D5—62no—
449D5—241no—
450C23—41no—
451C23—602no—
452Q8—21no—
453Q8—151no—
454Q8—301no—
455Q8—302no—
456Q8—602no—
457Q8—601no—
458D4—22no—
459D4—21no—
460D4—41no—
461D4—41no—
462D4—152no—
463D4—151no—
464D4—301no—
465D4—602no—
466D4—602no—
467D4—602no—
468D4—601no—
469C2×C4—41no—
470C2×C4—152no—
471C2×C4—602no—
472C2×C4—602no—
473C2×C4—602no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4D4×D1511yescharacteristic
477C8—152no—
478C8D4×D1511yescharacteristic
479C8C23×D1511yescharacteristic
480C2×C3—21no—
481C2×C3—82no—
482C2×C3—81no—
483C2×C3C2×D5×D811yescharacteristic
484D3—102no—
485D3—401no—
486C5#8203711yescharacteristic, complemented, Sylow
487C22—41no—
488C22—42no—
489C22—152no—
490C22—161no—
491C22—601no—
492C22—2402no—
493C22D8×D1511yescharacteristic
494C4—41no—
495C4—152no—
496C4—601no—
497C4—602no—
498C4D8×D1511yescharacteristic
499C4C2×D4×D1511yescharacteristic
500C3#1061376811yescharacteristic, complemented, Sylow
501C2—21no—
502C2—82no—
503C2—81no—
504C2—302no—
505C2—1201no—
506C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC2C2×D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC3×C5×#509C2
socleC2×C3×C5C22×D8
hypercenter#509D15
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #11756530C2semidirect
2. #11756516C2semidirect
3. C3×C5×#509C2semidirect
4. #11751295C2semidirect
5. C2×#91111C2semidirect
6. #11751016C2semidirect
7. D15×SD32C2semidirect
8. #11751013C2semidirect
9. #11751012C2semidirect
10. #11751010C2semidirect
11. #11751008C2semidirect
15. C3×C5×#135C22semidirect
19. Q16×D15C22semidirect
22. #91801C22semidirect
25. C2×Dic60C22semidirect
28. C3×C5×SD32C22semidirect
29. C3×C5×D16C22semidirect
30. C3×C5×M32C22semidirect
31. #91113C22semidirect
32. #91112C22semidirect
33. #91111C22semidirect
34. #91111C22semidirect
35. #91111C22semidirect
36. #91110C22semidirect
37. C2×C3⋊#672C22semidirect
38. Dic120C22semidirect
39. #91084C22semidirect
40. #91082C22semidirect
41. C16×D15C22semidirect
45. C5×#509D3semidirect
92. C3×#509D5semidirect
103. C5×#135C2×D3semidirect
116. C5×SD32C2×D3semidirect
117. C5×D16C2×D3semidirect
118. C5×M32C2×D3semidirect
163. C3×#135C2×D5semidirect
176. C3×SD32C2×D5semidirect
177. C3×D16C2×D5semidirect
178. C3×M32C2×D5semidirect
231. #509D15semidirect
325. #135C2×D15semidirect
338. SD32C2×D15semidirect
340. D16C2×D15semidirect
342. M32C2×D15semidirect
430. C3×C5#3416semidirect
486. C5#82037semidirect
500. C3#10613768semidirect

Maximal subgroups

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

subgroupindex
#117565302
#117565162
C3×C5×#5092
#117512952
C2×#911112
#117510162
D15×SD322
#117510132
#117510122
#117510102
#117510082
#106137683
#820375