Finite Group Databasebeta

← #14478539

Subgroups — #14478539

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#11756528C211yesmaximal, characteristic, complemented
3C3×C5×#508C211yesmaximal, characteristic, complemented
4#11751296C211yesmaximal, characteristic, complemented
5#11751294C211yesmaximal, characteristic, complemented
6#11751019C212yesmaximal, complemented
7#11751017C212yesmaximal, complemented
8D15×SD32C212yesmaximal, complemented
9#11751012C212yesmaximal, complemented
10C2×#91084C211yesmaximal, characteristic, complemented
11#11751002C211yesmaximal, characteristic, complemented
12#10613763—31nomaximal, Hall
13#92101—21no—
14#92100—21no—
15C3×C5×#135C2211yescharacteristic
16C3×C5×#135C2211yescharacteristic, complemented
17#91840—21no—
18#91838—21no—
19#91808C2212yes—
20Q16×D15C2212yescomplemented
21#91804—22no—
22#91803—22no—
23#91801C2212yescomplemented
24D8×D15C2212yes—
25C2×Dic60C2211yescharacteristic, complemented
26C2×D120C2211yescharacteristic
27#91790C2211yescharacteristic
28C3×C5×Q32C2211yescharacteristic, complemented
29C3×C5×SD32C2211yescharacteristic, complemented
30C3×C5×SD32C2211yescharacteristic, complemented
31C3×C5×D16C2211yescharacteristic, complemented
32C2×C3×C5×C16C2211yescharacteristic, complemented
33#91113C2212yescomplemented
34#91112C2212yescomplemented
35#91111C2212yescomplemented
36#91110C2212yescomplemented
37#91096C2211yescharacteristic, complemented
38#91084C2212yescomplemented
39#91084C2212yescomplemented
40#91082C2212yescomplemented
41C16×D15C2212yescomplemented
42#82032—51nomaximal, Hall
43#66105—31no—
44#66103—31no—
45C5×#508D311yescharacteristic, complemented
46#65484—31no—
47#65482—31no—
48#65207—32no—
49#65205—32no—
50D5×SD32—32no—
51#65200—32no—
52C2×#3932—31no—
53#65190—31no—
54C3×C5×#41—21no—
55C3×C5×#41—21no—
56#6821—22no—
57Q8×D15—22no—
58#6819—22no—
59#6819—42no—
60D4×D15—22no—
61D4×D15—42no—
62#6817—41no—
63#6817—41no—
64#6817D411yescharacteristic
65C2×D60—21no—
66C2×D60—41no—
67C2×Dic30—21no—
68C2×Dic30—41no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×Q16C2311yescharacteristic
71C3×C5×SD16—21no—
72C3×C5×SD16—21no—
73C3×C5×D8C2311yescharacteristic
74C3×C5×D8C2311yescharacteristic
75C2×C3×C5×C8C2311yescharacteristic
76#6718—22no—
77#6717—22no—
78#6716—22no—
79#6715—22no—
80#6710D411yescharacteristic
81Dic60—21no—
82Dic60C2312yes—
83D120—21no—
84D120C2312yes—
85#6705D412yes—
86C8×D15C2312yes—
87C3×C5×C16C2311yescharacteristic
88C3×C5×C16C2311yescharacteristic
89C3⋊#672C2312yes—
90#5771—51no—
91#5769—51no—
92C3×#508D511yescharacteristic, complemented
93#5195—51no—
94#5193—51no—
95#4918—52no—
96#4916—52no—
97D3×SD32—52no—
98#4911—52no—
99C2×#800—51no—
100#4901—51no—
101#4150—61no—
102#4149—61no—
103C5×#135C2×D311yescharacteristic
104C5×#135C2×D311yescharacteristic, complemented
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×Dic20—31no—
114C2×D40—31no—
115#4047—31no—
116C5×Q32C2×D311yescharacteristic, complemented
117C5×SD32C2×D311yescharacteristic, complemented
118C5×SD32C2×D311yescharacteristic, complemented
119C5×D16C2×D311yescharacteristic, complemented
120C2×C5×C16C2×D311yescharacteristic, complemented
121#3961—32no—
122#3960—32no—
123#3959—32no—
124#3958—32no—
125#3944—31no—
126#3932—32no—
127#3932—32no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×D15—41no—
132C22×D15—42no—
133C3×C5×Q8—21no—
134C3×C5×Q8—21no—
135C3×C5×D4—21no—
136C3×C5×D4—21no—
137C3×C5×D4—41no—
138C3×C5×D4—41no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5—41no—
141C2×C3×C4×C5C2×D411yescharacteristic
142#1220—42no—
143#1220—42no—
144#1220D812yes—
145C2×Dic15—41no—
146C2×Dic15—42no—
147D60—22no—
148D60—42no—
149D60—41no—
150D60D811yescharacteristic
151C4×D15—42no—
152C4×D15—42no—
153C4×D15C2×D412yes—
154Dic30—22no—
155Dic30—41no—
156Dic30—42no—
157Dic30D811yescharacteristic
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1010—101no—
162#1009—101no—
163C3×#135C2×D511yescharacteristic
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×D24—51no—
175#901—51no—
176C3×Q32C2×D511yescharacteristic, complemented
177C3×SD32C2×D511yescharacteristic, complemented
178C3×SD32C2×D511yescharacteristic, complemented
179C3×D16C2×D511yescharacteristic, complemented
180C2×C3×C16C2×D511yescharacteristic, complemented
181#829—52no—
182#828—52no—
183#827—52no—
184#826—52no—
185#812—51no—
186#800—52no—
187#800—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C5×#41—21no—
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—61no—
202C2×D20—121no—
203C2×Dic10—61no—
204C2×Dic10—121no—
205C5×Q16C22×D311yescharacteristic
206C5×Q16C22×D311yescharacteristic
207C5×SD16—21no—
208C5×SD16—21no—
209C5×D8C22×D311yescharacteristic
210C5×D8C22×D311yescharacteristic
211C2×C5×C8C22×D311yescharacteristic
212#689—62no—
213#688—62no—
214#687—62no—
215#686—62no—
216#681—31no—
217Dic20—32no—
218Dic20—61no—
219D40—32no—
220D40—61no—
221#676—32no—
222C8×D5—32no—
223C5×C16C22×D311yescharacteristic
224C5×C16C22×D311yescharacteristic
225#672—32no—
226#578—151no—
227#576—151no—
228#510—151no—
229#510—152no—
230#509—151no—
231#509—152no—
232#508—152no—
233#508D1511yescharacteristic, complemented
234C2×SD32—152no—
235C2×SD32—151no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5C2×D811yescharacteristic
240C2×D15—42no—
241C2×D15—162no—
242C2×D15—161no—
243C2×D15C2×D812yes—
244C3×C4×C5—41no—
245C3×C4×C5—41no—
246C3×C4×C5C2×D811yescharacteristic
247C3×C4×C5C22×D411yescharacteristic
248Dic15—42no—
249Dic15C2×D812yes—
250C3×#41—21no—
251C3×#41—21no—
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—101no—
262C2×D12—201no—
263C2×Dic6—101no—
264C2×Dic6—201no—
265C3×Q16C22×D511yescharacteristic
266C3×Q16C22×D511yescharacteristic
267C3×SD16—21no—
268C3×SD16—21no—
269C3×D8C22×D511yescharacteristic
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—52no—
280D24—101no—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16C22×D511yescharacteristic
284C3×C16C22×D511yescharacteristic
285C3⋊C16—52no—
286C22×D5—122no—
287C22×D5—121no—
288C5×Q8—21no—
289C5×Q8—21no—
290C5×D4—21no—
291C5×D4—21no—
292C5×D4—41no—
293C5×D4—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5D3×D411yescharacteristic
297C22⋊D5—32no—
298C22⋊D5—122no—
299C22⋊D5—122no—
300C2×Dic5—122no—
301C2×Dic5—121no—
302D20—31no—
303D20—62no—
304D20—122no—
305D20—121no—
306C4×D5—32no—
307C4×D5—122no—
308C4×D5—122no—
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—152no—
323#135—152no—
324#135C2×D1511yescharacteristic
325#135C2×D1511yescharacteristic, complemented
326C2×Q16—152no—
327C2×Q16—151no—
328C2×D8—152no—
329C2×D8—151no—
330#131—151no—
331Q32—152no—
332Q32C2×D1511yescharacteristic, complemented
333SD32—152no—
334SD32—152no—
335SD32—152no—
336SD32—152no—
337SD32C2×D1511yescharacteristic, complemented
338SD32C2×D1511yescharacteristic, complemented
339D16—152no—
340D16C2×D1511yescharacteristic, complemented
341M32—151no—
342M32—152no—
343C2×C16—152no—
344C2×C16C2×D1511yescharacteristic, complemented
345C2×C3×C5—21no—
346C2×C3×C5—81no—
347C2×C3×C5—81no—
348C2×C3×C5C22×D811yescharacteristic
349D15—22no—
350D15—82no—
351C22×D3—202no—
352C22×D3—201no—
353C3×Q8—21no—
354C3×Q8—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—41no—
358C3×D4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4D4×D511yescharacteristic
362#67—52no—
363#67—202no—
364#67—202no—
365C2×Dic3—202no—
366C2×Dic3—201no—
367D12—51no—
368D12—102no—
369D12—202no—
370D12—201no—
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—41no—
383C22×C5D3×D811yescharacteristic
384C2×D5—32no—
385C2×D5—122no—
386C2×D5—482no—
387C2×D5—481no—
388C4×C5—41no—
389C4×C5—41no—
390C4×C5D3×D811yescharacteristic
391C4×C5C2×D3×D411yescharacteristic
392Dic5—32no—
393Dic5—122no—
394#41—21no—
395#41—21no—
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—302no—
406C2×D4—301no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—152no—
410Q16—302no—
411Q16—301no—
412Q16C22×D1511yescharacteristic
413Q16C22×D1511yescharacteristic
414SD16—21no—
415SD16—21no—
416SD16—302no—
417SD16—302no—
418D8—152no—
419D8—302no—
420D8—301no—
421D8C22×D1511yescharacteristic
422D8C22×D1511yescharacteristic
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C22×D1511yescharacteristic
427C16—152no—
428C16C22×D1511yescharacteristic
429C16C22×D1511yescharacteristic
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—41no—
432C22×C3—41no—
433C22×C3D5×D811yescharacteristic
434C2×D3—52no—
435C2×D3—202no—
436C2×D3—802no—
437C2×D3—801no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—52no—
443Dic3—202no—
444C2×C5—21no—
445C2×C5—81no—
446C2×C5—81no—
447C2×C5C2×D3×D811yescharacteristic
448D5—62no—
449D5—242no—
450C23—602no—
451C23—601no—
452Q8—21no—
453Q8—21no—
454Q8—151no—
455Q8—302no—
456Q8—602no—
457Q8—601no—
458D4—21no—
459D4—21no—
460D4—41no—
461D4—41no—
462D4—152no—
463D4—151no—
464D4—302no—
465D4—602no—
466D4—602no—
467D4—602no—
468D4—601no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—152no—
472C2×C4—602no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—601no—
476C2×C4D4×D1511yescharacteristic
477C8—152no—
478C8D4×D1511yescharacteristic
479C8C23×D1511yescharacteristic
480C2×C3—21no—
481C2×C3—81no—
482C2×C3—81no—
483C2×C3C2×D5×D811yescharacteristic
484D3—102no—
485D3—402no—
486C5#8203211yescharacteristic, complemented, Sylow
487C22—41no—
488C22—41no—
489C22—152no—
490C22—602no—
491C22—2401no—
492C22—2402no—
493C22D8×D1511yescharacteristic
494C4—41no—
495C4—41no—
496C4—152no—
497C4—602no—
498C4D8×D1511yescharacteristic
499C4C2×D4×D1511yescharacteristic
500C3#1061376311yescharacteristic, complemented, Sylow
501C2—21no—
502C2—81no—
503C2—81no—
504C2—302no—
505C2—1202no—
506C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC2C2×D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC3×C5×#508C2
socleC2×C3×C5C22×D8
hypercenter#508D15
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #11756530C2semidirect
2. #11756528C2semidirect
3. C3×C5×#508C2semidirect
4. #11751296C2semidirect
5. #11751294C2semidirect
6. #11751019C2semidirect
7. #11751017C2semidirect
8. D15×SD32C2semidirect
9. #11751012C2semidirect
10. C2×#91084C2semidirect
11. #11751002C2semidirect
16. C3×C5×#135C22semidirect
20. Q16×D15C22semidirect
23. #91801C22semidirect
25. C2×Dic60C22semidirect
28. C3×C5×Q32C22semidirect
29. C3×C5×SD32C22semidirect
30. C3×C5×SD32C22semidirect
31. C3×C5×D16C22semidirect
32. C2×C3×C5×C16C22semidirect
33. #91113C22semidirect
34. #91112C22semidirect
35. #91111C22semidirect
36. #91110C22semidirect
37. #91096C22semidirect
38. #91084C22semidirect
39. #91084C22semidirect
40. #91082C22semidirect
41. C16×D15C22semidirect
45. C5×#508D3semidirect
92. C3×#508D5semidirect
104. C5×#135C2×D3semidirect
116. C5×Q32C2×D3semidirect
117. C5×SD32C2×D3semidirect
118. C5×SD32C2×D3semidirect
119. C5×D16C2×D3semidirect
120. C2×C5×C16C2×D3semidirect
164. C3×#135C2×D5semidirect
176. C3×Q32C2×D5semidirect
177. C3×SD32C2×D5semidirect
178. C3×SD32C2×D5semidirect
179. C3×D16C2×D5semidirect
180. C2×C3×C16C2×D5semidirect
233. #508D15semidirect
325. #135C2×D15semidirect
332. Q32C2×D15semidirect
337. SD32C2×D15semidirect
338. SD32C2×D15semidirect
340. D16C2×D15semidirect
344. C2×C16C2×D15semidirect
430. C3×C5#3416semidirect
486. C5#82032semidirect
500. C3#10613763semidirect

Maximal subgroups

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

subgroupindex
#117565302
#117565282
C3×C5×#5082
#117512962
#117512942
#117510192
#117510172
D15×SD322
#117510122
C2×#910842
#117510022
#106137633
#820325