Finite Group Databasebeta

← #14478545

Subgroups — #14478545

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#11756528C211yesmaximal, characteristic, complemented
2#11756525C211yesmaximal, characteristic, complemented
3C3×C5×#510C211yesmaximal, characteristic, complemented
4#11751295C211yesmaximal, characteristic, complemented
5C2×#91112C211yesmaximal, characteristic, complemented
6#11751020C212yesmaximal, complemented
7#11751019C212yesmaximal, complemented
8#11751015C212yesmaximal, complemented
9D15×SD32C212yesmaximal, complemented
10#11751009C211yesmaximal, characteristic, complemented
11#11751008C211yesmaximal, characteristic, complemented
12#10613771—31nomaximal, Hall
13#92100—21no—
14#92098—21no—
15C3×C5×#135C2211yescharacteristic
16C2×C3×C5×Q16C2211yescharacteristic, complemented
17#91838—21no—
18#91831—21no—
19#91808C2212yes—
20#91808C2212yescomplemented
21#91807—22no—
22Q16×D15C2212yescomplemented
23#91803—22no—
24D8×D15C2212yes—
25#91793C2211yescharacteristic, complemented
26C2×D120C2211yescharacteristic
27#91790C2211yescharacteristic
28C3×C5×Q32C2212yescomplemented
29C3×C5×SD32C2212yescomplemented
30C3×C5×M32C2211yescharacteristic, complemented
31#91113C2211yescharacteristic, complemented
32#91112C2212yescomplemented
33#91112C2212yescomplemented
34#91112C2211yescharacteristic, complemented
35#91111C2211yescharacteristic, complemented
36#91110C2211yescharacteristic, complemented
37C2×C3⋊#672C2211yescharacteristic, complemented
38#91084C2212yescomplemented
39D240C2212yescomplemented
40#91082C2212yescomplemented
41C16×D15C2212yescomplemented
42#82040—51nomaximal, Hall
43#66103—31no—
44#66100—31no—
45C5×#510D311yescharacteristic, complemented
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—
55C2×C3×C5×Q8—21no—
56#6821—22no—
57#6821—22no—
58#6821—41no—
59Q8×D15—22no—
60Q8×D15—41no—
61D4×D15—22no—
62D4×D15—42no—
63#6817—21no—
64#6817—42no—
65#6817—41no—
66#6817D411yescharacteristic
67C2×D60—21no—
68C2×D60—41no—
69C3×C5×Q16—21no—
70C3×C5×Q16C2312yes—
71C3×C5×Q16C2311yescharacteristic
72C3×C5×SD16—21no—
73C3×C5×D8C2311yescharacteristic
74C2×C3×C5×C8C2311yescharacteristic
75#6718—22no—
76#6717—22no—
77#6717—22no—
78#6715—22no—
79#6710D411yescharacteristic
80Dic60C2311yescharacteristic
81D120—21no—
82D120C2312yes—
83D120C2311yescharacteristic
84#6706—21no—
85#6705D412yes—
86C8×D15C2312yes—
87C3×C5×C16C2312yes—
88C3⋊#672C2311yescharacteristic
89C3⋊#672C2311yescharacteristic
90#5769—51no—
91#5766—51no—
92C3×#510D511yescharacteristic, complemented
93#5194—51no—
94C2×#828—51no—
95#4919—52no—
96#4918—52no—
97#4914—52no—
98D3×SD32—52no—
99#4908—51no—
100#4907—51no—
101#4149—61no—
102#4147—61no—
103C5×#135C2×D311yescharacteristic
104C2×C5×Q16C2×D311yescharacteristic, complemented
105#4095—61no—
106#4088—61no—
107#4065—32no—
108#4065—32no—
109#4064—62no—
110D5×Q16—32no—
111#4060—62no—
112D5×D8—32no—
113#4050—31no—
114C2×D40—31no—
115#4047—31no—
116C5×Q32C2×D312yescomplemented
117C5×SD32C2×D312yescomplemented
118C5×M32C2×D311yescharacteristic, complemented
119#3961—31no—
120#3960—32no—
121#3960—32no—
122#3960—31no—
123#3959—31no—
124#3958—31no—
125C2×#672—31no—
126#3932—32no—
127D80—32no—
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×D15—41no—
132C22×D15—42no—
133C3×C5×Q8—21no—
134C3×C5×Q8—22no—
135C3×C5×Q8—41no—
136C3×C5×D4—21no—
137C3×C5×D4—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5C2×D411yescharacteristic
141#1220—41no—
142#1220—42no—
143#1220D812yes—
144D60—21no—
145D60—22no—
146D60—42no—
147D60—42no—
148D60—41no—
149D60D811yescharacteristic
150C4×D15—42no—
151C4×D15—41no—
152C4×D15—42no—
153C4×D15—42no—
154C4×D15C2×D412yes—
155Dic30—21no—
156Dic30—42no—
157Dic30D811yescharacteristic
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1009—101no—
162#1007—101no—
163C3×#135C2×D511yescharacteristic
164C2×C3×Q16C2×D511yescharacteristic, complemented
165#949—101no—
166#942—101no—
167#919—52no—
168#919—52no—
169#918—102no—
170D3×Q16—52no—
171#914—102no—
172D3×D8—52no—
173#904—51no—
174C2×D24—51no—
175#901—51no—
176C3×Q32C2×D512yescomplemented
177C3×SD32C2×D512yescomplemented
178C3×M32C2×D511yescharacteristic, complemented
179#829—51no—
180#828—52no—
181#828—52no—
182#828—51no—
183#827—51no—
184#826—51no—
185C2×C3⋊C16—51no—
186#800—52no—
187D48—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C2×C5×Q8—21no—
192#713—62no—
193#713—62no—
194#713—121no—
195Q8×D5—62no—
196Q8×D5—121no—
197D4×D5—62no—
198D4×D5—122no—
199#709—31no—
200#709—61no—
201#709—121no—
202#709—122no—
203C2×D20—61no—
204C2×D20—121no—
205C5×Q16—21no—
206C5×Q16C22×D312yes—
207C5×Q16C22×D311yescharacteristic
208C5×SD16—21no—
209C5×D8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211#689—62no—
212#688—62no—
213#688—62no—
214#686—62no—
215#681—31no—
216Dic20—31no—
217D40—31no—
218D40—32no—
219D40—61no—
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#510D1511yescharacteristic, complemented
230#509—152no—
231#509—151no—
232#508—151no—
233#508—152no—
234C2×SD32—151no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×D15—41no—
240C2×D15—42no—
241C2×D15—162no—
242C2×D15—161no—
243C2×D15C2×D812yes—
244C3×C4×C5—42no—
245C3×C4×C5—41no—
246C3×C4×C5C2×D811yescharacteristic
247C3×C4×C5C22×D411yescharacteristic
248Dic15—41no—
249Dic15C2×D812yes—
250C3×#41—21no—
251C2×C3×Q8—21no—
252#239—102no—
253#239—102no—
254#239—201no—
255D3×Q8—102no—
256D3×Q8—201no—
257D3×D4—102no—
258D3×D4—202no—
259#235—51no—
260#235—101no—
261#235—201no—
262#235—202no—
263C2×D12—101no—
264C2×D12—201no—
265C3×Q16—21no—
266C3×Q16C22×D512yes—
267C3×Q16C22×D511yescharacteristic
268C3×SD16—21no—
269C3×D8C22×D511yescharacteristic
270C2×C3×C8C22×D511yescharacteristic
271#216—102no—
272#215—102no—
273#215—102no—
274#213—102no—
275#208—51no—
276Dic12—51no—
277D24—51no—
278D24—52no—
279D24—101no—
280#204—101no—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16C22×D512yes—
284C3⋊C16—51no—
285C3⋊C16—51no—
286C22×D5—122no—
287C22×D5—121no—
288C5×Q8—21no—
289C5×Q8—22no—
290C5×Q8—41no—
291C5×D4—21no—
292C5×D4—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5D3×D411yescharacteristic
296C22⋊D5—32no—
297C22⋊D5—122no—
298C22⋊D5—121no—
299D20—31no—
300D20—61no—
301D20—62no—
302D20—122no—
303D20—122no—
304D20—121no—
305C4×D5—32no—
306C4×D5—122no—
307C4×D5—122no—
308C4×D5—122no—
309C4×D5—121no—
310Dic10—31no—
311Dic10—61no—
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—152no—
323#135—152no—
324#135—151no—
325#135C2×D1511yescharacteristic
326C2×Q16—152no—
327C2×Q16C2×D1511yescharacteristic, complemented
328C2×D8—152no—
329C2×D8—151no—
330#131—151no—
331Q32—151no—
332Q32C2×D1512yescomplemented
333SD32—152no—
334SD32—152no—
335SD32—151no—
336SD32—151no—
337SD32—152no—
338SD32C2×D1512yescomplemented
339D16—151no—
340D16—152no—
341M32—152no—
342M32C2×D1511yescharacteristic, complemented
343C2×C16—151no—
344C2×C16—152no—
345C2×C3×C5—21no—
346C2×C3×C5—81no—
347C2×C3×C5C22×D811yescharacteristic
348D15—22no—
349D15—81no—
350D15—82no—
351C22×D3—202no—
352C22×D3—201no—
353C3×Q8—21no—
354C3×Q8—22no—
355C3×Q8—41no—
356C3×D4—21no—
357C3×D4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4D4×D511yescharacteristic
361#67—52no—
362#67—202no—
363#67—201no—
364D12—51no—
365D12—101no—
366D12—102no—
367D12—202no—
368D12—202no—
369D12—201no—
370C4×D3—52no—
371C4×D3—202no—
372C4×D3—202no—
373C4×D3—202no—
374C4×D3—201no—
375Dic6—51no—
376Dic6—101no—
377Dic6—202no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—41no—
382C22×C5D3×D811yescharacteristic
383C2×D5—32no—
384C2×D5—121no—
385C2×D5—122no—
386C2×D5—482no—
387C2×D5—481no—
388C4×C5—42no—
389C4×C5—41no—
390C4×C5D3×D811yescharacteristic
391C4×C5C2×D3×D411yescharacteristic
392Dic5—32no—
393Dic5—121no—
394#41—21no—
395#41—151no—
396#41—302no—
397#41—302no—
398#41—301no—
399#41—602no—
400#41—601no—
401#41—601no—
402C2×Q8—21no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—302no—
406C2×D4—301no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—21no—
410Q16—151no—
411Q16—302no—
412Q16C22×D1512yes—
413Q16C22×D1511yescharacteristic
414SD16—21no—
415SD16—302no—
416SD16—302no—
417SD16—301no—
418D8—151no—
419D8—152no—
420D8—302no—
421D8—301no—
422D8C22×D1511yescharacteristic
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×C3D5×D811yescharacteristic
433C2×D3—52no—
434C2×D3—201no—
435C2×D3—202no—
436C2×D3—802no—
437C2×D3—801no—
438C3×C4—42no—
439C3×C4—41no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—52no—
443Dic3—201no—
444C2×C5—21no—
445C2×C5—81no—
446C2×C5C2×D3×D811yescharacteristic
447D5—62no—
448D5—242no—
449D5—241no—
450C23—602no—
451C23—601no—
452Q8—21no—
453Q8—22no—
454Q8—41no—
455Q8—151no—
456Q8—301no—
457Q8—602no—
458D4—21no—
459D4—41no—
460D4—152no—
461D4—151no—
462D4—302no—
463D4—301no—
464D4—602no—
465D4—602no—
466D4—602no—
467D4—601no—
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×C3C2×D5×D811yescharacteristic
483D3—102no—
484D3—402no—
485D3—401no—
486C5#8204011yescharacteristic, complemented, Sylow
487C22—41no—
488C22—152no—
489C22—601no—
490C22—602no—
491C22—2401no—
492C22—2402no—
493C22D8×D1511yescharacteristic
494C4—41no—
495C4—42no—
496C4—152no—
497C4—601no—
498C4D8×D1511yescharacteristic
499C4C2×D4×D1511yescharacteristic
500C3#1061377111yescharacteristic, complemented, Sylow
501C2—21no—
502C2—81no—
503C2—302no—
504C2—1202no—
505C2—1201no—
506C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC2C2×D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC3×C5×#510C2
socleC2×C3×C5C22×D8
hypercenter#510D15
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. #11756528C2semidirect
2. #11756525C2semidirect
3. C3×C5×#510C2semidirect
4. #11751295C2semidirect
5. C2×#91112C2semidirect
6. #11751020C2semidirect
7. #11751019C2semidirect
8. #11751015C2semidirect
9. D15×SD32C2semidirect
10. #11751009C2semidirect
11. #11751008C2semidirect
16. C2×C3×C5×Q16C22semidirect
20. #91808C22semidirect
22. Q16×D15C22semidirect
25. #91793C22semidirect
28. C3×C5×Q32C22semidirect
29. C3×C5×SD32C22semidirect
30. C3×C5×M32C22semidirect
31. #91113C22semidirect
32. #91112C22semidirect
33. #91112C22semidirect
34. #91112C22semidirect
35. #91111C22semidirect
36. #91110C22semidirect
37. C2×C3⋊#672C22semidirect
38. #91084C22semidirect
39. D240C22semidirect
40. #91082C22semidirect
41. C16×D15C22semidirect
45. C5×#510D3semidirect
92. C3×#510D5semidirect
104. C2×C5×Q16C2×D3semidirect
116. C5×Q32C2×D3semidirect
117. C5×SD32C2×D3semidirect
118. C5×M32C2×D3semidirect
164. C2×C3×Q16C2×D5semidirect
176. C3×Q32C2×D5semidirect
177. C3×SD32C2×D5semidirect
178. C3×M32C2×D5semidirect
229. #510D15semidirect
327. C2×Q16C2×D15semidirect
332. Q32C2×D15semidirect
338. SD32C2×D15semidirect
342. M32C2×D15semidirect
430. C3×C5#3416semidirect
486. C5#82040semidirect
500. C3#10613771semidirect

Maximal subgroups

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

subgroupindex
#117565282
#117565252
C3×C5×#5102
#117512952
C2×#911122
#117510202
#117510192
#117510152
D15×SD322
#117510092
#117510082
#106137713
#820405