Finite Group Databasebeta

← #14478570

Subgroups — #14478570

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
1C5×#5766C211yesmaximal, characteristic, complemented
2#11753973C211yesmaximal, characteristic, complemented
3C2×#91112C211yesmaximal, characteristic, complemented
4C3×#65468C211yesmaximal, characteristic, complemented
5#11748307C212yesmaximal, complemented
6#11748306C212yesmaximal, complemented
7#11748291C212yesmaximal, complemented
8D3×#3960C212yesmaximal, complemented
9#11747548C211yesmaximal, characteristic, complemented
10#11747538C211yesmaximal, characteristic, complemented
11#11747529C211yesmaximal, characteristic, complemented
12#10615747—31nomaximal, Hall
13C5×#1007—21no—
14#92019—21no—
15C2×C3×C5×Q16C2211yescharacteristic, complemented
16C2×D120C2211yescharacteristic
17C5×#942—21no—
18C5×#919C2212yescomplemented
19C5×#918—22no—
20C5×D3×Q16C2212yescomplemented
21C5×#904C2211yescharacteristic, complemented
22C5×#901C2211yescharacteristic
23C3×#4050C2211yescharacteristic
24#91301—21no—
25#91275C2212yes—
26#91253—22no—
27D3×D40C2212yes—
28#91112C2212yescomplemented
29#91112C2212yescomplemented
30C2×C3⋊#672C2211yescharacteristic, complemented
31C3×#3961C2212yescomplemented
32C3×#3960C2212yescomplemented
33C3×#3944C2211yescharacteristic, complemented
34#90946C2211yescharacteristic, complemented
35#90945C2212yescomplemented
36#90941C2211yescharacteristic, complemented
37#90940C2211yescharacteristic, complemented
38#90939C2212yescomplemented
39#90937C2211yescharacteristic, complemented
40#90935C2212yescomplemented
41D3×#672C2212yescomplemented
42#82040—51nomaximal, Hall
43C5×#578—31no—
44#66086—31no—
45#65483—31no—
46#65483—32no—
47#65482—32no—
48#65482—31no—
49#65468—32no—
50#65468D311yescharacteristic, complemented
51C2×#3960—32no—
52C2×#3960—31no—
53#65429—31no—
54C2×C3×C5×Q8—21no—
55C2×D60—21no—
56C5×#239—22no—
57C5×#239—41no—
58C5×D3×Q8—22no—
59C5×D3×Q8—41no—
60C5×#235—21no—
61C5×#235—42no—
62C5×#235D411yescharacteristic
63C3×#709—21no—
64#6790—42no—
65D3×D20—22no—
66D5×D12—41no—
67#6773—41no—
68#6769—22no—
69C3×C5×Q16—21no—
70C3×C5×Q16C2312yes—
71C2×C3×C5×C8C2311yescharacteristic
72D120—21no—
73D120C2312yes—
74C5×#216—22no—
75C5×#215—22no—
76C5×#208D411yescharacteristic
77C5×Dic12C2311yescharacteristic
78C5×D24C2311yescharacteristic
79C5×#204—21no—
80C5×ΓL(1,𝔽25)D412yes—
81C5×D3×C8C2312yes—
82C3×Dic20C2311yescharacteristic
83C3×D40C2311yescharacteristic
84C3×#677—21no—
85#6658—22no—
86#6653—22no—
87C3⋊#672C2311yescharacteristic
88C3⋊#672C2311yescharacteristic
89C3×#672C2312yes—
90#5769—51no—
91#5766D511yescharacteristic, complemented
92C3×#510—51no—
93#5194—51no—
94C2×#828—51no—
95#4919—52no—
96#4918—52no—
97#4914—52no—
98D3×SD32—52no—
99#4908—51no—
100#4907—51no—
101C5×2−1+4—61no—
102#4149—61no—
103C5×#137—62no—
104C5×#137—61no—
105C5×#135—32no—
106C5×#135—31no—
107C2×C5×Q16—32no—
108C2×C5×Q16C2×D311yescharacteristic, complemented
109C5×#131—31no—
110#4054—62no—
111#4054—61no—
112#4050—32no—
113#4050C2×D311yescharacteristic
114C2×D40—31no—
115C2×D40—32no—
116#3961—31no—
117#3961C2×D312yescomplemented
118#3960—32no—
119#3960—32no—
120#3960—31no—
121#3960—32no—
122#3960C2×D312yescomplemented
123#3959—31no—
124#3958—31no—
125#3958—32no—
126#3944—32no—
127#3944C2×D311yescharacteristic, complemented
128C2×#672—31no—
129C2×#672—32no—
130#3416—151noSylow
131C22×D15—41no—
132C2×D3×D5—42no—
133C3×C5×Q8—22no—
134C3×C5×Q8—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5C2×D411yescharacteristic
137D60—22no—
138D60—41no—
139C5×#67—41no—
140C5×#67D812yes—
141C5×D12—21no—
142C5×D12—42no—
143C5×D12D811yescharacteristic
144C4×C5×D3—42no—
145C4×C5×D3—41no—
146C4×C5×D3—42no—
147C4×C5×D3C2×D412yes—
148C5×Dic6—21no—
149C5×Dic6—42no—
150C5×Dic6D811yescharacteristic
151C3×C22⋊D5—41no—
152C3×D20—21no—
153C3×C4×D5—41no—
154C3×Dic10—21no—
155#1203—42no—
156#1202—42no—
157#1200—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C5×C3⋊C8C2×D412yes—
161#1009—101no—
162#1007—21no—
163C3×#135—51no—
164C2×C3×Q16C2×D511yescharacteristic, complemented
165#949—101no—
166#942—21no—
167#919—52no—
168#919C2×D512yescomplemented
169#918—22no—
170D3×Q16C2×D512yescomplemented
171#914—102no—
172D3×D8—52no—
173#904C2×D511yescharacteristic, complemented
174C2×D24—51no—
175#901C2×D511yescharacteristic
176C3×Q32—52no—
177C3×SD32—52no—
178C3×M32—51no—
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—31no—
191C5×#41—62no—
192C5×#41—61no—
193C5×#41—122no—
194C5×#41—121no—
195C2×C5×Q8—21no—
196C2×C5×Q8—62no—
197C2×C5×Q8—121no—
198#713—121no—
199D4×D5—121no—
200D4×D5—122no—
201#709—21no—
202#709—62no—
203C2×D20—62no—
204C2×D20—61no—
205C5×Q16—21no—
206C5×Q16—31no—
207C5×Q16—62no—
208C5×Q16C22×D312yes—
209C5×SD16—62no—
210C5×SD16—61no—
211C5×D8—31no—
212C5×M16—31no—
213C5×M16—32no—
214C2×C5×C8—32no—
215C2×C5×C8C22×D311yescharacteristic
216Dic20C22×D311yescharacteristic
217D40—32no—
218D40—62no—
219D40—61no—
220D40C22×D311yescharacteristic
221#677—21no—
222#677—62no—
223#672—31no—
224#672—31no—
225#672C22×D312yes—
226#578—31no—
227#576—151no—
228#510—51no—
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×C5C2×D811yescharacteristic
238C2×D15—42no—
239C2×D15—161no—
240C2×C5×D3—41no—
241C2×C5×D3C2×D812yes—
242C2×C3×D5—41no—
243D3×D5—162no—
244C3×C4×C5—42no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247C3×Dic5—41no—
248C5×Dic3—41no—
249C5×Dic3C2×D812yes—
250C3×#41—101no—
251C2×C3×Q8—21no—
252#239—22no—
253#239—41no—
254#239—102no—
255D3×Q8—22no—
256D3×Q8—41no—
257D3×D4—102no—
258D3×D4—202no—
259#235—21no—
260#235—42no—
261#235—201no—
262#235C22⋊D511yescharacteristic
263C2×D12—101no—
264C2×D12—201no—
265C3×Q16—21no—
266C3×Q16—51no—
267C3×Q16C22×D512yes—
268C3×SD16—101no—
269C3×D8—51no—
270C2×C3×C8C22×D511yescharacteristic
271#216—22no—
272#215—22no—
273#215—102no—
274#213—102no—
275#208C22⋊D511yescharacteristic
276Dic12C22×D511yescharacteristic
277D24—52no—
278D24—101no—
279D24C22×D511yescharacteristic
280#204—21no—
281ΓL(1,𝔽25)C22⋊D512yes—
282D3×C8C22×D512yes—
283C3×C16—52no—
284C3⋊C16—51no—
285C3⋊C16—51no—
286C22×D5—122no—
287C22×D5—121no—
288C5×Q8—22no—
289C5×Q8—31no—
290C5×Q8—41no—
291C5×Q8—61no—
292C5×Q8—122no—
293C5×D4—32no—
294C5×D4—31no—
295C5×D4—61no—
296C5×D4—122no—
297C5×D4—121no—
298C2×C4×C5—32no—
299C2×C4×C5—41no—
300C2×C4×C5—122no—
301C2×C4×C5—122no—
302C2×C4×C5—121no—
303C2×C4×C5D3×D411yescharacteristic
304C22⋊D5—41no—
305C22⋊D5—122no—
306D20—21no—
307D20—62no—
308D20—122no—
309D20—121no—
310C4×D5—41no—
311C4×D5—122no—
312Dic10—21no—
313C5×C8—32no—
314C5×C8D3×D411yescharacteristic
315C5×C8C23×D311yescharacteristic
3162−1+4—61no—
317H(5,𝔽2)—301no—
318#137—62no—
319#137—61no—
320AGL(1,ℤ/8)—302no—
321AGL(1,ℤ/8)—301no—
322#135—32no—
323#135—31no—
324#135—51no—
325#135—152no—
326C2×Q16—32no—
327C2×Q16D3×D511yescharacteristic, complemented
328C2×D8—152no—
329C2×D8—151no—
330#131—31no—
331Q32—52no—
332Q32—151no—
333SD32—52no—
334SD32—152no—
335SD32—151no—
336SD32—151no—
337SD32—152no—
338SD32—152no—
339D16—152no—
340D16—151no—
341M32—51no—
342M32—152no—
343C2×C16—152no—
344C2×C16—151no—
345C2×C3×C5—21no—
346C2×C3×C5C22×D811yescharacteristic
347D15—82no—
348C3×D5—81no—
349C5×D3—22no—
350C5×D3—81no—
351C22×D3—201no—
352C22×D3—202no—
353C3×Q8—22no—
354C3×Q8—41no—
355C3×Q8—101no—
356C3×D4—101no—
357C3×D4—201no—
358C2×C3×C4—41no—
359C2×C3×C4—201no—
360C2×C3×C4C2×C22⋊D511yescharacteristic
361#67—41no—
362#67—202no—
363#67#68612yes—
364D12—21no—
365D12—42no—
366D12—102no—
367D12—202no—
368D12—201no—
369D12#68611yescharacteristic
370C4×D3—42no—
371C4×D3—41no—
372C4×D3—42no—
373C4×D3—202no—
374C4×D3C2×C22⋊D512yes—
375Dic6—21no—
376Dic6—42no—
377Dic6#68611yescharacteristic
378C3×C8C2×C22⋊D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8C2×C22⋊D512yes—
381C22×C5—32no—
382C22×C5—121no—
383C22×C5D3×D811yescharacteristic
384C2×D5—41no—
385C2×D5—122no—
386C2×D5—482no—
387C2×D5—481no—
388C4×C5—32no—
389C4×C5—42no—
390C4×C5—121no—
391C4×C5D3×D811yescharacteristic
392C4×C5C2×D3×D411yescharacteristic
393Dic5—41no—
394#41—31no—
395#41—62no—
396#41—61no—
397#41—101no—
398#41—122no—
399#41—121no—
400#41—302no—
401#41—601no—
402C2×Q8—21no—
403C2×Q8—62no—
404C2×Q8—121no—
405C2×D4—302no—
406C2×D4—301no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—21no—
410Q16—31no—
411Q16—51no—
412Q16—62no—
413Q16C2×D3×D512yes—
414SD16—62no—
415SD16—61no—
416SD16—101no—
417SD16—302no—
418D8—31no—
419D8—51no—
420D8—152no—
421D8—302no—
422D8—301no—
423M16—31no—
424M16—32no—
425C2×C8—32no—
426C2×C8C2×D3×D511yescharacteristic
427C16—52no—
428C16—151no—
429C16—151no—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—201no—
432C22×C3C2×#68611yescharacteristic
433C2×D3—41no—
434C2×D3—202no—
435C2×D3—802no—
436C2×D3—801no—
437C2×D3C2×#68612yes—
438C3×C4—42no—
439C3×C4—201no—
440C3×C4C2×#68611yescharacteristic
441C3×C4C22×C22⋊D511yescharacteristic
442Dic3—41no—
443Dic3C2×#68612yes—
444C2×C5—21no—
445C2×C5—62no—
446C2×C5—241no—
447C2×C5C2×D3×D811yescharacteristic
448D5—81no—
449D5—242no—
450C23—602no—
451C23—601no—
452Q8—22no—
453Q8—31no—
454Q8—41no—
455Q8—61no—
456Q8—101no—
457Q8—122no—
458D4—32no—
459D4—31no—
460D4—61no—
461D4—101no—
462D4—122no—
463D4—121no—
464D4—201no—
465D4—302no—
466D4—602no—
467D4—602no—
468D4—601no—
469C2×C4—32no—
470C2×C4—41no—
471C2×C4—122no—
472C2×C4—122no—
473C2×C4—121no—
474C2×C4—201no—
475C2×C4—602no—
476C2×C4D3×C22⋊D511yescharacteristic
477C8—32no—
478C8D3×C22⋊D511yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—401no—
482C2×C3C22×#68611yescharacteristic
483D3—22no—
484D3—81no—
485D3—402no—
486C5#8204011yescharacteristic, complemented, Sylow
487C22—32no—
488C22—121no—
489C22—201no—
490C22—602no—
491C22—2401no—
492C22—2402no—
493C22D3×#68611yescharacteristic
494C4—32no—
495C4—42no—
496C4—121no—
497C4—201no—
498C4D3×#68611yescharacteristic
499C4C2×D3×C22⋊D511yescharacteristic
500C3#1061574711yescharacteristic, complemented, Sylow
501C2—21no—
502C2—62no—
503C2—241no—
504C2—401no—
505C2—1202no—
506C2C2×D3×#68611yescharacteristic
subgroupG/H
centerC2C2×D3×#686
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC2×C3×C5C22×D8
hypercenterC2×Q16D3×D5
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C5×#5766C2semidirect
2. #11753973C2semidirect
3. C2×#91112C2semidirect
4. C3×#65468C2semidirect
5. #11748307C2semidirect
6. #11748306C2semidirect
7. #11748291C2semidirect
8. D3×#3960C2semidirect
9. #11747548C2semidirect
10. #11747538C2semidirect
11. #11747529C2semidirect
15. C2×C3×C5×Q16C22semidirect
18. C5×#919C22semidirect
20. C5×D3×Q16C22semidirect
21. C5×#904C22semidirect
28. #91112C22semidirect
29. #91112C22semidirect
30. C2×C3⋊#672C22semidirect
31. C3×#3961C22semidirect
32. C3×#3960C22semidirect
33. C3×#3944C22semidirect
34. #90946C22semidirect
35. #90945C22semidirect
36. #90941C22semidirect
37. #90940C22semidirect
38. #90939C22semidirect
39. #90937C22semidirect
40. #90935C22semidirect
41. D3×#672C22semidirect
50. #65468D3semidirect
91. #5766D5semidirect
108. C2×C5×Q16C2×D3semidirect
117. #3961C2×D3semidirect
122. #3960C2×D3semidirect
127. #3944C2×D3semidirect
164. C2×C3×Q16C2×D5semidirect
168. #919C2×D5semidirect
170. D3×Q16C2×D5semidirect
173. #904C2×D5semidirect
327. C2×Q16D3×D5semidirect
430. C3×C5#3416semidirect
486. C5#82040semidirect
500. C3#10615747semidirect

Maximal subgroups

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

subgroupindex
C5×#57662
#117539732
C2×#911122
C3×#654682
#117483072
#117483062
#117482912
D3×#39602
#117475482
#117475382
#117475292
#106157473
#820405