Finite Group Databasebeta

← #14478596

Subgroups — #14478596

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#11753988C211yesmaximal, characteristic, complemented
3#11751296C211yesmaximal, characteristic, complemented
4C5×#5194C211yesmaximal, characteristic, complemented
5#11748301C212yesmaximal, complemented
6#11748295C212yesmaximal, complemented
7#11748276C212yesmaximal, complemented
8D5×#827C212yesmaximal, complemented
9C2×#90942C211yesmaximal, characteristic, complemented
10#11747539C211yesmaximal, characteristic, complemented
11#11747524C211yesmaximal, characteristic, complemented
12#10613763—31nomaximal, Hall
13C3×#4149—21no—
14#92001—21no—
15C3×C5×#135C2211yescharacteristic
16C2×Dic60C2211yescharacteristic, complemented
17C5×#904C2211yescharacteristic, complemented
18C3×#4095—21no—
19C3×#4065C2212yes—
20C3×#4060—22no—
21C3×D5×D8C2212yes—
22C2×C3×D40C2211yescharacteristic
23C3×#4047C2211yescharacteristic
24#91322—21no—
25#91270C2212yescomplemented
26#91260—22no—
27D5×Dic12C2212yescomplemented
28#91113C2212yescomplemented
29#91111C2212yescomplemented
30#91096C2211yescharacteristic, complemented
31C5×#829C2211yescharacteristic, complemented
32C5×#828C2211yescharacteristic, complemented
33C5×#827C2211yescharacteristic, complemented
34C5×#826C2211yescharacteristic, complemented
35C2×C5×C3⋊C16C2211yescharacteristic, complemented
36#90942C2212yescomplemented
37#90942C2212yescomplemented
38#90940C2212yescomplemented
39#90937C2212yescomplemented
40#90934C2212yescomplemented
41D5×C3⋊C16C2212yescomplemented
42#84008—51nomaximal, Hall
43#66105—31no—
44#66103D311yescharacteristic, complemented
45C5×#508—31no—
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—
55C2×Dic30—21no—
56C5×#235—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#6780—42no—
65#6772—22no—
66D3×Dic10—41no—
67#6765—41no—
68D5×Dic6—22no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8C2311yescharacteristic
72C2×C3×C5×C8C2311yescharacteristic
73Dic60—21no—
74Dic60C2312yes—
75C5×Dic12C2311yescharacteristic
76C5×D24C2311yescharacteristic
77C5×#204—21no—
78C3×#688—22no—
79C3×#686—22no—
80C3×#681D411yescharacteristic
81C3×D40—21no—
82C3×D40C2312yes—
83C3×#676D412yes—
84C3×C8×D5C2312yes—
85#6663—22no—
86#6659—22no—
87C3⋊#672C2312yes—
88C5×C3⋊C16C2311yescharacteristic
89C5×C3⋊C16C2311yescharacteristic
90C3×#576—51no—
91#5753—51no—
92#5195—51no—
93#5195—52no—
94#5194—52no—
95#5194D511yescharacteristic, complemented
96C2×#827—52no—
97C2×#827—51no—
98#5147—51no—
99#5147—52no—
100#5140—51no—
101#4150—61no—
102#4149—21no—
103C5×#135—31no—
104C5×#135C2×D311yescharacteristic
105#4097—61no—
106#4095—21no—
107#4065C2×D312yes—
108D5×Q16—32no—
109#4061—62no—
110#4060—22no—
111#4058—32no—
112D5×D8C2×D312yes—
113C2×Dic20—31no—
114C2×D40C2×D311yescharacteristic
115#4047C2×D311yescharacteristic
116C5×Q32—31no—
117C5×SD32—31no—
118C5×SD32—31no—
119C5×D16—31no—
120C2×C5×C16—31no—
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×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
138C2×Dic15—41no—
139Dic30—22no—
140Dic30—41no—
141C5×#67—41no—
142C5×D12—21no—
143C4×C5×D3—41no—
144C5×Dic6—21no—
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#1201—42no—
156D3×Dic5—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—51no—
173C2×Dic12—52no—
174#904—52no—
175#904C2×D511yescharacteristic, complemented
176#829—52no—
177#829C2×D511yescharacteristic, complemented
178#828C2×D511yescharacteristic, complemented
179#827—52no—
180#827—52no—
181#827—52no—
182#827—52no—
183#827C2×D511yescharacteristic, complemented
184#826—52no—
185#826C2×D511yescharacteristic, complemented
186#812—51no—
187#812—52no—
188C2×C3⋊C16—52no—
189C2×C3⋊C16C2×D511yescharacteristic, complemented
190C5×#41—21no—
191C5×#41—61no—
192#713—22no—
193Q8×D5—62no—
194#711—62no—
195#711—122no—
196D4×D5—22no—
197D4×D5—42no—
198#709—41no—
199#709—121no—
200#709#6711yescharacteristic
201C2×D20—21no—
202C2×D20—41no—
203C2×Dic10—61no—
204C2×Dic10—121no—
205C5×Q16—31no—
206C5×Q16C22×D311yescharacteristic
207C5×SD16—21no—
208C5×SD16—61no—
209C5×D8—31no—
210C5×D8C22×D311yescharacteristic
211C2×C5×C8C22×D311yescharacteristic
212#689—62no—
213#688—22no—
214#687—62no—
215#686—22no—
216#681#6711yescharacteristic
217Dic20—32no—
218Dic20—61no—
219D40—21no—
220D40C22×D312yes—
221#676#6712yes—
222C8×D5C22×D312yes—
223C5×C16—31no—
224C5×C16—31no—
225#672—32no—
226#578—151no—
227#576—51no—
228#510—152no—
229#510—151no—
230#509—152no—
231#509—151no—
232#508—31no—
233#508—152no—
234C2×SD32—151no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×C5×D3—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—42no—
248C3×Dic5C2×D812yes—
249C5×Dic3—41no—
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—21no—
262#235—102no—
263C2×Dic6—102no—
264C2×Dic6—101no—
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—52no—
277Dic12—102no—
278Dic12—101no—
279Dic12C22×D511yescharacteristic
280D24C22×D511yescharacteristic
281#204—21no—
282#204—102no—
283C3⋊C16—52no—
284C3⋊C16C22×D511yescharacteristic
285C3⋊C16C22×D511yescharacteristic
286C22×D5—41no—
287C22×D5—42no—
288C5×Q8—21no—
289C5×Q8—61no—
290C5×D4—21no—
291C5×D4—41no—
292C5×D4—61no—
293C5×D4—121no—
294C2×C4×C5—41no—
295C2×C4×C5—121no—
296C2×C4×C5C2×#6711yescharacteristic
297C22⋊D5—42no—
298C22⋊D5—122no—
299C22⋊D5#21312yes—
300C2×Dic5—121no—
301C2×Dic5—122no—
302D20—22no—
303D20—42no—
304D20—41no—
305D20#21311yescharacteristic
306C4×D5—42no—
307C4×D5—122no—
308C4×D5C2×#6712yes—
309Dic10—62no—
310Dic10—121no—
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—31no—
323#135—52no—
324#135—152no—
325#135D3×D511yescharacteristic
326C2×Q16—152no—
327C2×Q16—151no—
328C2×D8—52no—
329C2×D8—51no—
330#131—51no—
331Q32—31no—
332Q32—152no—
333SD32—31no—
334SD32—31no—
335SD32—152no—
336SD32—152no—
337SD32—152no—
338SD32—152no—
339D16—31no—
340D16—152no—
341M32—152no—
342M32—151no—
343C2×C16—31no—
344C2×C16—152no—
345C2×C3×C5—21no—
346C2×C3×C5—81no—
347C2×C3×C5C22×D811yescharacteristic
348C3×D5—22no—
349C3×D5—82no—
350C5×D3—81no—
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—41no—
368#67—202no—
369C2×Dic3—202no—
370C2×Dic3—201no—
371D12—21no—
372C4×D3—41no—
373C4×D3—202no—
374Dic6—21no—
375Dic6—102no—
376Dic6—202no—
377Dic6—201no—
378C3×C8—52no—
379C3×C8D4×D511yescharacteristic
380C3×C8C23×D511yescharacteristic
381C22×C5—41no—
382C22×C5—121no—
383C22×C5C2×#21311yescharacteristic
384C2×D5—42no—
385C2×D5—162no—
386C2×D5—161no—
387C2×D5C2×#21312yes—
388C4×C5—41no—
389C4×C5—121no—
390C4×C5C2×#21311yescharacteristic
391C4×C5C22×#6711yescharacteristic
392Dic5—122no—
393Dic5C2×#21312yes—
394#41—21no—
395#41—51no—
396#41—61no—
397#41—102no—
398#41—201no—
399#41—302no—
400#41—601no—
401#41—602no—
402C2×Q8—302no—
403C2×Q8—301no—
404C2×Q8—601no—
405C2×D4—102no—
406C2×D4—101no—
407C2×D4—201no—
408C2×D4—202no—
409Q16—31no—
410Q16—152no—
411Q16—302no—
412Q16—301no—
413Q16C2×D3×D511yescharacteristic
414SD16—21no—
415SD16—61no—
416SD16—102no—
417SD16—302no—
418D8—31no—
419D8—52no—
420D8—102no—
421D8—101no—
422D8C2×D3×D511yescharacteristic
423M16—51no—
424M16—52no—
425C2×C8—52no—
426C2×C8C2×D3×D511yescharacteristic
427C16—31no—
428C16—31no—
429C16—152no—
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—41no—
438C3×C4—41no—
439C3×C4—52no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—41no—
443Dic3—202no—
444C2×C5—21no—
445C2×C5—81no—
446C2×C5—241no—
447C2×C5C22×#21311yescharacteristic
448D5—22no—
449D5—82no—
450C23—202no—
451C23—201no—
452Q8—21no—
453Q8—51no—
454Q8—61no—
455Q8—302no—
456Q8—602no—
457Q8—601no—
458D4—21no—
459D4—41no—
460D4—52no—
461D4—51no—
462D4—61no—
463D4—102no—
464D4—121no—
465D4—202no—
466D4—202no—
467D4—201no—
468D4—602no—
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—81no—
486C5#8400811yescharacteristic, complemented, Sylow
487C22—41no—
488C22—52no—
489C22—121no—
490C22—202no—
491C22—801no—
492C22—802no—
493C22D5×#21311yescharacteristic
494C4—41no—
495C4—52no—
496C4—121no—
497C4—602no—
498C4D5×#21311yescharacteristic
499C4C2×D5×#6711yescharacteristic
500C3#1061376311yescharacteristic, complemented, Sylow
501C2—21no—
502C2—81no—
503C2—102no—
504C2—241no—
505C2—402no—
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. #11753988C2semidirect
3. #11751296C2semidirect
4. C5×#5194C2semidirect
5. #11748301C2semidirect
6. #11748295C2semidirect
7. #11748276C2semidirect
8. D5×#827C2semidirect
9. C2×#90942C2semidirect
10. #11747539C2semidirect
11. #11747524C2semidirect
16. C2×Dic60C22semidirect
17. C5×#904C22semidirect
25. #91270C22semidirect
27. D5×Dic12C22semidirect
28. #91113C22semidirect
29. #91111C22semidirect
30. #91096C22semidirect
31. C5×#829C22semidirect
32. C5×#828C22semidirect
33. C5×#827C22semidirect
34. C5×#826C22semidirect
35. C2×C5×C3⋊C16C22semidirect
36. #90942C22semidirect
37. #90942C22semidirect
38. #90940C22semidirect
39. #90937C22semidirect
40. #90934C22semidirect
41. D5×C3⋊C16C22semidirect
44. #66103D3semidirect
95. #5194D5semidirect
175. #904C2×D5semidirect
177. #829C2×D5semidirect
178. #828C2×D5semidirect
183. #827C2×D5semidirect
185. #826C2×D5semidirect
189. C2×C3⋊C16C2×D5semidirect
430. C3×C5#3416semidirect
486. C5#84008semidirect
500. C3#10613763semidirect

Maximal subgroups

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

subgroupindex
C3×#661032
#117539882
#117512962
C5×#51942
#117483012
#117482952
#117482762
D5×#8272
C2×#909422
#117475392
#117475242
#106137633
#840085