Finite Group Databasebeta

← #14478572

Subgroups — #14478572

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×#66100C211yesmaximal, characteristic, complemented
2#11753963C211yesmaximal, characteristic, complemented
3C2×#91112C211yesmaximal, characteristic, complemented
4C5×#5179C211yesmaximal, characteristic, complemented
5#11748303C212yesmaximal, complemented
6#11748302C212yesmaximal, complemented
7#11748289C212yesmaximal, complemented
8D5×#828C212yesmaximal, complemented
9#11747544C211yesmaximal, characteristic, complemented
10#11747538C211yesmaximal, characteristic, complemented
11#11747525C211yesmaximal, characteristic, complemented
12#10613771—31nomaximal, Hall
13C3×#4147—21no—
14#92019—21no—
15C2×C3×C5×Q16C2211yescharacteristic, complemented
16C2×D120C2211yescharacteristic
17C5×#904C2211yescharacteristic
18C3×#4088—21no—
19C3×#4065C2212yescomplemented
20C3×#4064—22no—
21C3×D5×Q16C2212yescomplemented
22C3×#4050C2211yescharacteristic, complemented
23C3×#4047C2211yescharacteristic
24#91305—21no—
25#91271C2212yes—
26#91249—22no—
27D5×D24C2212yes—
28#91112C2212yescomplemented
29#91112C2212yescomplemented
30C2×C3⋊#672C2211yescharacteristic, complemented
31C5×#829C2212yescomplemented
32C5×#828C2212yescomplemented
33C5×#812C2211yescharacteristic, complemented
34#90946C2211yescharacteristic, complemented
35#90943C2212yescomplemented
36#90941C2211yescharacteristic, complemented
37#90940C2211yescharacteristic, complemented
38#90938C2212yescomplemented
39#90937C2211yescharacteristic, complemented
40#90934C2212yescomplemented
41D5×C3⋊C16C2212yescomplemented
42#84016—51nomaximal, Hall
43#66103—31no—
44#66100D311yescharacteristic, complemented
45C5×#510—31no—
46#65483—31no—
47C2×#3960—31no—
48#65208—32no—
49#65207—32no—
50#65203—32no—
51D5×SD32—32no—
52#65197—31no—
53#65196—31no—
54C2×C3×C5×Q8—21no—
55C2×D60—21no—
56C5×#235—21no—
57C3×#713—22no—
58C3×#713—41no—
59C3×Q8×D5—22no—
60C3×Q8×D5—41no—
61C3×#709—21no—
62C3×#709—42no—
63C3×#709D411yescharacteristic
64#6790—42no—
65D3×D20—41no—
66D5×D12—22no—
67#6773—22no—
68#6769—41no—
69C3×C5×Q16—21no—
70C3×C5×Q16C2312yes—
71C2×C3×C5×C8C2311yescharacteristic
72D120—21no—
73D120C2312yes—
74C5×Dic12C2311yescharacteristic
75C5×D24C2311yescharacteristic
76C5×#204—21no—
77C3×#689—22no—
78C3×#688—22no—
79C3×#681D411yescharacteristic
80C3×Dic20C2311yescharacteristic
81C3×D40C2311yescharacteristic
82C3×#677—21no—
83C3×#676D412yes—
84C3×C8×D5C2312yes—
85#6660—22no—
86#6654—22no—
87C3⋊#672C2311yescharacteristic
88C3⋊#672C2311yescharacteristic
89C5×C3⋊C16C2312yes—
90C3×#578—51no—
91#5752—51no—
92#5194—51no—
93#5194—52no—
94#5193—52no—
95#5193—51no—
96#5179—52no—
97#5179D511yescharacteristic, complemented
98C2×#828—51no—
99C2×#828—52no—
100#5140—51no—
101#4149—61no—
102#4147—21no—
103C5×#135—31no—
104C2×C5×Q16C2×D311yescharacteristic, complemented
105#4095—61no—
106#4088—21no—
107#4065—32no—
108#4065C2×D312yescomplemented
109#4064—22no—
110D5×Q16C2×D312yescomplemented
111#4060—62no—
112D5×D8—32no—
113#4050C2×D311yescharacteristic, complemented
114C2×D40—31no—
115#4047C2×D311yescharacteristic
116C5×Q32—32no—
117C5×SD32—32no—
118C5×M32—31no—
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—
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×D12—21no—
141C4×C5×D3—41no—
142C5×Dic6—21no—
143C3×C22⋊D5—41no—
144C3×C22⋊D5D812yes—
145C3×D20—21no—
146C3×D20—42no—
147C3×D20D811yescharacteristic
148C3×C4×D5—42no—
149C3×C4×D5—41no—
150C3×C4×D5—42no—
151C3×C4×D5C2×D412yes—
152C3×Dic10—21no—
153C3×Dic10—42no—
154C3×Dic10D811yescharacteristic
155#1203—42no—
156#1202—42no—
157#1200—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3×#168C2×D412yes—
161C3×2−1+4—101no—
162#1009—101no—
163C3×#137—102no—
164C3×#137—101no—
165C3×#135—52no—
166C3×#135—51no—
167C2×C3×Q16—52no—
168C2×C3×Q16C2×D511yescharacteristic, complemented
169C3×#131—51no—
170#908—102no—
171#908—101no—
172#904—52no—
173#904C2×D511yescharacteristic
174C2×D24—51no—
175C2×D24—52no—
176#829—51no—
177#829C2×D512yescomplemented
178#828—52no—
179#828—52no—
180#828—51no—
181#828—52no—
182#828C2×D512yescomplemented
183#827—51no—
184#826—51no—
185#826—52no—
186#812—52no—
187#812C2×D511yescharacteristic, complemented
188C2×C3⋊C16—51no—
189C2×C3⋊C16—52no—
190C5×#41—61no—
191C2×C5×Q8—21no—
192#713—22no—
193#713—41no—
194#713—62no—
195Q8×D5—22no—
196Q8×D5—41no—
197D4×D5—62no—
198D4×D5—122no—
199#709—21no—
200#709—42no—
201#709—121no—
202#709#6711yescharacteristic
203C2×D20—61no—
204C2×D20—121no—
205C5×Q16—21no—
206C5×Q16—31no—
207C5×Q16C22×D312yes—
208C5×SD16—61no—
209C5×D8—31no—
210C2×C5×C8C22×D311yescharacteristic
211#689—22no—
212#688—22no—
213#688—62no—
214#686—62no—
215#681#6711yescharacteristic
216Dic20C22×D311yescharacteristic
217D40—32no—
218D40—61no—
219D40C22×D311yescharacteristic
220#677—21no—
221#676#6712yes—
222C8×D5C22×D312yes—
223C5×C16—32no—
224#672—31no—
225#672—31no—
226#578—51no—
227#576—151no—
228#510—31no—
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×C3×D5—41no—
242C2×C3×D5C2×D812yes—
243D3×D5—162no—
244C3×C4×C5—42no—
245C3×C4×C5C2×D811yescharacteristic
246C3×C4×C5C22×D411yescharacteristic
247C3×Dic5—41no—
248C3×Dic5C2×D812yes—
249C5×Dic3—41no—
250C3×#41—51no—
251C3×#41—102no—
252C3×#41—101no—
253C3×#41—202no—
254C3×#41—201no—
255C2×C3×Q8—21no—
256C2×C3×Q8—102no—
257C2×C3×Q8—201no—
258#239—201no—
259D3×D4—201no—
260D3×D4—202no—
261#235—21no—
262#235—102no—
263C2×D12—102no—
264C2×D12—101no—
265C3×Q16—21no—
266C3×Q16—51no—
267C3×Q16—102no—
268C3×Q16C22×D512yes—
269C3×SD16—102no—
270C3×SD16—101no—
271C3×D8—51no—
272C3×M16—51no—
273C3×M16—52no—
274C2×C3×C8—52no—
275C2×C3×C8C22×D511yescharacteristic
276Dic12C22×D511yescharacteristic
277D24—52no—
278D24—102no—
279D24—101no—
280D24C22×D511yescharacteristic
281#204—21no—
282#204—102no—
283C3⋊C16—51no—
284C3⋊C16—51no—
285C3⋊C16C22×D512yes—
286C22×D5—121no—
287C22×D5—122no—
288C5×Q8—22no—
289C5×Q8—41no—
290C5×Q8—61no—
291C5×D4—61no—
292C5×D4—121no—
293C2×C4×C5—41no—
294C2×C4×C5—121no—
295C2×C4×C5C2×#6711yescharacteristic
296C22⋊D5—41no—
297C22⋊D5—122no—
298C22⋊D5#21312yes—
299D20—21no—
300D20—42no—
301D20—62no—
302D20—122no—
303D20—121no—
304D20#21311yescharacteristic
305C4×D5—42no—
306C4×D5—41no—
307C4×D5—42no—
308C4×D5—122no—
309C4×D5C2×#6712yes—
310Dic10—21no—
311Dic10—42no—
312Dic10#21311yescharacteristic
313C5×C8C2×#6711yescharacteristic
314C5×C8C23×D311yescharacteristic
315#168C2×#6712yes—
3162−1+4—101no—
317H(5,𝔽2)—301no—
318#137—102no—
319#137—101no—
320AGL(1,ℤ/8)—302no—
321AGL(1,ℤ/8)—301no—
322#135—31no—
323#135—52no—
324#135—51no—
325#135—152no—
326C2×Q16—52no—
327C2×Q16D3×D511yescharacteristic, complemented
328C2×D8—152no—
329C2×D8—151no—
330#131—51no—
331Q32—32no—
332Q32—151no—
333SD32—32no—
334SD32—152no—
335SD32—151no—
336SD32—151no—
337SD32—152no—
338SD32—152no—
339D16—152no—
340D16—151no—
341M32—31no—
342M32—152no—
343C2×C16—152no—
344C2×C16—151no—
345C2×C3×C5—21no—
346C2×C3×C5C22×D811yescharacteristic
347D15—82no—
348C3×D5—22no—
349C3×D5—81no—
350C5×D3—81no—
351C22×D3—202no—
352C22×D3—201no—
353C3×Q8—22no—
354C3×Q8—41no—
355C3×Q8—51no—
356C3×Q8—101no—
357C3×Q8—202no—
358C3×D4—52no—
359C3×D4—51no—
360C3×D4—101no—
361C3×D4—202no—
362C3×D4—201no—
363C2×C3×C4—41no—
364C2×C3×C4—52no—
365C2×C3×C4—202no—
366C2×C3×C4—202no—
367C2×C3×C4—201no—
368C2×C3×C4D4×D511yescharacteristic
369#67—41no—
370#67—202no—
371D12—21no—
372D12—102no—
373D12—202no—
374D12—201no—
375C4×D3—41no—
376C4×D3—202no—
377Dic6—21no—
378C3×C8—52no—
379C3×C8D4×D511yescharacteristic
380C3×C8C23×D511yescharacteristic
381C22×C5—121no—
382C22×C5C2×#21311yescharacteristic
383C2×D5—41no—
384C2×D5—122no—
385C2×D5—482no—
386C2×D5—481no—
387C2×D5C2×#21312yes—
388C4×C5—42no—
389C4×C5—121no—
390C4×C5C2×#21311yescharacteristic
391C4×C5C22×#6711yescharacteristic
392Dic5—41no—
393Dic5C2×#21312yes—
394#41—51no—
395#41—61no—
396#41—102no—
397#41—101no—
398#41—202no—
399#41—201no—
400#41—302no—
401#41—601no—
402C2×Q8—21no—
403C2×Q8—102no—
404C2×Q8—201no—
405C2×D4—302no—
406C2×D4—301no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—21no—
410Q16—31no—
411Q16—51no—
412Q16—102no—
413Q16C2×D3×D512yes—
414SD16—61no—
415SD16—102no—
416SD16—101no—
417SD16—302no—
418D8—31no—
419D8—51no—
420D8—152no—
421D8—302no—
422D8—301no—
423M16—51no—
424M16—52no—
425C2×C8—52no—
426C2×C8C2×D3×D511yescharacteristic
427C16—32no—
428C16—151no—
429C16—151no—
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—52no—
432C22×C3—201no—
433C22×C3D5×D811yescharacteristic
434C2×D3—41no—
435C2×D3—202no—
436C2×D3—802no—
437C2×D3—801no—
438C3×C4—42no—
439C3×C4—52no—
440C3×C4—201no—
441C3×C4D5×D811yescharacteristic
442C3×C4C2×D4×D511yescharacteristic
443Dic3—41no—
444C2×C5—21no—
445C2×C5—241no—
446C2×C5C22×#21311yescharacteristic
447D5—22no—
448D5—81no—
449D5—242no—
450C23—602no—
451C23—601no—
452Q8—22no—
453Q8—41no—
454Q8—51no—
455Q8—61no—
456Q8—101no—
457Q8—202no—
458D4—52no—
459D4—51no—
460D4—61no—
461D4—101no—
462D4—121no—
463D4—202no—
464D4—201no—
465D4—302no—
466D4—602no—
467D4—602no—
468D4—601no—
469C2×C4—41no—
470C2×C4—52no—
471C2×C4—121no—
472C2×C4—202no—
473C2×C4—202no—
474C2×C4—201no—
475C2×C4—602no—
476C2×C4D5×#6711yescharacteristic
477C8—52no—
478C8D5×#6711yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—102no—
482C2×C3—401no—
483C2×C3C2×D5×D811yescharacteristic
484D3—81no—
485D3—402no—
486C5#8401611yescharacteristic, complemented, Sylow
487C22—52no—
488C22—121no—
489C22—201no—
490C22—602no—
491C22—2401no—
492C22—2402no—
493C22D5×#21311yescharacteristic
494C4—42no—
495C4—52no—
496C4—121no—
497C4—201no—
498C4D5×#21311yescharacteristic
499C4C2×D5×#6711yescharacteristic
500C3#1061377111yescharacteristic, complemented, Sylow
501C2—21no—
502C2—102no—
503C2—241no—
504C2—401no—
505C2—1202no—
506C2C2×D5×#21311yescharacteristic
subgroupG/H
centerC2C2×D5×#213
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. C3×#66100C2semidirect
2. #11753963C2semidirect
3. C2×#91112C2semidirect
4. C5×#5179C2semidirect
5. #11748303C2semidirect
6. #11748302C2semidirect
7. #11748289C2semidirect
8. D5×#828C2semidirect
9. #11747544C2semidirect
10. #11747538C2semidirect
11. #11747525C2semidirect
15. C2×C3×C5×Q16C22semidirect
19. C3×#4065C22semidirect
21. C3×D5×Q16C22semidirect
22. C3×#4050C22semidirect
28. #91112C22semidirect
29. #91112C22semidirect
30. C2×C3⋊#672C22semidirect
31. C5×#829C22semidirect
32. C5×#828C22semidirect
33. C5×#812C22semidirect
34. #90946C22semidirect
35. #90943C22semidirect
36. #90941C22semidirect
37. #90940C22semidirect
38. #90938C22semidirect
39. #90937C22semidirect
40. #90934C22semidirect
41. D5×C3⋊C16C22semidirect
44. #66100D3semidirect
97. #5179D5semidirect
104. C2×C5×Q16C2×D3semidirect
108. #4065C2×D3semidirect
110. D5×Q16C2×D3semidirect
113. #4050C2×D3semidirect
168. C2×C3×Q16C2×D5semidirect
177. #829C2×D5semidirect
182. #828C2×D5semidirect
187. #812C2×D5semidirect
327. C2×Q16D3×D5semidirect
430. C3×C5#3416semidirect
486. C5#84016semidirect
500. C3#10613771semidirect

Maximal subgroups

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

subgroupindex
C3×#661002
#117539632
C2×#911122
C5×#51792
#117483032
#117483022
#117482892
D5×#8282
#117475442
#117475382
#117475252
#106137713
#840165