Finite Group Databasebeta

← #14478580

Subgroups — #14478580

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#11754008C211yesmaximal, characteristic, complemented
2#11753983C211yesmaximal, characteristic, complemented
3#11751002C211yesmaximal, characteristic, complemented
4C2×C5×#800C211yesmaximal, characteristic, complemented
5C3×#65193C211yesmaximal, characteristic, complemented
6#11747550C211yesmaximal, characteristic, complemented
7#11747540C211yesmaximal, characteristic, complemented
8#11746843C212yesmaximal, complemented
9#11746840C212yesmaximal, complemented
10#11746824C212yesmaximal, complemented
11#11746823C212yesmaximal, complemented
12#10613755—31nomaximal, Hall
13#92018—21no—
14#92000—21no—
15#91790C2211yescharacteristic
16C2×C5×Dic12C2211yescharacteristic, complemented
17C2×C5×D24C2211yescharacteristic
18C3×#4050C2211yescharacteristic
19C3×#4050C2211yescharacteristic, complemented
20#91307—21no—
21#91299—21no—
22#91279C2212yes—
23#91278—22no—
24#91277C2212yescomplemented
25#91264C2212yescomplemented
26#91257—22no—
27#91256C2212yes—
28C2×C3×C5×C16C2211yescharacteristic, complemented
29#91096C2211yescharacteristic, complemented
30#91082C2212yescomplemented
31C16×D15C2212yescomplemented
32C5×#800C2212yescomplemented
33C5×#800C2212yescomplemented
34C3×Dic40C2211yescharacteristic, complemented
35C3×#3932C2211yescharacteristic, complemented
36C3×#3932C2211yescharacteristic, complemented
37C3×D80C2211yescharacteristic, complemented
38#90946C2212yescomplemented
39#90941C2212yescomplemented
40#90940C2212yescomplemented
41#90937C2212yescomplemented
42#82032—51nomaximal, Hall
43#66100—31no—
44#66091—31no—
45C2×C5×SD32—31no—
46#65468—31no—
47#65436—31no—
48#65205—32no—
49#65204—32no—
50#65203—32no—
51D5×SD32—32no—
52#65193D311yescharacteristic, complemented
53#65190—31no—
54#6817D411yescharacteristic
55C2×C5×D12—21no—
56C2×C5×Dic6—21no—
57C3×#709—21no—
58C3×#709—21no—
59D3×C22⋊D5—42no—
60#6779—42no—
61#6777—22no—
62D5×D12—41no—
63#6773—41no—
64#6772—41no—
65D15⋊Q8—22no—
66#6768—22no—
67#6766—22no—
68D5×Dic6—41no—
69C2×C3×C5×C8C2311yescharacteristic
70#6710D411yescharacteristic
71#6705D412yes—
72C8×D15C2312yes—
73C5×Dic12—21no—
74C5×Dic12C2312yes—
75C5×D24—21no—
76C5×D24C2312yes—
77C3×Dic20C2311yescharacteristic
78C3×Dic20C2311yescharacteristic
79C3×D40C2311yescharacteristic
80C3×D40C2311yescharacteristic
81C3×#677—21no—
82C3×#677—21no—
83#6661—22no—
84#6656—22no—
85#6655—22no—
86#6652—22no—
87C3×C5×C16C2311yescharacteristic
88C3×C5×C16C2311yescharacteristic
89C3⋊#672C2312yes—
90#5771—51no—
91#5769—51no—
92C3×#508—51no—
93#5195—51no—
94#5193—51no—
95#4918—52no—
96#4916—52no—
97D3×SD32—52no—
98#4911—52no—
99C2×#800D511yescharacteristic, complemented
100#4901—51no—
101#4147—61no—
102#4144—61no—
103C2×C5×Q16—31no—
104C2×C5×D8—31no—
105#4088—61no—
106#4078—61no—
107#4065—32no—
108#4064—62no—
109D5×Q16—32no—
110#4058—32no—
111#4057—62no—
112D5×D8—32no—
113#4050C2×D311yescharacteristic
114#4050C2×D311yescharacteristic, complemented
115#4047—31no—
116C5×SD32—32no—
117C5×SD32—32no—
118C2×C5×C16C2×D311yescharacteristic, complemented
119#3961—32no—
120#3960—32no—
121#3959—32no—
122#3958—32no—
123#3944—31no—
124Dic40C2×D311yescharacteristic, complemented
125#3932C2×D311yescharacteristic, complemented
126#3932C2×D311yescharacteristic, complemented
127D80C2×D311yescharacteristic, complemented
128#3930—32no—
129D5×C16—32no—
130#3416—151noSylow
131C22×C5×D3—41no—
132C2×D3×D5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134#1220D812yes—
135D60D811yescharacteristic
136C4×D15C2×D412yes—
137Dic30D811yescharacteristic
138C2×C5×Dic3—41no—
139C5×D12—22no—
140C5×D12—41no—
141C5×Dic6—22no—
142C5×Dic6—41no—
143C3×C22⋊D5—41no—
144C3×C22⋊D5—41no—
145C3×D20—21no—
146C3×D20—21no—
147C3×C4×D5—41no—
148C3×C4×D5—41no—
149C3×Dic10—21no—
150C3×Dic10—21no—
151#1204—42no—
152#1203—42no—
153#1202—42no—
154#1201—42no—
155#1200—42no—
156D3×Dic5—42no—
157D5×Dic3—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1010—101no—
162#1009—101no—
163C3×#135—51no—
164C3×#135—51no—
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×Dic12C2×D511yescharacteristic, complemented
174C2×D24C2×D511yescharacteristic
175#901—51no—
176C3×Q32—51no—
177C3×SD32—51no—
178C3×SD32—51no—
179C3×D16—51no—
180C2×C3×C16C2×D511yescharacteristic, complemented
181#829—52no—
182#828—52no—
183#827—52no—
184#826—52no—
185#812—51no—
186#800C2×D512yescomplemented
187#800C2×D512yescomplemented
188#798—52no—
189D3×C16—52no—
190C2×C5×Q8—61no—
191C2×C5×D4—61no—
192C2×C22⋊D5—122no—
193#713—62no—
194#713—121no—
195Q8×D5—62no—
196Q8×D5—121no—
197#711—62no—
198#711—121no—
199D4×D5—62no—
200D4×D5—121no—
201#709—21no—
202#709—21no—
203#709—31no—
204#709—122no—
205C5×Q16—32no—
206C5×Q16—61no—
207C5×D8—32no—
208C5×D8—61no—
209C2×C5×C8C22×D311yescharacteristic
210#689—62no—
211#688—62no—
212#687—62no—
213#686—62no—
214#681—31no—
215Dic20C22×D311yescharacteristic
216Dic20C22×D311yescharacteristic
217D40C22×D311yescharacteristic
218D40C22×D311yescharacteristic
219#677—21no—
220#677—21no—
221#676—32no—
222C8×D5—32no—
223C5×C16C22×D311yescharacteristic
224C5×C16C22×D311yescharacteristic
225#672—32no—
226#578—151no—
227#576—151no—
228#510—152no—
229#510—151no—
230#509—152no—
231#509—151no—
232#508—51no—
233#508—152no—
234C2×SD32—31no—
235C2×SD32—152no—
236#504—151no—
237C22×C3×C5C2×D811yescharacteristic
238C2×D15C2×D812yes—
239C2×C5×D3—42no—
240C2×C5×D3—161no—
241C2×C3×D5—41no—
242C2×C3×D5—41no—
243D3×D5—162no—
244C3×C4×C5C2×D811yescharacteristic
245C3×C4×C5C22×D411yescharacteristic
246Dic15C2×D812yes—
247C3×Dic5—41no—
248C3×Dic5—41no—
249C5×Dic3—42no—
250C3×#41—101no—
251C3×#41—101no—
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—21no—
262C2×D12—201no—
263C2×Dic6—21no—
264C2×Dic6—201no—
265C3×Q16—51no—
266C3×Q16—51no—
267C3×SD16—101no—
268C3×SD16—101no—
269C3×D8—51no—
270C3×D8—51no—
271C2×C3×C8C22×D511yescharacteristic
272#216—102no—
273#215—102no—
274#214—102no—
275#213—102no—
276#208—51no—
277Dic12—21no—
278Dic12C22×D512yes—
279D24—21no—
280D24C22×D512yes—
281ΓL(1,𝔽25)—52no—
282D3×C8—52no—
283C3×C16C22×D511yescharacteristic
284C3×C16C22×D511yescharacteristic
285C3⋊C16—52no—
286C23×C5—121no—
287C22×D5—122no—
288C5×Q8—62no—
289C5×Q8—121no—
290C5×D4—62no—
291C5×D4—121no—
292C2×C4×C5—121no—
293C2×C4×C5D3×D411yescharacteristic
294C22⋊D5—32no—
295C22⋊D5—41no—
296C22⋊D5—41no—
297C22⋊D5—122no—
298C22⋊D5—122no—
299C2×Dic5—122no—
300D20—21no—
301D20—21no—
302D20—31no—
303D20—122no—
304C4×D5—32no—
305C4×D5—41no—
306C4×D5—41no—
307C4×D5—122no—
308C4×D5—122no—
309Dic10—21no—
310Dic10—21no—
311Dic10—31no—
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—51no—
323#135—51no—
324#135—152no—
325#135—152no—
326C2×Q16—31no—
327C2×Q16—152no—
328C2×D8—31no—
329C2×D8—152no—
330#131—151no—
331Q32—51no—
332Q32—152no—
333SD32—32no—
334SD32—32no—
335SD32—51no—
336SD32—51no—
337SD32—152no—
338SD32—152no—
339D16—51no—
340D16—152no—
341M32—151no—
342M32—152no—
343C2×C16—152no—
344C2×C16D3×D511yescharacteristic, complemented
345C2×C3×C5—21no—
346C2×C3×C5C22×D811yescharacteristic
347D15—22no—
348C3×D5—81no—
349C3×D5—81no—
350C5×D3—82no—
351C22×D3—41no—
352C22×D3—202no—
353C3×Q8—101no—
354C3×Q8—101no—
355C3×D4—101no—
356C3×D4—101no—
357C3×D4—201no—
358C3×D4—201no—
359C2×C3×C4—201no—
360C2×C3×C4—201no—
361C2×C3×C4D4×D511yescharacteristic
362#67—52no—
363#67—202no—
364#67—202no—
365C2×Dic3—41no—
366C2×Dic3—202no—
367D12—22no—
368D12—41no—
369D12—51no—
370D12—202no—
371C4×D3—52no—
372C4×D3—202no—
373C4×D3—202no—
374Dic6—22no—
375Dic6—41no—
376Dic6—51no—
377Dic6—202no—
378C3×C8D4×D511yescharacteristic
379C3×C8C23×D511yescharacteristic
380C3⋊C8—52no—
381C22×C5—122no—
382C22×C5—481no—
383C22×C5D3×D811yescharacteristic
384C2×D5—32no—
385C2×D5—41no—
386C2×D5—41no—
387C2×D5—482no—
388C4×C5—122no—
389C4×C5D3×D811yescharacteristic
390C4×C5C2×D3×D411yescharacteristic
391Dic5—32no—
392Dic5—41no—
393Dic5—41no—
394#41—101no—
395#41—101no—
396#41—151no—
397#41—302no—
398#41—302no—
399#41—602no—
400#41—601no—
401#41—601no—
402C2×Q8—61no—
403C2×Q8—302no—
404C2×Q8—601no—
405C2×D4—61no—
406C2×D4—302no—
407C2×D4—601no—
408C2×D4—602no—
409Q16—32no—
410Q16—51no—
411Q16—51no—
412Q16—61no—
413Q16—302no—
414SD16—101no—
415SD16—101no—
416SD16—302no—
417SD16—302no—
418D8—32no—
419D8—51no—
420D8—51no—
421D8—61no—
422D8—302no—
423M16—151no—
424M16—152no—
425C2×C8—152no—
426C2×C8C2×D3×D511yescharacteristic
427C16—152no—
428C16C2×D3×D511yescharacteristic
429C16C2×D3×D511yescharacteristic
430C3×C5#341611yescharacteristic, complemented, Hall
431C22×C3—201no—
432C22×C3—201no—
433C22×C3D5×D811yescharacteristic
434C2×D3—42no—
435C2×D3—52no—
436C2×D3—161no—
437C2×D3—802no—
438C3×C4—201no—
439C3×C4—201no—
440C3×C4D5×D811yescharacteristic
441C3×C4C2×D4×D511yescharacteristic
442Dic3—42no—
443Dic3—52no—
444C2×C5—21no—
445C2×C5—242no—
446C2×C5C2×D3×D811yescharacteristic
447D5—62no—
448D5—81no—
449D5—81no—
450C23—121no—
451C23—602no—
452Q8—62no—
453Q8—101no—
454Q8—101no—
455Q8—121no—
456Q8—151no—
457Q8—602no—
458D4—62no—
459D4—101no—
460D4—101no—
461D4—121no—
462D4—152no—
463D4—151no—
464D4—201no—
465D4—201no—
466D4—602no—
467D4—602no—
468D4—602no—
469C2×C4—121no—
470C2×C4—152no—
471C2×C4—201no—
472C2×C4—201no—
473C2×C4—602no—
474C2×C4—602no—
475C2×C4—602no—
476C2×C4#677711yescharacteristic
477C8—152no—
478C8#677711yescharacteristic
479C8C22×D3×D511yescharacteristic
480C2×C3—21no—
481C2×C3—401no—
482C2×C3—401no—
483C2×C3C2×D5×D811yescharacteristic
484D3—82no—
485D3—102no—
486C5#8203211yescharacteristic, complemented, Sylow
487C22—122no—
488C22—152no—
489C22—201no—
490C22—201no—
491C22—481no—
492C22—2402no—
493C22#9125611yescharacteristic
494C4—122no—
495C4—152no—
496C4—201no—
497C4—201no—
498C4#9125611yescharacteristic
499C4C2×#677711yescharacteristic
500C3#1061375511yescharacteristic, complemented, Sylow
501C2—21no—
502C2—242no—
503C2—302no—
504C2—401no—
505C2—401no—
506C2C2×#9125611yescharacteristic
subgroupG/H
centerC2C2×#91256
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC2×C3×C5×C16C22
socleC2×C3×C5C22×D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#3416
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #11754008C2semidirect
2. #11753983C2semidirect
3. #11751002C2semidirect
4. C2×C5×#800C2semidirect
5. C3×#65193C2semidirect
6. #11747550C2semidirect
7. #11747540C2semidirect
8. #11746843C2semidirect
9. #11746840C2semidirect
10. #11746824C2semidirect
11. #11746823C2semidirect
16. C2×C5×Dic12C22semidirect
19. C3×#4050C22semidirect
24. #91277C22semidirect
25. #91264C22semidirect
28. C2×C3×C5×C16C22semidirect
29. #91096C22semidirect
30. #91082C22semidirect
31. C16×D15C22semidirect
32. C5×#800C22semidirect
33. C5×#800C22semidirect
34. C3×Dic40C22semidirect
35. C3×#3932C22semidirect
36. C3×#3932C22semidirect
37. C3×D80C22semidirect
38. #90946C22semidirect
39. #90941C22semidirect
40. #90940C22semidirect
41. #90937C22semidirect
52. #65193D3semidirect
99. C2×#800D5semidirect
114. #4050C2×D3semidirect
118. C2×C5×C16C2×D3semidirect
124. Dic40C2×D3semidirect
125. #3932C2×D3semidirect
126. #3932C2×D3semidirect
127. D80C2×D3semidirect
173. C2×Dic12C2×D5semidirect
180. C2×C3×C16C2×D5semidirect
186. #800C2×D5semidirect
187. #800C2×D5semidirect
344. C2×C16D3×D5semidirect
430. C3×C5#3416semidirect
486. C5#82032semidirect
500. C3#10613755semidirect

Maximal subgroups

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

subgroupindex
#117540082
#117539832
#117510022
C2×C5×#8002
C3×#651932
#117475502
#117475402
#117468432
#117468402
#117468242
#117468232
#106137553
#820325