Finite Group Databasebeta

← #14425261

Subgroups — #14425261

Order 1920.

1448 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757146C211yesmaximal, characteristic, complemented
2C5×#5832C211yesmaximal, characteristic, complemented
3#11754145C212yesmaximal, complemented
4C3×#65526C211yesmaximal, characteristic, complemented
5#11749396C212yesmaximal, complemented
6#11749389C212yesmaximal, complemented
7#11749150C212yesmaximal, complemented
8#11749143C212yesmaximal, complemented
9C2×#90980C212yesmaximal, complemented
10#10615053—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12#92101—22no—
13#92100—22no—
14#41×D15—24no—
15#92098C2212yes—
16#92095—22no—
17#92095C2212yes—
18C2×#6817—22no—
19C2×#6817C2212yes—
20C2×C5×#235C2211yescharacteristic, complemented
21C5×#947C2211yescharacteristic, complemented
22C5×#944C2211yescharacteristic, complemented
23C5×#940C2211yescharacteristic, complemented
24C5×#939—22no—
25C5×#936C2211yescharacteristic, complemented
26C4×C5×#67—22no—
27C2×C4×C5×Dic3C2211yescharacteristic, complemented
28C2×C3×#681C2212yescomplemented
29#91322—22no—
30#91321C2214yescomplemented
31#91305—22no—
32#91304C2214yescomplemented
33#91303—24no—
34C3×#3968C2212yescomplemented
35C3×#3965C2212yescomplemented
36#90980C2214yescomplemented
37#90980C2214yescomplemented
38#78716—51nomaximal, Hall
39#66283—31no—
40C5×#532—31no—
41#66156—32no—
42#65526D311yescharacteristic, complemented
43#65384—32no—
44#65366—32no—
45#65351—32no—
46#65350—32no—
47C2×#3937—32no—
48C3×C5×#41—22no—
49C3×C5×#41—22no—
50C2×C3×C5×Q8C2311yescharacteristic
51C2×C3×C5×D4D412yes—
52C2×C3×C5×D4C2311yescharacteristic
53C22×C3×C4×C5D412yes—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—24no—
56C2×#1220—22no—
57#6821—24no—
58Q8×D15—24no—
59#6819—28no—
60#6819—24no—
61D4×D15—28no—
62D4×D15—24no—
63#6817—24no—
64#6817—24no—
65#6817—22no—
66#6817—24no—
67#6817—22no—
68#6817D414yescomplemented
69#6817C2314yes—
70C2×D60—22no—
71C2×D60D412yescomplemented
72C2×C4×D15—24no—
73C2×C4×D15—22no—
74C2×Dic30—22no—
75C2×Dic30D412yescomplemented
76C2×C5×#67—22no—
77C2×C5×#67—21no—
78C22×C5×Dic3—21no—
79C5×#235—22no—
80C5×#235—22no—
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C2×C5×Dic6C2311yescharacteristic
84C5×#217—22no—
85C5×(C2×D3)⋊C4—22no—
86C5×Dic3⋊C4—22no—
87C4×C5×Dic3—21no—
88C4×C5×Dic3C2311yescharacteristic
89C4×C5×Dic3C2311yescharacteristic
90C3×#681—22no—
91C3×#681C2314yes—
92C2×C3×#168—22no—
93#6663—24no—
94#6660—24no—
95#6659—24no—
96#6654—24no—
97#5964—51no—
98#5832D511yescharacteristic, complemented
99#5748—52no—
100C3×#413—51no—
101C2×#825—52no—
102#4753—52no—
103#4752—52no—
104#4747—52no—
105#4746—52no—
106C2×C5×#41—31no—
107C2×C5×#41C2×D311yescharacteristic
108#4150—62no—
109#4149—62no—
110D5×#41—64no—
111#4147—32no—
112#4144—32no—
113#4144—62no—
114C2×#709—32no—
115C2×#709—62no—
116C5×C4⋊Q8—31no—
117C5×#127—31no—
118C5×#124—31no—
119C5×#124—31no—
120C5×#121—62no—
121C4×C5×D4—62no—
122C2×C42×C5—31no—
123#4097—62no—
124#4096—64no—
125#4095—62no—
126#4088—34no—
127#4078—34no—
128C2×#681C2×D312yescomplemented
129#3968C2×D312yescomplemented
130#3965C2×D312yescomplemented
131#3937—34no—
132#3937—34no—
133#3018—151noSylow
134C23×C3×C5C2×D412yes—
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—24no—
137C22×D15—22no—
138C22×C5×D3—21no—
139C3×C5×Q8—22no—
140C3×C5×D4—24no—
141C3×C5×D4—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—28no—
150#1220—24no—
151#1220—24no—
152C2×Dic15—24no—
153C2×Dic15—22no—
154D60—24no—
155D60—22no—
156D60C2×D414yes—
157C4×D15—28no—
158C4×D15—24no—
159C4×D15—24no—
160Dic30—24no—
161Dic30—22no—
162Dic30C2×D414yes—
163C5×#67—44no—
164C5×#67—42no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—21no—
167C2×C5×Dic3—21no—
168C2×C5×Dic3—42no—
169C5×D12—22no—
170C4×C5×D3—41no—
171C4×C5×D3—41no—
172C5×Dic6—22no—
173C3×#168—24no—
174C2×C3×#41C2×D511yescharacteristic
175#1010—102no—
176#1009—102no—
177D3×#41—104no—
178#1007—52no—
179#1004—52no—
180#1004—102no—
181C2×#235—52no—
182C2×#235—102no—
183C2×#235C2×D511yescharacteristic, complemented
184C2×C3×M16—52no—
185#947C2×D511yescharacteristic, complemented
186#944C2×D511yescharacteristic, complemented
187#940C2×D511yescharacteristic, complemented
188#939—22no—
189#936C2×D511yescharacteristic, complemented
190C4×#67—22no—
191C2×C4×Dic3C2×D511yescharacteristic, complemented
192#909—54no—
193#909—102no—
194#908—54no—
195#908—102no—
196#904—104no—
197C3×#101—52no—
198C3×#100—52no—
199#825—54no—
200#825—54no—
201C5×#41—22no—
202C5×#41—22no—
203C5×#41—62no—
204C5×#41—62no—
205C2×C5×Q8—31no—
206C2×C5×Q8C22×D311yescharacteristic
207C2×C5×D4—31no—
208C2×C5×D4—62no—
209C2×C5×D4—61no—
210C2×C5×D4D1212yes—
211C2×C5×D4C22×D311yescharacteristic
212C22×C4×C5—61no—
213C22×C4×C5—61no—
214C22×C4×C5D1212yes—
215C22×C4×C5C22×D311yescharacteristic
216C2×C22⋊D5—62no—
217C2×C22⋊D5—64no—
218#713—64no—
219Q8×D5—64no—
220#711—64no—
221#711—68no—
222D4×D5—64no—
223D4×D5—68no—
224#709—34no—
225#709—34no—
226#709—64no—
227#709—64no—
228#709—62no—
229#709—64no—
230#709—62no—
231C2×D20—32no—
232C2×D20—62no—
233C2×C4×D5—64no—
234C2×C4×D5—62no—
235C2×Dic10—32no—
236C2×Dic10—62no—
237C5×C4⋊C4—62no—
238C5×C22⋊C4—62no—
239C5×C22⋊C4—62no—
240C42×C5—31no—
241C42×C5—31no—
242C42×C5—61no—
243#689—64no—
244#688—64no—
245#687—64no—
246#686—64no—
247#681—22no—
248#681C22×D314yes—
249C2×#168—22no—
250#585—151no—
251#575—152no—
252#532—31no—
253#456—152no—
254#455—152no—
255#454—152no—
256#453—152no—
257C2×#104—152no—
258#413—51no—
259C22×C3×C5—22no—
260C22×C3×C5—41no—
261C22×C3×C5—42no—
262C22×C3×C5#12012yes—
263C22×C3×C5C22×D411yescharacteristic
264C2×D15—24no—
265C2×D15—82no—
266C2×D15—84no—
267C2×C5×D3—42no—
268C2×C5×D3—41no—
269C3×C4×C5—22no—
270C3×C4×C5#12011yescharacteristic
271C3×C4×C5#12011yescharacteristic
272C3×C4×C5C22×D412yes—
273Dic15—24no—
274C5×Dic3—22no—
275C5×Dic3—41no—
276C5×Dic3—41no—
277C3×#41—22no—
278C3×#41—22no—
279C2×C3×Q8C22×D511yescharacteristic
280C2×C3×D4C22⋊D512yes—
281C2×C3×D4C22×D511yescharacteristic
282C22×C3×C4C22⋊D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—22no—
285C2×#67—21no—
286C2×#67—102no—
287C2×#67—104no—
288C22×Dic3—21no—
289#239—104no—
290D3×Q8—104no—
291#237—104no—
292#237—108no—
293D3×D4—104no—
294D3×D4—108no—
295#235—22no—
296#235—22no—
297#235—54no—
298#235—54no—
299#235—104no—
300#235—104no—
301#235—102no—
302#235—102no—
303#235—104no—
304C2×D12—52no—
305C2×D12—102no—
306C2×D12C22×D511yescharacteristic
307C2×C4×D3—21no—
308C2×C4×D3—104no—
309C2×C4×D3—102no—
310C2×Dic6—52no—
311C2×Dic6—102no—
312C2×Dic6C22×D511yescharacteristic
313C3×M16—54no—
314C3×M16—102no—
315C2×C3×C8—102no—
316#217—22no—
317(C2×D3)⋊C4—22no—
318Dic3⋊C4—22no—
319C4×Dic3—21no—
320C4×Dic3C22×D511yescharacteristic
321C4×Dic3C22×D511yescharacteristic
322Dic12—104no—
323D24—104no—
324#204—104no—
325#204—104no—
326C23×C5—61no—
327C23×C5C2×D1212yes—
328C23×C5C2×D1211yescharacteristic
329C22×D5—64no—
330C22×D5—62no—
331C5×Q8—22no—
332C5×Q8—62no—
333C5×D4—24no—
334C5×D4—22no—
335C5×D4—62no—
336C5×D4—124no—
337C5×D4—122no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—61no—
341C2×C4×C5—61no—
342C2×C4×C5—61no—
343C2×C4×C5—122no—
344C2×C4×C5—121no—
345C2×C4×C5—121no—
346C2×C4×C5C2×D1212yes—
347C2×C4×C5C2×D1211yescharacteristic
348C2×C4×C5D3×D412yes—
349C2×C4×C5D3×D412yes—
350C2×C4×C5C23×D311yescharacteristic
351C22⋊D5—68no—
352C22⋊D5—64no—
353C22⋊D5—64no—
354C2×Dic5—64no—
355C2×Dic5—62no—
356D20—34no—
357D20—64no—
358D20—62no—
359C4×D5—68no—
360C4×D5—64no—
361C4×D5—64no—
362Dic10—34no—
363Dic10—64no—
364Dic10—62no—
365#168—24no—
3662−1+4—152no—
3672−1+4—302no—
368H(5,𝔽2)—152no—
369H(5,𝔽2)—302no—
370H(5,𝔽2)—302no—
371C2×#41—31no—
372C2×#41—152no—
373C2×#41—304no—
374C2×#41—302no—
375C2×#41D3×D511yescharacteristic
376#137—154no—
377#137—302no—
378AGL(1,ℤ/8)—154no—
379AGL(1,ℤ/8)—302no—
380#135—304no—
381C2×M16—52no—
382C4⋊Q8—31no—
383#127—31no—
384#124—31no—
385#124—31no—
386#121—62no—
387C4×D4—62no—
388C2×C42—31no—
389#104—154no—
390#104—154no—
391#101—52no—
392#100—52no—
393C2×C3×C5—21no—
394C2×C3×C5—22no—
395C2×C3×C5—42no—
396C2×C3×C5C2×#12011yescharacteristic
397D15—44no—
398C5×D3—81no—
399C23×C3C2×C22⋊D512yes—
400C23×C3C2×C22⋊D511yescharacteristic
401C22×D3—21no—
402C22×D3—104no—
403C22×D3—102no—
404C3×Q8—22no—
405C3×D4—24no—
406C3×D4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4D4×D512yes—
410C2×C3×C4D4×D512yes—
411C2×C3×C4C2×C22⋊D512yes—
412C2×C3×C4C2×C22⋊D511yescharacteristic
413C2×C3×C4C23×D511yescharacteristic
414#67—44no—
415#67—42no—
416#67—108no—
417#67—104no—
418#67—104no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—21no—
422C2×Dic3—42no—
423C2×Dic3—104no—
424C2×Dic3—102no—
425D12—22no—
426D12—54no—
427D12—104no—
428D12—102no—
429C4×D3—41no—
430C4×D3—41no—
431C4×D3—108no—
432C4×D3—104no—
433C4×D3—104no—
434Dic6—22no—
435Dic6—54no—
436Dic6—104no—
437Dic6—102no—
438C3×C8—104no—
439C22×C5—22no—
440C22×C5—41no—
441C22×C5—42no—
442C22×C5—122no—
443C22×C5—121no—
444C22×C5#88212yes—
445C22×C5C22×D1211yescharacteristic
446C2×D5—64no—
447C2×D5—242no—
448C2×D5—244no—
449C4×C5—22no—
450C4×C5—62no—
451C4×C5—121no—
452C4×C5—121no—
453C4×C5#88211yescharacteristic
454C4×C5#88211yescharacteristic
455C4×C5C2×D3×D412yes—
456Dic5—64no—
457#41—22no—
458#41—22no—
459#41—62no—
460#41—62no—
461#41—154no—
462#41—154no—
463#41—304no—
464#41—304no—
465#41—304no—
466#41—308no—
467#41—304no—
468#41—302no—
469#41—304no—
470#41—302no—
471C2×Q8—31no—
472C2×Q8—152no—
473C2×Q8—302no—
474C2×Q8—304no—
475C2×Q8C2×D3×D511yescharacteristic
476C2×D4—31no—
477C2×D4—62no—
478C2×D4—61no—
479C2×D4—152no—
480C2×D4—302no—
481C2×D4—304no—
482C2×D4—308no—
483C2×D4—302no—
484C2×D4—304no—
485C2×D4#120312yes—
486C2×D4C2×D3×D511yescharacteristic
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—304no—
490C22×C4—302no—
491C22×C4#120312yes—
492C22×C4C2×D3×D511yescharacteristic
493Q16—304no—
494SD16—304no—
495SD16—304no—
496D8—304no—
497M16—54no—
498M16—102no—
499C2×C8—102no—
500C4⋊C4—62no—
501C22⋊C4—62no—
502C22⋊C4—62no—
503C42—31no—
504C42—31no—
505C42—61no—
506C3×C5#301811yescharacteristic, complemented, Hall
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—42no—
510C22×C3#408312yes—
511C22×C3C22×C22⋊D511yescharacteristic
512C2×D3—42no—
513C2×D3—41no—
514C2×D3—104no—
515C2×D3—402no—
516C2×D3—404no—
517C3×C4—22no—
518C3×C4#408311yescharacteristic
519C3×C4#408311yescharacteristic
520C3×C4C2×D4×D512yes—
521Dic3—22no—
522Dic3—41no—
523Dic3—41no—
524Dic3—104no—
525C2×C5—21no—
526C2×C5—22no—
527C2×C5—42no—
528C2×C5—241no—
529C2×C5C2×#88211yescharacteristic
530D5—124no—
531C23—61no—
532C23—304no—
533C23—302no—
534C23C2×#120312yes—
535C23C2×#120311yescharacteristic
536Q8—22no—
537Q8—62no—
538Q8—154no—
539Q8—304no—
540Q8—302no—
541D4—24no—
542D4—22no—
543D4—62no—
544D4—124no—
545D4—122no—
546D4—154no—
547D4—304no—
548D4—308no—
549D4—304no—
550D4—304no—
551D4—302no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—122no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—308no—
561C2×C4—304no—
562C2×C4—302no—
563C2×C4—304no—
564C2×C4—304no—
565C2×C4C2×#120312yes—
566C2×C4C2×#120311yescharacteristic
567C2×C4#679012yes—
568C2×C4#679012yes—
569C2×C4C22×D3×D511yescharacteristic
570C8—104no—
571C2×C3—21no—
572C2×C3—22no—
573C2×C3—42no—
574C2×C3C2×#408311yescharacteristic
575D3—81no—
576D3—204no—
577C5#7871611yescharacteristic, complemented, Sylow
578C22—22no—
579C22—41no—
580C22—42no—
581C22—122no—
582C22—121no—
583C22—304no—
584C22—1202no—
585C22—1204no—
586C22#9157312yes—
587C22C22×#120311yescharacteristic
588C4—22no—
589C4—62no—
590C4—121no—
591C4—121no—
592C4—304no—
593C4#9157311yescharacteristic
594C4#9157311yescharacteristic
595C4C2×#679012yes—
596C3#1061505311yescharacteristic, complemented, Sylow
597C2—21no—
598C2—22no—
599C2—42no—
600C2—241no—
601C2—604no—
602C2C2×#9157311yescharacteristic
subgroupG/H
centerC4#91573
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3018
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11757146C2semidirect
2. C5×#5832C2semidirect
3. #11754145C2semidirect
4. C3×#65526C2semidirect
5. #11749396C2semidirect
6. #11749389C2semidirect
7. #11749150C2semidirect
8. #11749143C2semidirect
9. C2×#90980C2semidirect
20. C2×C5×#235C22semidirect
21. C5×#947C22semidirect
22. C5×#944C22semidirect
23. C5×#940C22semidirect
25. C5×#936C22semidirect
27. C2×C4×C5×Dic3C22semidirect
28. C2×C3×#681C22semidirect
30. #91321C22semidirect
32. #91304C22semidirect
34. C3×#3968C22semidirect
35. C3×#3965C22semidirect
36. #90980C22semidirect
37. #90980C22semidirect
42. #65526D3semidirect
68. #6817D4semidirect
71. C2×D60D4semidirect
75. C2×Dic30D4semidirect
98. #5832D5semidirect
128. C2×#681C2×D3semidirect
129. #3968C2×D3semidirect
130. #3965C2×D3semidirect
183. C2×#235C2×D5semidirect
185. #947C2×D5semidirect
186. #944C2×D5semidirect
187. #940C2×D5semidirect
189. #936C2×D5semidirect
191. C2×C4×Dic3C2×D5semidirect
506. C3×C5#3018semidirect
577. C5#78716semidirect
596. C3#10615053semidirect

Maximal subgroups

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

subgroupindex
#117571462
C5×#58322
#117541452
C3×#655262
#117493962
#117493892
#117491502
#117491432
C2×#909802
#106150533
#787165