Finite Group Databasebeta

← #14425498

Subgroups — #14425498

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757146C211yesmaximal, characteristic, complemented
2C3×#66164C211yesmaximal, characteristic, complemented
3C2×#91312C212yesmaximal, complemented
4C5×#5237C211yesmaximal, characteristic, complemented
5#11749388C214yesmaximal, complemented
6#11749142C214yesmaximal, complemented
7#11748429C212yesmaximal, complemented
8#10610448—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92101—22no—
11#92100—22no—
12#41×D15—24no—
13#92098C2212yescomplemented
14#92095—22no—
15#92095C2212yescomplemented
16C2×#6817—22no—
17C2×#6817C2212yes—
18C22×C3×D20C2211yescharacteristic, complemented
19C2×C5×#208C2212yescomplemented
20C3×#4093C2212yescomplemented
21C3×#4086C2212yescomplemented
22C3×#4083—22no—
23C3×#4076—22no—
24C3×#4072C2211yescharacteristic, complemented
25#91312—24no—
26#91312C2218yescomplemented
27C2×#6657—22no—
28C2×#6653—22no—
29C5×#836C2212yescomplemented
30C5×#833C2212yescomplemented
31#90981C2218yescomplemented
32#83395—51nomaximal, Hall
33#66283—31no—
34#66164D311yescharacteristic, complemented
35C2×#4054—32no—
36C5×#413—31no—
37#65428—32no—
38#65042—34no—
39#65036—34no—
40C23×C3×D5—21no—
41C3×C5×#41—22no—
42C3×C5×#41—22no—
43C2×C3×C5×Q8C2311yescharacteristic
44C2×C3×C5×D4D412yes—
45C2×C3×C5×D4C2311yescharacteristic
46C22×C3×C4×C5D412yes—
47C22×C3×C4×C5C2311yescharacteristic
48C2×#1220—24no—
49C2×#1220—22no—
50#6821—24no—
51Q8×D15—24no—
52#6819—28no—
53#6819—24no—
54D4×D15—28no—
55D4×D15—24no—
56#6817—24no—
57#6817—24no—
58#6817—22no—
59#6817—24no—
60#6817—22no—
61#6817D414yescomplemented
62#6817C2314yes—
63C2×D60—22no—
64C2×D60D412yescomplemented
65C2×C4×D15—24no—
66C2×C4×D15—22no—
67C2×Dic30—22no—
68C2×Dic30D412yescomplemented
69C2×C3×C22⋊D5—24no—
70C2×C3×D20—22no—
71C2×C3×D20—22no—
72C2×C3×D20—21no—
73C2×C3×D20C2312yes—
74C5×#208—22no—
75C5×#208C2314yes—
76C2×C5×C3⋊C8—22no—
77C3×C22⋊Dic5—21no—
78C3×#685—24no—
79C3×C4⋊Dic5—21no—
80C3×C4×Dic5C2312yes—
81#6657—28no—
82#6653—28no—
83#5964—51no—
84C3×#535—51no—
85C2×#932—52no—
86#5237D511yescharacteristic, complemented
87#5077—54no—
88#5062—54no—
89#5005—52no—
90C2×C5×#41C2×D311yescharacteristic
91#4150—62no—
92#4149—62no—
93D5×#41—64no—
94#4147—32no—
95#4144—32no—
96#4144—62no—
97C2×#709—32no—
98C2×#709—62no—
99C22×D20C2×D311yescharacteristic, complemented
100C2×C5×M16—32no—
101#4093C2×D312yescomplemented
102#4086C2×D312yescomplemented
103#4083—22no—
104#4076—22no—
105#4072C2×D311yescharacteristic, complemented
106#4054—38no—
107#4054—64no—
108C2×D40—62no—
109C2×#677—62no—
110C5×#101—32no—
111C5×#100—32no—
112#3957—38no—
113#3021—151noSylow
114C23×C3×C5C2×D412yes—
115C23×C3×C5C2×D411yescharacteristic
116C22×D15—24no—
117C22×D15—22no—
118C22×C3×D5—22no—
119C22×C3×D5—42no—
120C22×C3×D5—82no—
121C3×C5×Q8—22no—
122C3×C5×D4—24no—
123C3×C5×D4—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2411yescharacteristic
131#1220—28no—
132#1220—24no—
133#1220—24no—
134C2×Dic15—24no—
135C2×Dic15—22no—
136D60—24no—
137D60—22no—
138D60C2×D414yes—
139C4×D15—28no—
140C4×D15—24no—
141C4×D15—24no—
142Dic30—24no—
143Dic30—22no—
144Dic30C2×D414yes—
145C3×C22⋊D5—84no—
146C2×C3×Dic5—22no—
147C3×D20—24no—
148C3×D20—41no—
149C3×D20—41no—
150C5×C3⋊C8—24no—
151C2×C3×#41C2×D511yescharacteristic
152C22×C3×D4—51no—
153#1010—102no—
154#1009—102no—
155D3×#41—104no—
156#1007—52no—
157#1004—52no—
158#1004—102no—
159C2×#235—52no—
160C2×#235—102no—
161C3×#127—52no—
162C3×#124—52no—
163C3×#121—102no—
164C3×#120—102no—
165C3×#117—51no—
166C2×#214—102no—
167#932—58no—
168#932—104no—
169C2×#213—102no—
170C2×#208C2×D512yescomplemented
171#836C2×D512yescomplemented
172#833C2×D512yescomplemented
173#805—58no—
174C23×D5—21no—
175C5×#41—22no—
176C5×#41—22no—
177C2×C5×Q8C22×D311yescharacteristic
178C2×C5×D4#6712yes—
179C2×C5×D4C22×D311yescharacteristic
180C22×C4×C5#6712yes—
181C22×C4×C5C22×D311yescharacteristic
182C2×C22⋊D5—24no—
183C2×C22⋊D5—62no—
184C2×C22⋊D5—64no—
185#713—64no—
186Q8×D5—64no—
187#711—64no—
188#711—68no—
189D4×D5—64no—
190D4×D5—68no—
191#709—34no—
192#709—34no—
193#709—64no—
194#709—64no—
195#709—62no—
196#709—62no—
197#709—64no—
198C2×D20—22no—
199C2×D20—22no—
200C2×D20—21no—
201C2×D20—32no—
202C2×D20—62no—
203C2×D20C22×D312yes—
204C2×C4×D5—64no—
205C2×C4×D5—62no—
206C2×Dic10—32no—
207C2×Dic10—62no—
208C5×M16—34no—
209C5×M16—62no—
210C2×C5×C8—62no—
211C22⋊Dic5—21no—
212#685—24no—
213C4⋊Dic5—21no—
214C4×Dic5C22×D312yes—
215D40—68no—
216#677—68no—
217#585—151no—
218C2×AGL(1,ℤ/8)—152no—
219#535—51no—
220#454—154no—
221#453—154no—
222#421—152no—
223#413—31no—
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—42no—
227C22×C3×C5#12012yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×D15—24no—
230C2×D15—82no—
231C2×D15—84no—
232C2×C3×D5—44no—
233C2×C3×D5—42no—
234C2×C3×D5—84no—
235C3×C4×C5—22no—
236C3×C4×C5#12011yescharacteristic
237C3×C4×C5#12011yescharacteristic
238C3×C4×C5C22×D412yes—
239Dic15—24no—
240C3×Dic5—42no—
241C24×C3—101no—
242C3×#41—22no—
243C3×#41—22no—
244C2×C3×Q8C22×D511yescharacteristic
245C2×C3×D4—52no—
246C2×C3×D4—104no—
247C2×C3×D4—101no—
248C2×C3×D4—102no—
249C2×C3×D4—102no—
250C2×C3×D4D2012yes—
251C2×C3×D4C22×D511yescharacteristic
252C22×C3×C4D2012yes—
253C22×C3×C4C22×D511yescharacteristic
254C2×#67—102no—
255C2×#67—104no—
256#239—104no—
257D3×Q8—104no—
258#237—104no—
259#237—108no—
260D3×D4—104no—
261D3×D4—108no—
262#235—54no—
263#235—54no—
264#235—104no—
265#235—104no—
266#235—102no—
267#235—104no—
268#235—102no—
269C2×D12—52no—
270C2×D12—102no—
271C2×C4×D3—104no—
272C2×C4×D3—102no—
273C2×Dic6—52no—
274C2×Dic6—102no—
275C3×C4⋊C4—101no—
276C3×C22⋊C4—101no—
277C3×C22⋊C4—104no—
278C3×C42—52no—
279#214—108no—
280#213—108no—
281#208—22no—
282#208C22×D514yes—
283C2×C3⋊C8—22no—
284C23×C5C2×#6712yes—
285C23×C5C2×#6711yescharacteristic
286C22×D5—22no—
287C22×D5—42no—
288C22×D5—64no—
289C22×D5—62no—
290C22×D5—82no—
291C5×Q8—22no—
292C5×D4—24no—
293C5×D4—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5D3×D412yes—
297C2×C4×C5D3×D412yes—
298C2×C4×C5C2×#6712yes—
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—68no—
302C22⋊D5—64no—
303C22⋊D5—64no—
304C22⋊D5—84no—
305C2×Dic5—22no—
306C2×Dic5—64no—
307C2×Dic5—62no—
308D20—24no—
309D20—34no—
310D20—41no—
311D20—41no—
312D20—64no—
313D20—62no—
314C4×D5—68no—
315C4×D5—64no—
316C4×D5—64no—
317Dic10—34no—
318Dic10—64no—
319Dic10—62no—
320C5×C8—64no—
3212−1+4—152no—
3222−1+4—302no—
323H(5,𝔽2)—152no—
324H(5,𝔽2)—302no—
325H(5,𝔽2)—302no—
326C2×#41—152no—
327C2×#41—304no—
328C2×#41—302no—
329C2×#41D3×D511yescharacteristic
330C22×D4—51no—
331AGL(1,ℤ/8)—158no—
332AGL(1,ℤ/8)—304no—
333C2×SD16—302no—
334C2×D8—302no—
335C2×M16—32no—
336#127—52no—
337#124—52no—
338#121—102no—
339#120—102no—
340#117—51no—
341#104—158no—
342#101—32no—
343#100—32no—
344C2×C3×C5—21no—
345C2×C3×C5—22no—
346C2×C3×C5—42no—
347C2×C3×C5C2×#12011yescharacteristic
348D15—44no—
349C3×D5—82no—
350C23×C3—102no—
351C23×C3—202no—
352C23×C3—402no—
353C23×C3C2×D2012yes—
354C23×C3C2×D2011yescharacteristic
355C22×D3—104no—
356C22×D3—102no—
357C3×Q8—22no—
358C3×D4—24no—
359C3×D4—22no—
360C3×D4—104no—
361C3×D4—201no—
362C3×D4—201no—
363C3×D4—404no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—102no—
367C2×C3×C4C2×D2012yes—
368C2×C3×C4C2×D2011yescharacteristic
369C2×C3×C4D4×D512yes—
370C2×C3×C4D4×D512yes—
371C2×C3×C4C23×D511yescharacteristic
372#67—108no—
373#67—104no—
374#67—104no—
375C2×Dic3—104no—
376C2×Dic3—102no—
377D12—54no—
378D12—104no—
379D12—102no—
380C4×D3—108no—
381C4×D3—104no—
382C4×D3—104no—
383Dic6—54no—
384Dic6—104no—
385Dic6—102no—
386C3⋊C8—24no—
387C22×C5—22no—
388C22×C5—41no—
389C22×C5—42no—
390C22×C5#93712yes—
391C22×C5C22×#6711yescharacteristic
392C2×D5—44no—
393C2×D5—42no—
394C2×D5—64no—
395C2×D5—84no—
396C2×D5—242no—
397C2×D5—244no—
398C4×C5—22no—
399C4×C5#93711yescharacteristic
400C4×C5#93711yescharacteristic
401C4×C5C2×D3×D412yes—
402Dic5—42no—
403Dic5—64no—
404C24—101no—
405#41—22no—
406#41—22no—
407#41—154no—
408#41—154no—
409#41—304no—
410#41—304no—
411#41—304no—
412#41—308no—
413#41—304no—
414#41—302no—
415#41—304no—
416#41—302no—
417C2×Q8—152no—
418C2×Q8—302no—
419C2×Q8—304no—
420C2×Q8C2×D3×D511yescharacteristic
421C2×D4—52no—
422C2×D4—104no—
423C2×D4—101no—
424C2×D4—102no—
425C2×D4—102no—
426C2×D4—152no—
427C2×D4—302no—
428C2×D4—304no—
429C2×D4—308no—
430C2×D4—302no—
431C2×D4—304no—
432C2×D4#120212yes—
433C2×D4C2×D3×D511yescharacteristic
434C22×C4—304no—
435C22×C4—302no—
436C22×C4#120212yes—
437C22×C4C2×D3×D511yescharacteristic
438SD16—308no—
439D8—308no—
440M16—34no—
441M16—62no—
442C2×C8—62no—
443C4⋊C4—101no—
444C22⋊C4—101no—
445C22⋊C4—104no—
446C42—52no—
447C3×C5#302111yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—41no—
450C22×C3—42no—
451C22×C3—204no—
452C22×C3—202no—
453C22×C3—404no—
454C22×C3#402812yes—
455C22×C3C22×D2011yescharacteristic
456C2×D3—104no—
457C2×D3—402no—
458C2×D3—404no—
459C3×C4—22no—
460C3×C4—202no—
461C3×C4#402811yescharacteristic
462C3×C4#402811yescharacteristic
463C3×C4C2×D4×D512yes—
464Dic3—104no—
465C2×C5—21no—
466C2×C5—22no—
467C2×C5—42no—
468C2×C5C2×#93711yescharacteristic
469D5—82no—
470D5—124no—
471C23—102no—
472C23—202no—
473C23—304no—
474C23—302no—
475C23—402no—
476C23C2×#120212yes—
477C23C2×#120211yescharacteristic
478Q8—22no—
479Q8—154no—
480Q8—304no—
481Q8—302no—
482D4—24no—
483D4—22no—
484D4—104no—
485D4—154no—
486D4—201no—
487D4—201no—
488D4—304no—
489D4—308no—
490D4—304no—
491D4—304no—
492D4—302no—
493D4—404no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—102no—
497C2×C4—308no—
498C2×C4—304no—
499C2×C4—302no—
500C2×C4—304no—
501C2×C4—304no—
502C2×C4C2×#120212yes—
503C2×C4C2×#120211yescharacteristic
504C2×C4#679012yes—
505C2×C4#679012yes—
506C2×C4C22×D3×D511yescharacteristic
507C8—64no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3—42no—
511C2×C3—402no—
512C2×C3C2×#402811yescharacteristic
513D3—204no—
514C5#8339511yescharacteristic, complemented, Sylow
515C22—22no—
516C22—41no—
517C22—42no—
518C22—204no—
519C22—202no—
520C22—304no—
521C22—404no—
522C22—1202no—
523C22—1204no—
524C22#9157212yes—
525C22C22×#120211yescharacteristic
526C4—22no—
527C4—202no—
528C4—304no—
529C4#9157211yescharacteristic
530C4#9157211yescharacteristic
531C4C2×#679012yes—
532C3#1061044811yescharacteristic, complemented, Sylow
533C2—21no—
534C2—22no—
535C2—42no—
536C2—402no—
537C2—604no—
538C2C2×#9157211yescharacteristic
subgroupG/H
centerC2C2×#91572
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3021
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11757146C2semidirect
2. C3×#66164C2semidirect
3. C2×#91312C2semidirect
4. C5×#5237C2semidirect
5. #11749388C2semidirect
6. #11749142C2semidirect
7. #11748429C2semidirect
13. #92098C22semidirect
15. #92095C22semidirect
18. C22×C3×D20C22semidirect
19. C2×C5×#208C22semidirect
20. C3×#4093C22semidirect
21. C3×#4086C22semidirect
24. C3×#4072C22semidirect
26. #91312C22semidirect
29. C5×#836C22semidirect
30. C5×#833C22semidirect
31. #90981C22semidirect
34. #66164D3semidirect
61. #6817D4semidirect
64. C2×D60D4semidirect
68. C2×Dic30D4semidirect
86. #5237D5semidirect
99. C22×D20C2×D3semidirect
101. #4093C2×D3semidirect
102. #4086C2×D3semidirect
105. #4072C2×D3semidirect
170. C2×#208C2×D5semidirect
171. #836C2×D5semidirect
172. #833C2×D5semidirect
447. C3×C5#3021semidirect
514. C5#83395semidirect
532. C3#10610448semidirect

Maximal subgroups

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

subgroupindex
#117571462
C3×#661642
C2×#913122
C5×#52372
#117493882
#117491422
#117484292
#106104483
#833955