Finite Group Databasebeta

← #14439475

Subgroups — #14439475

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756575C211yesmaximal, characteristic, complemented
2C2×C5×#942C211yesmaximal, characteristic, complemented
3C22×C3×#688C211yesmaximal, characteristic, complemented
4#11754600C211yesmaximal, characteristic, complemented
5C2×#91312C211yesmaximal, characteristic, complemented
6C2×#91303C211yesmaximal, characteristic, complemented
7#11749343C212yesmaximal, complemented
8#11749341C212yesmaximal, complemented
9#11749320C212yesmaximal, complemented
10#11749318C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615705—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91836C2212yescomplemented
18#91835—22no—
19#91833C2212yescomplemented
20#91818—22no—
21#91815C2211yescharacteristic
22C2×C5×#216C2212yescomplemented
23C5×#942—24no—
24C2×C5×#215C2212yescomplemented
25C2×C5×#208C2211yescharacteristic
26C2×C3×#688—24no—
27C2×C3×#688C2212yes—
28C2×C3×#688C2212yes—
29C22×C3×#168C2211yescharacteristic
30#91563—22no—
31#91463C2212yes—
32#91456—22no—
33#91368C2212yes—
34C2×#6663C2211yescharacteristic, complemented
35C2×#6660C2211yescharacteristic, complemented
36C2×#6659C2211yescharacteristic, complemented
37#91312—24no—
38C2×#6657C2212yes—
39#91303—24no—
40C2×#6654C2211yescharacteristic, complemented
41C2×#6653C2212yes—
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83854—51nomaximal, Hall
45C2×C5×#137—31no—
46#66164—31no—
47C2×#4096—31no—
48#66150—31no—
49C22×#688D311yescharacteristic, complemented
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65464—32no—
55#65411—31no—
56C23×C3×D5—21no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×#67—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6C2311yescharacteristic
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20—21no—
78C2×C3×D20C2312yes—
79C2×#1201—24no—
80#6719D412yes—
81#6714—24no—
82C4⋊Dic15D412yes—
83#6712—24no—
84C4×Dic15C2312yes—
85C5×#216—24no—
86C5×#215—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×#688—24no—
90C3×#688—24no—
91C2×C3×#168D414yescomplemented
92C2×C3×#168C2311yescharacteristic
93C2×C3×#168C2311yescharacteristic
94#6665—24no—
95#6663—22no—
96#6660—22no—
97#6659—22no—
98#6657—24no—
99#6654—22no—
100#6653—24no—
101C22×C3×SD16—51no—
102#5816—51no—
103C2×#942D511yescharacteristic, complemented
104#5805—51no—
105C2×#932—51no—
106C2×#904—51no—
107#5176—52no—
108#5175—52no—
109#5168—52no—
110#5167—52no—
111#5101—51no—
112C2×C5×#41—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C22×D20C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4096—64no—
121#4093—32no—
122#4093—32no—
123#4092—62no—
124#4090—32no—
125C2×#689—31no—
126C2×#688—24no—
127C2×#688—31no—
128C2×#688C2×D312yes—
129C2×#688C2×D312yes—
130#4086—32no—
131#4083—62no—
132C2×#687—31no—
133C2×#686—31no—
134#4076—62no—
135#4075—62no—
136#4072—31no—
137C22×#168C2×D311yescharacteristic
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C5×D3—21no—
147C22×C3×D5—22no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C3×C5×Q8—22no—
151C3×C5×Q8—22no—
152C3×C5×Q8—42no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—42no—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5C2411yescharacteristic
159#1220—42no—
160C2×Dic15—21no—
161C2×Dic15C2×D414yes—
162D60—21no—
163D60—21no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C5×#67—42no—
168C2×C5×Dic3—21no—
169C5×D12—21no—
170C5×D12—21no—
171C4×C5×D3—42no—
172C5×Dic6—21no—
173C5×Dic6—21no—
174C3×D20—22no—
175C3×D20—22no—
176C3×D20—42no—
177#1201—84no—
178C3×#168C2×D412yes—
179C3×#168C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C22×C3×Q8C2×D511yescharacteristic
182C22×C3×D4—51no—
183C2×#235—51no—
184C2×#235C2×D511yescharacteristic
185C2×C3×SD16—52no—
186C2×C3×SD16—52no—
187C2×C3×SD16—104no—
188C22×C3×C8—51no—
189#953—102no—
190#947—52no—
191#946—102no—
192#944—52no—
193C2×#216C2×D512yescomplemented
194#942—24no—
195C2×#215C2×D512yescomplemented
196#940—52no—
197#938—102no—
198#936—52no—
199C2×#214—52no—
200#932—104no—
201C2×#213—52no—
202#929—102no—
203#926—51no—
204C2×#208C2×D511yescharacteristic
205C2×Dic12—51no—
206#904—104no—
207C2×D24—51no—
208C2×#204—51no—
209C2×#204—51no—
210#815—52no—
211C8×Dic3—52no—
212C23×D5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—21no—
216C2×C5×Q8—22no—
217C2×C5×Q8—22no—
218C2×C5×Q8—31no—
219C2×C5×Q8C22×D312yes—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—21no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—64no—
226C2×C22⋊D5—61no—
227#709—62no—
228#709—62no—
229C2×D20—22no—
230C2×D20—22no—
231C2×D20—21no—
232C2×D20—31no—
233C2×D20C22×D312yes—
234C2×C4×D5—61no—
235C2×Dic10—31no—
236C5×Q16—64no—
237C5×SD16—64no—
238C5×M16—34no—
239C2×C5×C8—32no—
240C22⋊Dic5—32no—
241#689—62no—
242#688—24no—
243#688—24no—
244#688—62no—
245#687—62no—
246#686—62no—
247#685—64no—
248#685—64no—
249C4⋊Dic5—32no—
250#683—64no—
251C4×Dic5—32no—
252C2×#168#6714yescomplemented
253C2×#168C22×D311yescharacteristic
254C2×#168C22×D311yescharacteristic
255D40—64no—
256#677—64no—
257C2×#137—31no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—51no—
261#536—151no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—41no—
272C2×D15—42no—
273C2×C5×D3—41no—
274C2×C5×D3—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—24no—
283Dic15—41no—
284C5×Dic3—41no—
285C24×C3—101no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8C22×D512yes—
290C2×C3×D4—52no—
291C2×C3×D4—102no—
292C2×C3×D4—101no—
293C2×C3×D4—102no—
294C22×C3×C4—21no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—21no—
297C2×#67—104no—
298C2×#67—101no—
299#235—22no—
300#235—22no—
301#235—102no—
302#235—102no—
303C2×D12—51no—
304C2×D12C22×D511yescharacteristic
305C2×C4×D3—21no—
306C2×C4×D3—101no—
307C2×Dic6—51no—
308C2×Dic6C22×D511yescharacteristic
309C3×SD16—104no—
310C3×SD16—104no—
311C2×C3×C8—54no—
312C2×C3×C8—51no—
313C2×C3×C8—51no—
314#217—52no—
315#217—104no—
316#216—24no—
317#215—24no—
318#214—104no—
319#213—104no—
320(C2×D3)⋊C4—104no—
321C4⋊Dic3—52no—
322Dic3⋊C4—104no—
323C4×Dic3—52no—
324#208C22⋊D514yescomplemented
325C2×C3⋊C8C22×D512yes—
326Dic12—102no—
327D24—102no—
328#204—102no—
329#204—102no—
330C23×C5—61no—
331C23×C5D3×D411yescharacteristic
332C22×D5—22no—
333C22×D5—42no—
334C22×D5—61no—
335C22×D5—82no—
336C5×Q8—22no—
337C5×Q8—22no—
338C5×Q8—42no—
339C5×Q8—61no—
340C5×Q8—61no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—22no—
345C2×C4×C5—42no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—122no—
353C22⋊D5—244no—
354C2×Dic5—34no—
355C2×Dic5—61no—
356D20—22no—
357D20—22no—
358D20—42no—
359D20—61no—
360D20—61no—
361C4×D5—122no—
362Dic10—61no—
363Dic10—61no—
364C5×C8—34no—
365#168C2×#6712yes—
366#168C2×#6712yes—
367C2×#41—31no—
368C2×#41—151no—
369C22×Q8D3×D511yescharacteristic
370C22×D4—51no—
371#137—64no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—32no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—52no—
378C2×SD16—52no—
379C2×SD16—104no—
380C2×SD16—152no—
381C2×SD16—151no—
382C2×SD16—151no—
383C2×D8—152no—
384C2×D8—151no—
385C2×M16—31no—
386C22×C8—51no—
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—151no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401D15—81no—
402C3×D5—82no—
403C5×D3—81no—
404C23×C3—102no—
405C23×C3—202no—
406C23×C3—402no—
407C23×C3D4×D511yescharacteristic
408C22×D3—21no—
409C22×D3—101no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—42no—
413C3×D4—102no—
414C3×D4—102no—
415C3×D4—202no—
416C2×C3×C4—22no—
417C2×C3×C4—42no—
418C2×C3×C4D4×D512yes—
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4C2×C22⋊D512yes—
421C2×C3×C4C23×D511yescharacteristic
422#67—42no—
423#67—202no—
424#67—404no—
425C2×Dic3—21no—
426C2×Dic3—54no—
427C2×Dic3—101no—
428D12—21no—
429D12—21no—
430D12—101no—
431D12—101no—
432C4×D3—42no—
433C4×D3—202no—
434Dic6—21no—
435Dic6—21no—
436Dic6—101no—
437Dic6—101no—
438C3×C8—52no—
439C3×C8—52no—
440C3⋊C8C2×C22⋊D514yes—
441C22×C5—22no—
442C22×C5—122no—
443C22×C5—121no—
444C22×C5#94012yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—44no—
447C2×D5—42no—
448C2×D5—84no—
449C2×D5—122no—
450C2×D5—121no—
451C4×C5—42no—
452C4×C5—121no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C22×#6711yescharacteristic
456Dic5—64no—
457Dic5—121no—
458C24—101no—
459#41—62no—
460#41—62no—
461#41—302no—
462#41—302no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—31no—
467C2×Q8—151no—
468C2×Q8C2×D3×D512yes—
469C2×D4—31no—
470C2×D4—52no—
471C2×D4—61no—
472C2×D4—102no—
473C2×D4—102no—
474C2×D4—101no—
475C2×D4—151no—
476C2×D4—304no—
477C2×D4—301no—
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—64no—
483Q16—302no—
484SD16—64no—
485SD16—104no—
486SD16—104no—
487SD16—304no—
488SD16—302no—
489SD16—302no—
490D8—304no—
491D8—302no—
492M16—34no—
493C2×C8—32no—
494C2×C8—54no—
495C2×C8—51no—
496C2×C8—51no—
497C4⋊C4—152no—
498C4⋊C4—304no—
499C22⋊C4—152no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—152no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—204no—
506C22×C3—202no—
507C22×C3—404no—
508C22×C3#408612yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—42no—
511C2×D3—41no—
512C2×D3—202no—
513C2×D3—201no—
514C3×C4—42no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—41no—
519Dic3—104no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5#576212yes—
524C2×C5C2×#94011yescharacteristic
525D5—82no—
526D5—241no—
527C23—61no—
528C23—102no—
529C23—202no—
530C23—301no—
531C23—402no—
532C23#679011yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—61no—
537Q8—61no—
538Q8—301no—
539Q8—301no—
540D4—61no—
541D4—61no—
542D4—102no—
543D4—102no—
544D4—122no—
545D4—202no—
546D4—301no—
547D4—301no—
548D4—602no—
549D4—1204no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—61no—
553C2×C4—122no—
554C2×C4—154no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D512yes—
559C2×C4#679011yescharacteristic
560C2×C4C22×D3×D511yescharacteristic
561C8—34no—
562C8—52no—
563C8—52no—
564C2×C3—22no—
565C2×C3—402no—
566C2×C3#6611212yes—
567C2×C3C2×#408611yescharacteristic
568D3—81no—
569D3—401no—
570C5#8385411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—122no—
573C22—121no—
574C22—204no—
575C22—202no—
576C22—404no—
577C22—602no—
578C22—601no—
579C22#9156712yes—
580C22C2×#679011yescharacteristic
581C4—42no—
582C4—121no—
583C4—304no—
584C4—601no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×D3×C22⋊D511yescharacteristic
588C3#1061570511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—402no—
592C2—1201no—
593C2#1175509712yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #11756575C2semidirect
2. C2×C5×#942C2semidirect
3. C22×C3×#688C2semidirect
4. #11754600C2semidirect
5. C2×#91312C2semidirect
6. C2×#91303C2semidirect
7. #11749343C2semidirect
8. #11749341C2semidirect
9. #11749320C2semidirect
10. #11749318C2semidirect
11. #11748324C2semidirect
17. #91836C22semidirect
19. #91833C22semidirect
22. C2×C5×#216C22semidirect
24. C2×C5×#215C22semidirect
34. C2×#6663C22semidirect
35. C2×#6660C22semidirect
36. C2×#6659C22semidirect
40. C2×#6654C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
49. C22×#688D3semidirect
87. C5×#208D4semidirect
91. C2×C3×#168D4semidirect
103. C2×#942D5semidirect
193. C2×#216C2×D5semidirect
195. C2×#215C2×D5semidirect
252. C2×#168#67semidirect
324. #208C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83854semidirect
588. C3#10615705semidirect

Maximal subgroups

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

subgroupindex
#117565752
C2×C5×#9422
C22×C3×#6882
#117546002
C2×#913122
C2×#913032
#117493432
#117493412
#117493202
#117493182
#117483242
#106157053
#838545