Finite Group Databasebeta

← #14439262

Subgroups — #14439262

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756591C211yesmaximal, characteristic
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C2×C3×#4097C211yesmaximal, characteristic, complemented
4C2×#91385C211yesmaximal, characteristic, complemented
5C2×#91321C211yesmaximal, characteristic, complemented
6C2×#91315C211yesmaximal, characteristic, complemented
7#11749356C212yesmaximal, complemented
8#11749355C212yesmaximal, complemented
9#11749111C212yesmaximal, complemented
10#11749109C212yesmaximal, complemented
11#11748328C211yesmaximal, characteristic, complemented
12#10615703—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91836C2211yescharacteristic
18#91833C2211yescharacteristic
19#91829C2211yescharacteristic
20#91828—22no—
21#91825C2211yescharacteristic
22C4×#1220—22no—
23C2×C4×Dic15C2211yescharacteristic
24C5×#951—24no—
25C2×C5×#216C2212yes—
26C2×C5×#214C2212yes—
27C2×C5×#208C2211yescharacteristic
28C3×#4097—24no—
29C2×C3×#689C2212yes—
30C2×C3×#687C2212yes—
31C2×C3×#681C2211yescharacteristic
32C2×#6669—22no—
33#91385—22no—
34#91385C2212yes—
35#91385C2212yes—
36#91321—24no—
37C2×#6663C2212yes—
38C2×#6662C2212yes—
39C2×#6660C2212yes—
40#91315—24no—
41C2×#6658C2212yes—
42#90954C2212yes—
43#90951C2212yes—
44#83972—51nomaximal, Hall
45C2×C5×#137—31no—
46#66166—31no—
47C2×#4097D311yescharacteristic, complemented
48C2×#4090—31no—
49C2×#4088—31no—
50C2×#4055—31no—
51#65479—32no—
52#65470—32no—
53#65464—32no—
54#65456—32no—
55M16×Dic5—31no—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C2×#1220—22no—
65C22×Dic15D412yes—
66#6817—22no—
67#6817—22no—
68C2×D60C2311yescharacteristic
69C2×C4×D15—21no—
70C2×Dic30C2311yescharacteristic
71C22×C5×Dic3—21no—
72C2×C5×Dic6—22no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6—21no—
75C2×C5×Dic6C2312yes—
76C22×C3×Dic5—21no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10—21no—
80C2×C3×Dic10C2312yes—
81#6719—22no—
82#6714—22no—
83#6712—22no—
84C4×Dic15D412yes—
85C4×Dic15C2311yescharacteristic
86C4×Dic15C2311yescharacteristic
87C5×#216—24no—
88C5×#214—24no—
89C5×#208D414yescomplemented
90C2×C5×C3⋊C8C2312yes—
91C3×#689—24no—
92C3×#687—24no—
93C3×#681D414yescomplemented
94C2×C3×#168C2312yes—
95#6669—24no—
96#6669—24no—
97#6663—24no—
98#6662—24no—
99#6660—24no—
100#6658—24no—
101C2×C3×#137—51no—
102#5832—51no—
103C2×#951D511yescharacteristic, complemented
104C2×#944—51no—
105C2×#942—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5175—52no—
110#5167—52no—
111Dic3×M16—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4097—24no—
121#4093—31no—
122#4090—31no—
123#4090—32no—
124#4090—32no—
125#4090—62no—
126C2×#689—32no—
127C2×#689C2×D312yes—
128#4088—64no—
129C2×#688—32no—
130#4086—31no—
131#4085—62no—
132#4082—31no—
133C2×#687C2×D312yes—
134C4×C22⋊D5—62no—
135C2×#683—62no—
136C2×C4×Dic5—31no—
137C2×#681C2×D311yescharacteristic
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3152—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C3×C5×Q8—21no—
148C3×C5×Q8—21no—
149C3×C5×D4—21no—
150C3×C5×D4—21no—
151C3×C5×D4—42no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—42no—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—42no—
159#1220—44no—
160C2×Dic15—24no—
161C2×Dic15—21no—
162C2×Dic15C2×D412yes—
163C2×Dic15C2×D412yes—
164D60—21no—
165D60—21no—
166C4×D15—42no—
167Dic30—21no—
168Dic30—21no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—42no—
171C5×Dic6—22no—
172C5×Dic6—22no—
173C5×Dic6—42no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—42no—
176C3×Dic10—22no—
177C3×Dic10—22no—
178C3×Dic10—42no—
179C3×#168C2×D414yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8—51no—
183C2×#235—51no—
184C22×Dic6C2×D511yescharacteristic
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16—51no—
189#951—24no—
190#947—51no—
191#944—51no—
192#944—52no—
193#944—52no—
194#944—102no—
195C2×#216—52no—
196C2×#216C2×D512yes—
197#942—104no—
198C2×#215—52no—
199#940—51no—
200#939—102no—
201#936—51no—
202C2×#214C2×D512yes—
203C4×#67—102no—
204C2×Dic3⋊C4—102no—
205C2×C4×Dic3—51no—
206C2×#208C2×D511yescharacteristic
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C5×#41—22no—
213C5×#41—22no—
214C2×C5×Q8—32no—
215C2×C5×Q8—61no—
216C2×C5×Q8—62no—
217C2×C5×Q8—62no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4C22×D311yescharacteristic
221C22×C4×C5—21no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—62no—
225C2×C22⋊D5—61no—
226C22×Dic5—21no—
227C22×Dic5—32no—
228#709—62no—
229#709—62no—
230C2×D20—31no—
231C2×C4×D5—61no—
232C2×Dic10—22no—
233C2×Dic10—22no—
234C2×Dic10—21no—
235C2×Dic10—31no—
236C2×Dic10C22×D312yes—
237C5×Q16—64no—
238C5×SD16—64no—
239C5×M16—34no—
240C2×C5×C8—32no—
241C22⋊Dic5—62no—
242#689—24no—
243#689—64no—
244#688—64no—
245#687—24no—
246#685—62no—
247#683—64no—
248#683—64no—
249#683—62no—
250C4×Dic5—32no—
251C4×Dic5—31no—
252C4×Dic5—31no—
253#681#6714yescomplemented
254C2×#168C22×D312yes—
255Dic20—64no—
256#677—64no—
257C2×#137—31no—
258C2×#137—51no—
259C2×#137—151no—
260C2×#137—151no—
261#532—151no—
262C2×C4⋊Q8—151no—
263#497—152no—
264#497—152no—
265#494—152no—
266#492—152no—
267C4×M16—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—41no—
274C2×D15—42no—
275C3×C4×C5—41no—
276C3×C4×C5#12712yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C22×D411yescharacteristic
279Dic15—22no—
280Dic15—41no—
281Dic15#13714yescomplemented
282C3×Dic5—42no—
283C5×Dic3—42no—
284C3×#41—22no—
285C3×#41—22no—
286C2×C3×Q8—52no—
287C2×C3×Q8—101no—
288C2×C3×Q8—102no—
289C2×C3×Q8—102no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4C22×D511yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—102no—
297C2×#67—101no—
298C22×Dic3—21no—
299C22×Dic3—52no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—21no—
307C2×Dic6—51no—
308C2×Dic6C22×D512yes—
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16—54no—
312C2×C3×C8—52no—
313#217—102no—
314#216—24no—
315#216—104no—
316#215—104no—
317#214—24no—
318(C2×D3)⋊C4—102no—
319Dic3⋊C4—104no—
320Dic3⋊C4—104no—
321Dic3⋊C4—102no—
322C4×Dic3—52no—
323C4×Dic3—51no—
324C4×Dic3—51no—
325#208C22⋊D514yescomplemented
326C2×C3⋊C8C22×D512yes—
327Dic12—104no—
328#204—104no—
329C23×C5—21no—
330C23×C5D3×D411yescharacteristic
331C22×D5—61no—
332C5×Q8—21no—
333C5×Q8—21no—
334C5×Q8—62no—
335C5×Q8—62no—
336C5×Q8—122no—
337C5×D4—21no—
338C5×D4—21no—
339C5×D4—42no—
340C2×C4×C5—21no—
341C2×C4×C5—42no—
342C2×C4×C5—62no—
343C2×C4×C5—122no—
344C2×C4×C5D3×D412yes—
345C2×C4×C5D3×D411yescharacteristic
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—124no—
349C22⋊D5—122no—
350C2×Dic5—22no—
351C2×Dic5—32no—
352C2×Dic5—32no—
353C2×Dic5—42no—
354C2×Dic5—64no—
355C2×Dic5—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—22no—
360Dic10—22no—
361Dic10—42no—
362Dic10—61no—
363Dic10—61no—
364C5×C8—34no—
365#168C2×#6714yes—
366C2×#41—151no—
367C2×#41D3×D511yescharacteristic
368C22×Q8—31no—
369C22×Q8—51no—
370#137—64no—
371#137—104no—
372#137—304no—
373#137—304no—
374C2×Q16—32no—
375C2×Q16—52no—
376C2×Q16—152no—
377C2×Q16—152no—
378C2×SD16—32no—
379C2×SD16—52no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×M16—31no—
383C2×M16—51no—
384C4⋊Q8—152no—
385C4⋊Q8—152no—
386C4⋊Q8—151no—
387C4⋊Q8—302no—
388#127—151no—
389#124—151no—
390#124—151no—
391#121—302no—
392C4×D4—302no—
393C2×C4⋊C4—302no—
394C2×C42—151no—
395#97—152no—
396C4×C8—152no—
397C2×C3×C5—22no—
398C2×C3×C5—81no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5C2×#13712yes—
401D15—81no—
402C23×C3—21no—
403C23×C3D4×D511yescharacteristic
404C22×D3—101no—
405C3×Q8—21no—
406C3×Q8—21no—
407C3×Q8—102no—
408C3×Q8—102no—
409C3×Q8—202no—
410C3×D4—21no—
411C3×D4—21no—
412C3×D4—42no—
413C2×C3×C4—21no—
414C2×C3×C4—42no—
415C2×C3×C4—102no—
416C2×C3×C4—202no—
417C2×C3×C4D4×D512yes—
418C2×C3×C4D4×D511yescharacteristic
419C2×C3×C4C2×C22⋊D512yes—
420C2×C3×C4C23×D511yescharacteristic
421#67—204no—
422#67—202no—
423C2×Dic3—22no—
424C2×Dic3—42no—
425C2×Dic3—52no—
426C2×Dic3—52no—
427C2×Dic3—104no—
428C2×Dic3—101no—
429D12—101no—
430D12—101no—
431C4×D3—202no—
432Dic6—22no—
433Dic6—22no—
434Dic6—42no—
435Dic6—101no—
436Dic6—101no—
437C3×C8—54no—
438C3⋊C8C2×C22⋊D514yes—
439C22×C5—22no—
440C22×C5—42no—
441C22×C5—41no—
442C22×C5#94012yes—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—122no—
445C2×D5—121no—
446C4×C5—41no—
447C4×C5—122no—
448C4×C5#94012yes—
449C4×C5C2×D3×D411yescharacteristic
450C4×C5C22×#6711yescharacteristic
451Dic5—34no—
452Dic5—42no—
453Dic5—62no—
454Dic5—121no—
455#41—22no—
456#41—22no—
457#41—302no—
458#41—302no—
459C2×Q8—32no—
460C2×Q8—52no—
461C2×Q8—61no—
462C2×Q8—62no—
463C2×Q8—62no—
464C2×Q8—101no—
465C2×Q8—102no—
466C2×Q8—102no—
467C2×Q8—151no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—151no—
471C2×D4—302no—
472C2×D4—301no—
473C2×D4C2×D3×D511yescharacteristic
474C22×C4—21no—
475C22×C4—61no—
476C22×C4—101no—
477C22×C4—152no—
478C22×C4—301no—
479C22×C4C2×D3×D511yescharacteristic
480Q16—64no—
481Q16—104no—
482Q16—304no—
483Q16—304no—
484SD16—64no—
485SD16—104no—
486SD16—304no—
487SD16—304no—
488M16—34no—
489M16—54no—
490C2×C8—32no—
491C2×C8—52no—
492C4⋊C4—302no—
493C4⋊C4—304no—
494C4⋊C4—304no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C42—152no—
498C42—151no—
499C42—151no—
500C3×C5#315211yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3#408612yes—
505C22×C3C2×D4×D511yescharacteristic
506C2×D3—202no—
507C2×D3—201no—
508C3×C4—41no—
509C3×C4—202no—
510C3×C4#408612yes—
511C3×C4C2×D4×D511yescharacteristic
512C3×C4C22×C22⋊D511yescharacteristic
513Dic3—42no—
514Dic3—54no—
515Dic3—102no—
516Dic3—201no—
517C2×C5—22no—
518C2×C5—81no—
519C2×C5D3×#13712yes—
520C2×C5C2×#94011yescharacteristic
521D5—241no—
522C23—21no—
523C23—301no—
524C23#679011yescharacteristic
525Q8—21no—
526Q8—21no—
527Q8—62no—
528Q8—62no—
529Q8—102no—
530Q8—102no—
531Q8—122no—
532Q8—202no—
533Q8—301no—
534Q8—301no—
535D4—21no—
536D4—21no—
537D4—42no—
538D4—301no—
539D4—301no—
540D4—604no—
541D4—602no—
542C2×C4—21no—
543C2×C4—42no—
544C2×C4—62no—
545C2×C4—102no—
546C2×C4—122no—
547C2×C4—152no—
548C2×C4—152no—
549C2×C4—202no—
550C2×C4—304no—
551C2×C4—301no—
552C2×C4—602no—
553C2×C4D5×#6712yes—
554C2×C4D3×C22⋊D512yes—
555C2×C4#679011yescharacteristic
556C2×C4C22×D3×D511yescharacteristic
557C8—34no—
558C8—54no—
559C2×C3—22no—
560C2×C3—81no—
561C2×C3D5×#13712yes—
562C2×C3C2×#408611yescharacteristic
563D3—401no—
564C5#8397211yescharacteristic, complemented, Sylow
565C22—22no—
566C22—42no—
567C22—41no—
568C22—602no—
569C22—601no—
570C22#9156712yes—
571C22C2×#679011yescharacteristic
572C4—41no—
573C4—122no—
574C4—154no—
575C4—202no—
576C4—302no—
577C4—601no—
578C4#9156712yes—
579C4C2×D5×#6711yescharacteristic
580C4C2×D3×C22⋊D511yescharacteristic
581C3#1061570311yescharacteristic, complemented, Sylow
582C2—22no—
583C2—81no—
584C2—1201no—
585C2#1175534212yes—
586C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radical#11756591C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3152
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C5×#951C2semidirect
3. C2×C3×#4097C2semidirect
4. C2×#91385C2semidirect
5. C2×#91321C2semidirect
6. C2×#91315C2semidirect
7. #11749356C2semidirect
8. #11749355C2semidirect
9. #11749111C2semidirect
10. #11749109C2semidirect
11. #11748328C2semidirect
47. C2×#4097D3semidirect
89. C5×#208D4semidirect
93. C3×#681D4semidirect
103. C2×#951D5semidirect
253. #681#67semidirect
281. Dic15#137semidirect
325. #208C22⋊D5semidirect
500. C3×C5#3152semidirect
564. C5#83972semidirect
581. C3#10615703semidirect

Maximal subgroups

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

subgroupindex
#117565912
C2×C5×#9512
C2×C3×#40972
C2×#913852
C2×#913212
C2×#913152
#117493562
#117493552
#117491112
#117491092
#117483282
#106157033
#839725