Finite Group Databasebeta

← #14439203

Subgroups — #14439203

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
1C2×C3×C5×#137C211yesmaximal, characteristic, complemented
2#11756591C211yesmaximal, characteristic
3C2×#91840C211yesmaximal, characteristic, complemented
4C2×#91833C211yesmaximal, characteristic, complemented
5C2×#91831C211yesmaximal, characteristic, complemented
6C2×#91798C211yesmaximal, characteristic, complemented
7#11751291C212yesmaximal, complemented
8#11751284C212yesmaximal, complemented
9#11751276C212yesmaximal, complemented
10#11751268C212yesmaximal, complemented
11M16×Dic15C211yesmaximal, characteristic, complemented
12#10615703—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×C5×Q8C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C22×Dic30C2211yescharacteristic
17C3×C5×#137—24no—
18C2×C3×C5×Q16C2212yes—
19C2×C3×C5×SD16C2212yes—
20C2×C3×C5×M16C2211yescharacteristic
21#91840—24no—
22#91836C2211yescharacteristic
23#91833—22no—
24#91833C2212yes—
25#91833C2212yes—
26#91833C2211yescharacteristic
27C2×#6718C2212yes—
28C2×#6718C2212yes—
29#91831—24no—
30C2×#6717C2212yes—
31#91829C2211yescharacteristic
32#91828—22no—
33#91825C2211yescharacteristic
34C2×#6716C2212yes—
35C4×#1220—22no—
36C2×#6712—22no—
37C2×C4×Dic15C2211yescharacteristic
38C2×#6710C2211yescharacteristic
39#91798—24no—
40C2×Dic60C2212yes—
41C2×#6706C2212yes—
42#91099C2212yes—
43C8×Dic15C2212yes—
44#83972—51nomaximal, Hall
45C2×C5×#137D311yescharacteristic, complemented
46#66166—31no—
47C2×#4097—31no—
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×Q8—21no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8—22no—
61C2×C3×C5×Q8C2312yes—
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4—21no—
64C2×C3×C5×D4C2311yescharacteristic
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—21no—
69C2×#1220—22no—
70C22×Dic15—21no—
71C22×Dic15D412yes—
72#6817—22no—
73#6817—22no—
74C2×D60C2311yescharacteristic
75C2×C4×D15—21no—
76C2×Dic30—22no—
77C2×Dic30—22no—
78C2×Dic30—21no—
79C2×Dic30C2312yes—
80C2×Dic30C2311yescharacteristic
81C3×C5×Q16—24no—
82C3×C5×SD16—24no—
83C3×C5×M16D414yescomplemented
84C2×C3×C5×C8C2312yes—
85#6719—22no—
86#6718—24no—
87#6718—24no—
88#6717—24no—
89#6716—24no—
90#6714—22no—
91#6712—24no—
92#6712—24no—
93#6712—22no—
94C4×Dic15D412yes—
95C4×Dic15C2311yescharacteristic
96C4×Dic15C2311yescharacteristic
97#6710D414yescomplemented
98C2×C3⋊#168C2312yes—
99Dic60—24no—
100#6706—24no—
101C2×C3×#137D511yescharacteristic, complemented
102#5832—51no—
103C2×#951—51no—
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×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C22×Dic10—31no—
116C5×#137—24no—
117C2×C5×Q16C2×D312yes—
118C2×C5×SD16C2×D312yes—
119C2×C5×M16C2×D311yescharacteristic
120#4097—64no—
121#4093—31no—
122#4090—32no—
123#4090—32no—
124#4090—31no—
125#4090—62no—
126C2×#689—32no—
127C2×#689—32no—
128#4088—64no—
129C2×#688—32no—
130#4086—31no—
131#4085—62no—
132#4082—31no—
133C2×#687—32no—
134C4×C22⋊D5—62no—
135C2×#683—62no—
136C2×C4×Dic5—31no—
137C2×#681—31no—
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—22no—
148C3×C5×Q8—21no—
149C3×C5×Q8—22no—
150C3×C5×Q8—21no—
151C3×C5×Q8—42no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—42no—
158C2×C3×C4×C5—42no—
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5C2411yescharacteristic
163#1220—42no—
164#1220—44no—
165C2×Dic15—24no—
166C2×Dic15—22no—
167C2×Dic15—21no—
168C2×Dic15—42no—
169C2×Dic15C2×D412yes—
170C2×Dic15C2×D412yes—
171D60—21no—
172D60—21no—
173C4×D15—42no—
174Dic30—22no—
175Dic30—21no—
176Dic30—22no—
177Dic30—21no—
178Dic30—42no—
179C3×C5×C8C2×D414yes—
180C3⋊#168C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8C2×D511yescharacteristic
183C2×#235—51no—
184C22×Dic6—51no—
185C3×#137—24no—
186C2×C3×Q16C2×D512yes—
187C2×C3×SD16C2×D512yes—
188C2×C3×M16C2×D511yescharacteristic
189#951—104no—
190#947—51no—
191#944—52no—
192#944—52no—
193#944—51no—
194#944—102no—
195C2×#216—52no—
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199#940—51no—
200#939—102no—
201#936—51no—
202C2×#214—52no—
203C4×#67—102no—
204C2×Dic3⋊C4—102no—
205C2×C4×Dic3—51no—
206C2×#208—51no—
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C5×#41—22no—
213C5×#41—22no—
214C2×C5×Q8—21no—
215C2×C5×Q8—22no—
216C2×C5×Q8—22no—
217C2×C5×Q8C22×D312yes—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4C22×D311yescharacteristic
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—62no—
225C2×C22⋊D5—61no—
226C22×Dic5—32no—
227C22×Dic5—61no—
228#709—62no—
229#709—62no—
230C2×D20—31no—
231C2×C4×D5—61no—
232C2×Dic10—32no—
233C2×Dic10—31no—
234C2×Dic10—62no—
235C2×Dic10—62no—
236C2×Dic10—61no—
237C5×Q16—24no—
238C5×SD16—24no—
239C5×M16#6714yescomplemented
240C2×C5×C8C22×D312yes—
241C22⋊Dic5—62no—
242#689—64no—
243#689—64no—
244#688—64no—
245#687—64no—
246#685—62no—
247#683—64no—
248#683—64no—
249#683—62no—
250C4×Dic5—32no—
251C4×Dic5—31no—
252C4×Dic5—31no—
253#681—34no—
254C2×#168—32no—
255Dic20—64no—
256#677—64no—
257C2×#137—151no—
258C2×#137—151no—
259C2×#137—151no—
260C2×#137D1511yescharacteristic, complemented
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—42no—
277C3×C4×C5#12712yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C22×D411yescharacteristic
280Dic15—22no—
281Dic15—42no—
282Dic15—41no—
283Dic15#13714yescomplemented
284C3×#41—22no—
285C3×#41—22no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8C22×D512yes—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4C22×D511yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—102no—
297C2×#67—101no—
298C22×Dic3—52no—
299C22×Dic3—101no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—52no—
305C2×Dic6—51no—
306C2×Dic6—102no—
307C2×Dic6—102no—
308C2×Dic6—101no—
309C3×Q16—24no—
310C3×SD16—24no—
311C3×M16C22⋊D514yescomplemented
312C2×C3×C8C22×D512yes—
313#217—102no—
314#216—104no—
315#216—104no—
316#215—104no—
317#214—104no—
318(C2×D3)⋊C4—102no—
319Dic3⋊C4—104no—
320Dic3⋊C4—104no—
321Dic3⋊C4—102no—
322C4×Dic3—52no—
323C4×Dic3—51no—
324C4×Dic3—51no—
325#208—54no—
326C2×C3⋊C8—52no—
327Dic12—104no—
328#204—104no—
329C23×C5—21no—
330C23×C5D3×D411yescharacteristic
331C22×D5—61no—
332C5×Q8—22no—
333C5×Q8—21no—
334C5×Q8—22no—
335C5×Q8—21no—
336C5×Q8—42no—
337C5×D4—21no—
338C5×D4—21no—
339C5×D4—42no—
340C2×C4×C5—22no—
341C2×C4×C5—21no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5D3×D412yes—
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—124no—
349C22⋊D5—122no—
350C2×Dic5—32no—
351C2×Dic5—32no—
352C2×Dic5—64no—
353C2×Dic5—62no—
354C2×Dic5—61no—
355C2×Dic5—122no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—62no—
360Dic10—61no—
361Dic10—62no—
362Dic10—61no—
363Dic10—122no—
364C5×C8C2×#6714yes—
365#168—34no—
366C2×#41—151no—
367C2×#41C2×D1511yescharacteristic
368C22×Q8—151no—
369C22×Q8C2×D1511yescharacteristic
370#137—24no—
371#137—304no—
372#137—304no—
373#137—304no—
374C2×Q16—152no—
375C2×Q16—152no—
376C2×Q16—152no—
377C2×Q16C2×D1512yes—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16C2×D1512yes—
382C2×M16—151no—
383C2×M16C2×D1511yescharacteristic
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—22no—
406C3×Q8—21no—
407C3×Q8—22no—
408C3×Q8—21no—
409C3×Q8—42no—
410C3×D4—21no—
411C3×D4—21no—
412C3×D4—42no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
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—52no—
424C2×Dic3—52no—
425C2×Dic3—104no—
426C2×Dic3—102no—
427C2×Dic3—101no—
428C2×Dic3—202no—
429D12—101no—
430D12—101no—
431C4×D3—202no—
432Dic6—102no—
433Dic6—101no—
434Dic6—102no—
435Dic6—101no—
436Dic6—202no—
437C3×C8C2×C22⋊D514yes—
438C3⋊C8—54no—
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—42no—
448C4×C5#94012yes—
449C4×C5C2×D3×D411yescharacteristic
450C4×C5C22×#6711yescharacteristic
451Dic5—34no—
452Dic5—62no—
453Dic5—122no—
454Dic5—121no—
455#41—22no—
456#41—22no—
457#41—302no—
458#41—302no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—151no—
463C2×Q8—152no—
464C2×Q8—301no—
465C2×Q8—302no—
466C2×Q8—302no—
467C2×Q8C22×D1511yescharacteristic
468C2×Q8C22×D1512yes—
469C2×D4—21no—
470C2×D4—151no—
471C2×D4—302no—
472C2×D4—301no—
473C2×D4C22×D1511yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—152no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4C22×D1511yescharacteristic
480Q16—24no—
481Q16—304no—
482Q16—304no—
483Q16—304no—
484SD16—24no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488M16—154no—
489M16#122014yescomplemented
490C2×C8—152no—
491C2×C8C22×D1512yes—
492C4⋊C4—304no—
493C4⋊C4—304no—
494C4⋊C4—302no—
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—42no—
510C3×C4#408612yes—
511C3×C4C2×D4×D511yescharacteristic
512C3×C4C22×C22⋊D511yescharacteristic
513Dic3—54no—
514Dic3—102no—
515Dic3—202no—
516Dic3—201no—
517C2×C5—22no—
518C2×C5—81no—
519C2×C5D3×#13712yes—
520C2×C5C2×#94011yescharacteristic
521D5—241no—
522C23—21no—
523C23—301no—
524C23D4×D1511yescharacteristic
525Q8—22no—
526Q8—21no—
527Q8—22no—
528Q8—21no—
529Q8—42no—
530Q8—302no—
531Q8—301no—
532Q8—302no—
533Q8—301no—
534Q8—602no—
535D4—21no—
536D4—21no—
537D4—42no—
538D4—301no—
539D4—301no—
540D4—604no—
541D4—602no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—152no—
547C2×C4—152no—
548C2×C4—304no—
549C2×C4—301no—
550C2×C4—302no—
551C2×C4—602no—
552C2×C4—602no—
553C2×C4D4×D1511yescharacteristic
554C2×C4D4×D1512yes—
555C2×C4C2×#122012yes—
556C2×C4C23×D1511yescharacteristic
557C8—154no—
558C8C2×#122014yes—
559C2×C3—22no—
560C2×C3—81no—
561C2×C3D5×#13712yes—
562C2×C3C2×#408611yescharacteristic
563D3—401no—
564C5#8397211yescharacteristic, complemented, Sylow
565C22—22no—
566C22—41no—
567C22—42no—
568C22—601no—
569C22—602no—
570C22#9182912yes—
571C22C2×D4×D1511yescharacteristic
572C4—41no—
573C4—42no—
574C4—154no—
575C4—302no—
576C4—601no—
577C4—602no—
578C4#9182912yes—
579C4C2×D4×D1511yescharacteristic
580C4C22×#122011yescharacteristic
581C3#1061570311yescharacteristic, complemented, Sylow
582C2—22no—
583C2—81no—
584C2—1201no—
585C2D15×#13712yes—
586C2C2×#9182911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
prime radical#11756591C2
hypercenterC2×#137D15
hypocenterC3×C5#3152
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#137C2semidirect
3. C2×#91840C2semidirect
4. C2×#91833C2semidirect
5. C2×#91831C2semidirect
6. C2×#91798C2semidirect
7. #11751291C2semidirect
8. #11751284C2semidirect
9. #11751276C2semidirect
10. #11751268C2semidirect
11. M16×Dic15C2semidirect
45. C2×C5×#137D3semidirect
83. C3×C5×M16D4semidirect
97. #6710D4semidirect
101. C2×C3×#137D5semidirect
239. C5×M16#67semidirect
260. C2×#137D15semidirect
283. Dic15#137semidirect
311. C3×M16C22⋊D5semidirect
489. M16#1220semidirect
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
C2×C3×C5×#1372
#117565912
C2×#918402
C2×#918332
C2×#918312
C2×#917982
#117512912
#117512842
#117512762
#117512682
M16×Dic152
#106157033
#839725