Finite Group Databasebeta

← #14439252

Subgroups — #14439252

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×#91798C211yesmaximal, characteristic, complemented
2C2×C5×#909C211yesmaximal, characteristic, complemented
3#11754572C211yesmaximal, characteristic
4C2×#91376C211yesmaximal, characteristic, complemented
5C2×#91322C211yesmaximal, characteristic, complemented
6C2×#91321C211yesmaximal, characteristic, complemented
7C3×M16×Dic5C211yesmaximal, characteristic, complemented
8#11748026C212yesmaximal, complemented
9#11748024C212yesmaximal, complemented
10#11748018C212yesmaximal, complemented
11#11747994C212yesmaximal, complemented
12#10615703—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C5×Dic6C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91798—24no—
19C2×Dic60C2212yes—
20C2×#6706C2212yes—
21C5×#909—24no—
22C2×C5×Dic12C2212yes—
23C2×C5×#204C2212yes—
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91566—22no—
27C2×#6668—22no—
28#91451C2211yescharacteristic
29C4×#1203—22no—
30#91376—22no—
31#91376C2212yes—
32#91376C2212yes—
33#91376C2211yescharacteristic
34#91375C2211yescharacteristic
35#91373C2211yescharacteristic
36#91322—24no—
37#91321—24no—
38C2×#6663C2212yes—
39C2×#6663C2212yes—
40C2×#6660C2212yes—
41C2×#6659C2212yes—
42C3×#3947C2212yes—
43C3×C8×Dic5C2212yes—
44#78538—51nomaximal, Hall
45C2×C5×#137—31no—
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×Dic5D311yescharacteristic, complemented
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30—22no—
64C2×Dic30—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C2×Dic30C2311yescharacteristic
68C2×C5×#67—21no—
69C22×C5×Dic3—21no—
70C5×#235—22no—
71C5×#235—22no—
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6—22no—
75C2×C5×Dic6—22no—
76C2×C5×Dic6—21no—
77C2×C5×Dic6C2312yes—
78C2×C5×Dic6C2311yescharacteristic
79C22×C3×Dic5D412yes—
80C2×#1203—22no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83Dic60—24no—
84#6706—24no—
85C5×Dic12—24no—
86C5×#204—24no—
87C3×C4×Dic5D412yes—
88C3×C4×Dic5C2311yescharacteristic
89C3×C4×Dic5C2311yescharacteristic
90C3×#681D414yescomplemented
91C2×C3×#168C2312yes—
92#6668—22no—
93#6668—24no—
94#6668—24no—
95#6667—22no—
96(C2×D3)⋊Dic5—22no—
97#6663—24no—
98#6663—24no—
99#6660—24no—
100#6659—24no—
101C2×#909—51no—
102C2×#909—51no—
103C2×#909—51no—
104C2×#909D511yescharacteristic, complemented
105#5477—51no—
106C2×#869—51no—
107C3×C4×M16—51no—
108#4715—52no—
109#4715—52no—
110#4699—52no—
111#4693—52no—
112C2×C5×#41—31no—
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×Dic10—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
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×Dic5C2×D311yescharacteristic
137C2×#681C2×D311yescharacteristic
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947C2×D312yes—
142C8×Dic5C2×D312yes—
143#3152—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C5×D3—21no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—42no—
152C2×Dic15—21no—
153C2×Dic15—22no—
154C2×Dic15—42no—
155D60—21no—
156D60—21no—
157C4×D15—42no—
158Dic30—22no—
159Dic30—21no—
160Dic30—22no—
161Dic30—21no—
162Dic30—42no—
163C5×#67—42no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—42no—
167C5×D12—21no—
168C5×D12—21no—
169C4×C5×D3—42no—
170C5×Dic6—22no—
171C5×Dic6—21no—
172C5×Dic6—22no—
173C5×Dic6—21no—
174C5×Dic6—42no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5C2×D412yes—
178#1203—44no—
179C3×C5×C8C2×D414yes—
180C3×#168C2×D414yes—
181C2×#235—51no—
182C2×#235C2×D511yescharacteristic
183C22×Dic6—51no—
184C22×Dic6C2×D511yescharacteristic
185C2×C3×M16—51no—
186C2×C3×M16C2×D511yescharacteristic
187C2×C3×C42—51no—
188#930—102no—
189C2×C4⋊Dic3—102no—
190#909—24no—
191#909—104no—
192#909—104no—
193#909—104no—
194C2×Dic12—52no—
195C2×Dic12—52no—
196C2×Dic12—52no—
197C2×Dic12C2×D512yes—
198C2×#204—52no—
199C2×#204—52no—
200C2×#204—52no—
201C2×#204C2×D512yes—
202#875—51no—
203#875—51no—
204#874—51no—
205C4×D12—102no—
206#869—52no—
207#869—51no—
208#869—52no—
209#869—102no—
210C3×#97—52no—
211C3×C4×C8—52no—
212C5×#41—62no—
213C5×#41—62no—
214C2×C5×Q8—32no—
215C2×C5×Q8—31no—
216C2×C5×Q8—61no—
217C2×C5×Q8—62no—
218C2×C5×Q8—62no—
219C2×C5×D4—31no—
220C2×C5×D4—61no—
221C22×C4×C5—61no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—61no—
225C2×C22⋊D5—62no—
226C22×Dic5—61no—
227C22×Dic5D1212yes—
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—64no—
238C5×SD16—64no—
239C5×M16D1214yescomplemented
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×Dic5D1212yes—
251C4×Dic5C22×D311yescharacteristic
252C4×Dic5C22×D311yescharacteristic
253#681D1214yescomplemented
254C2×#168C22×D312yes—
255Dic20—64no—
256#677—64no—
257C2×#137—31no—
258C2×#137—151no—
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—51no—
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—
275C3×C4×C5#12712yes—
276C3×C4×C5C22×D411yescharacteristic
277C3×C4×C5C22×D411yescharacteristic
278Dic15—42no—
279Dic15—41no—
280C3×Dic5—22no—
281C3×Dic5#13714yescomplemented
282C5×Dic3—42no—
283C5×Dic3—41no—
284C22×C3×C4—52no—
285C22×C3×C4C22×D511yescharacteristic
286C2×#67—21no—
287C2×#67—101no—
288C22×Dic3—21no—
289C22×Dic3—101no—
290#235—22no—
291#235—22no—
292#235—102no—
293#235—102no—
294C2×D12—51no—
295C2×D12—102no—
296C2×D12C22×D511yescharacteristic
297C2×C4×D3—21no—
298C2×C4×D3—101no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6—52no—
303C2×Dic6—51no—
304C2×Dic6—102no—
305C2×Dic6—102no—
306C2×Dic6—101no—
307C2×Dic6C22×D512yes—
308C2×Dic6C22×D511yescharacteristic
309C3×M16—54no—
310C3×M16C22⋊D514yescomplemented
311C2×C3×C8—52no—
312C2×C3×C8C22×D512yes—
313C3×C42—52no—
314C3×C42—51no—
315C3×C42—51no—
316(C2×D3)⋊C4—102no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—104no—
319C4⋊Dic3—104no—
320C4⋊Dic3—102no—
321Dic12—24no—
322Dic12—104no—
323Dic12—104no—
324Dic12—104no—
325#204—24no—
326#204—104no—
327#204—104no—
328#204—104no—
329C23×C5—61no—
330C23×C5C2×D1211yescharacteristic
331C22×D5—61no—
332C5×Q8—62no—
333C5×Q8—61no—
334C5×Q8—62no—
335C5×Q8—61no—
336C5×Q8—122no—
337C5×D4—61no—
338C5×D4—61no—
339C5×D4—122no—
340C2×C4×C5—62no—
341C2×C4×C5—61no—
342C2×C4×C5—122no—
343C2×C4×C5—122no—
344C2×C4×C5C2×D1211yescharacteristic
345C2×C4×C5C2×D1212yes—
346C2×C4×C5C2×D1212yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—122no—
349C22⋊D5—124no—
350C2×Dic5—24no—
351C2×Dic5—62no—
352C2×Dic5—61no—
353C2×Dic5—122no—
354C2×Dic5C2×D1212yes—
355C2×Dic5C2×D1212yes—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—62no—
360Dic10—61no—
361Dic10—62no—
362Dic10—61no—
363Dic10—122no—
364C5×C8C2×D1214yes—
365#168C2×D1214yes—
366C2×#41—31no—
367C2×#41—151no—
368C22×Q8—31no—
369C22×Q8—151no—
370#137—64no—
371#137—304no—
372#137—304no—
373#137—304no—
374C2×Q16—32no—
375C2×Q16—152no—
376C2×Q16—152no—
377C2×Q16—152no—
378C2×SD16—32no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×M16—51no—
383C2×M16D3×D511yescharacteristic
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—51no—
395#97—52no—
396C4×C8—52no—
397C2×C3×C5—22no—
398C2×C3×C5C2×#12711yescharacteristic
399C2×C3×C5C2×#13712yes—
400D15—81no—
401C5×D3—81no—
402C23×C3D4×D511yescharacteristic
403C22×D3—21no—
404C22×D3—101no—
405C2×C3×C4—52no—
406C2×C3×C4—52no—
407C2×C3×C4—104no—
408C2×C3×C4D4×D512yes—
409C2×C3×C4D4×D511yescharacteristic
410C2×C3×C4C2×C22⋊D512yes—
411C2×C3×C4C23×D511yescharacteristic
412#67—42no—
413#67—202no—
414C2×Dic3—22no—
415C2×Dic3—21no—
416C2×Dic3—42no—
417C2×Dic3—102no—
418C2×Dic3—101no—
419C2×Dic3—202no—
420D12—21no—
421D12—21no—
422D12—101no—
423D12—101no—
424D12—204no—
425C4×D3—42no—
426C4×D3—202no—
427Dic6—22no—
428Dic6—21no—
429Dic6—22no—
430Dic6—21no—
431Dic6—42no—
432Dic6—102no—
433Dic6—101no—
434Dic6—102no—
435Dic6—101no—
436Dic6—202no—
437C3×C8—54no—
438C3×C8C2×C22⋊D514yes—
439C22×C5—22no—
440C22×C5—121no—
441C22×C5—122no—
442C22×C5#87412yes—
443C22×C5C22×D1211yescharacteristic
444C2×D5—121no—
445C2×D5—122no—
446C4×C5—121no—
447C4×C5—122no—
448C4×C5#87412yes—
449C4×C5C22×D1211yescharacteristic
450C4×C5C22×D1211yescharacteristic
451Dic5—22no—
452Dic5—122no—
453Dic5—121no—
454Dic5#90914yescomplemented
455#41—62no—
456#41—62no—
457#41—302no—
458#41—302no—
459C2×Q8—31no—
460C2×Q8—32no—
461C2×Q8—61no—
462C2×Q8—62no—
463C2×Q8—62no—
464C2×Q8—151no—
465C2×Q8—152no—
466C2×Q8—301no—
467C2×Q8—302no—
468C2×Q8—302no—
469C2×D4—31no—
470C2×D4—61no—
471C2×D4—151no—
472C2×D4—302no—
473C2×D4—301no—
474C22×C4—52no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4C2×D3×D511yescharacteristic
480Q16—64no—
481Q16—304no—
482Q16—304no—
483Q16—304no—
484SD16—64no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488M16—54no—
489M16#120314yescomplemented
490C2×C8—52no—
491C2×C8C2×D3×D512yes—
492C4⋊C4—304no—
493C4⋊C4—304no—
494C4⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C42—52no—
498C42—51no—
499C42—51no—
500C3×C5#315211yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3#408612yes—
503C22×C3C2×D4×D511yescharacteristic
504C2×D3—42no—
505C2×D3—41no—
506C2×D3—202no—
507C2×D3—201no—
508C3×C4—54no—
509C3×C4—102no—
510C3×C4#408612yes—
511C3×C4C2×D4×D511yescharacteristic
512C3×C4C22×C22⋊D511yescharacteristic
513Dic3—42no—
514Dic3—41no—
515Dic3—202no—
516Dic3—201no—
517C2×C5—22no—
518C2×C5—241no—
519C2×C5C2×#87411yescharacteristic
520C2×C5C2×#90912yes—
521D5—241no—
522C23—61no—
523C23—301no—
524C23D5×D1211yescharacteristic
525Q8—62no—
526Q8—61no—
527Q8—62no—
528Q8—61no—
529Q8—122no—
530Q8—302no—
531Q8—301no—
532Q8—302no—
533Q8—301no—
534Q8—602no—
535D4—61no—
536D4—61no—
537D4—122no—
538D4—301no—
539D4—301no—
540D4—604no—
541D4—602no—
542C2×C4—52no—
543C2×C4—52no—
544C2×C4—61no—
545C2×C4—62no—
546C2×C4—104no—
547C2×C4—122no—
548C2×C4—122no—
549C2×C4—301no—
550C2×C4—302no—
551C2×C4—602no—
552C2×C4—602no—
553C2×C4D5×D1211yescharacteristic
554C2×C4D5×D1212yes—
555C2×C4C2×#120312yes—
556C2×C4C22×D3×D511yescharacteristic
557C8—54no—
558C8C2×#120314yes—
559C2×C3—22no—
560C2×C3D5×#13712yes—
561C2×C3C2×#408611yescharacteristic
562D3—81no—
563D3—401no—
564C5#7853811yescharacteristic, complemented, Sylow
565C22—22no—
566C22—122no—
567C22—121no—
568C22—602no—
569C22—601no—
570C22#9145112yes—
571C22C2×D5×D1211yescharacteristic
572C4—54no—
573C4—102no—
574C4—121no—
575C4—122no—
576C4—601no—
577C4—602no—
578C4#9145112yes—
579C4C2×D5×D1211yescharacteristic
580C4C22×#120311yescharacteristic
581C3#1061570311yescharacteristic, complemented, Sylow
582C2—22no—
583C2—241no—
584C2—1201no—
585C2D5×#90912yes—
586C2C2×#9145111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radical#11754572C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3152
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91798C2semidirect
2. C2×C5×#909C2semidirect
4. C2×#91376C2semidirect
5. C2×#91322C2semidirect
6. C2×#91321C2semidirect
7. C3×M16×Dic5C2semidirect
8. #11748026C2semidirect
9. #11748024C2semidirect
10. #11748018C2semidirect
11. #11747994C2semidirect
55. M16×Dic5D3semidirect
81. C3×C5×M16D4semidirect
90. C3×#681D4semidirect
104. C2×#909D5semidirect
239. C5×M16D12semidirect
253. #681D12semidirect
281. C3×Dic5#137semidirect
310. C3×M16C22⋊D5semidirect
454. Dic5#909semidirect
489. M16#1203semidirect
500. C3×C5#3152semidirect
564. C5#78538semidirect
581. C3#10615703semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
C2×C5×#9092
#117545722
C2×#913762
C2×#913222
C2×#913212
C3×M16×Dic52
#117480262
#117480242
#117480182
#117479942
#106157033
#785385