Finite Group Databasebeta

← #14424506

Subgroups — #14424506

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3#11754609C211yesmaximal, characteristic, complemented
4C22×#6658C211yesmaximal, characteristic, complemented
5C5×#5233C211yesmaximal, characteristic, complemented
6#11749268C214yesmaximal, complemented
7#11749026C214yesmaximal, complemented
8#11748399C211yesmaximal, characteristic, complemented
9#11748342C211yesmaximal, characteristic, complemented
10#10610567—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×D60C2211yescharacteristic
13C3×#4150—24no—
14C3×#4150—24no—
15C2×C3×Q8×D5C2212yescomplemented
16C2×C3×#711—22no—
17C2×C3×#711C2212yescomplemented
18C2×C3×#709—21no—
19C2×C3×#709C2211yescharacteristic
20C22×C3×Dic10—21no—
21C22×C3×Dic10C2211yescharacteristic
22#91838—24no—
23C2×#6717C2212yes—
24C2×#6715C2212yes—
25C2×#6710C2211yescharacteristic
26C5×#926C2211yescharacteristic
27C22×C5×C3⋊C8C2211yescharacteristic
28#91572—22no—
29#91458—21no—
30#91450C2214yes—
31#91374—21no—
32C2×#6658—24no—
33C2×#6658C2214yes—
34C5×#835C2212yescomplemented
35C5×#832C2212yescomplemented
36#90970C2214yescomplemented
37#90955C2214yescomplemented
38#84113—51nomaximal, Hall
39C2×#4150D311yescharacteristic, complemented
40C2×#4095—31no—
41C22×#677—31no—
42#65859—31no—
43C5×#416—31no—
44#65399—31no—
45#65293—31no—
46#65095—34no—
47#65070—34no—
48C23×D15—21no—
49C3×C5×#41—22no—
50C3×C5×#41D414yescomplemented
51C2×C3×C5×Q8C2311yescharacteristic
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4C2311yescharacteristic
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×D60—22no—
57C2×D60—22no—
58C2×D60—21no—
59C2×D60C2312yes—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5D412yes—
62C22×C3×Dic5—21no—
63C22×C3×Dic5—22no—
64C3×Q8×D5—24no—
65C3×Q8×D5—24no—
66C3×#711—216no—
67C3×#711—24no—
68C3×#711—24no—
69C3×#709—28no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20D411yescharacteristic
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5C2312yes—
75C2×C3×Dic10—28no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—22no—
79C2×C3×Dic10D411yescharacteristic
80C2×C3×Dic10D414yescomplemented
81C2×C3×Dic10C2312yes—
82C2×#1202—24no—
83#6717—24no—
84#6715—24no—
85#6710—22no—
86C2×C3⋊#168C2312yes—
87C5×#217—21no—
88C5×C4⋊Dic3C2312yes—
89C4×C5×Dic3—21no—
90C2×C5×C3⋊C8—22no—
91C2×C5×C3⋊C8C2312yes—
92#6667—24no—
93#6658—28no—
94C2×C3×2−1+4—51no—
95#5830—51no—
96C2×#949—51no—
97C22×#215—51no—
98#5238—54no—
99#5234—51no—
100#5233D511yescharacteristic, complemented
101#5227—54no—
102#5225—51no—
103C2×C5×#41C2×D311yescharacteristic
104#4150—24no—
105#4150—24no—
106C2×Q8×D5C2×D312yescomplemented
107C2×#711—22no—
108C2×#711C2×D312yescomplemented
109C2×#709—21no—
110C2×#709C2×D311yescharacteristic
111C22×D20—31no—
112C22×Dic10—21no—
113C22×Dic10C2×D311yescharacteristic
114C22×C5×C8—31no—
115C5×#117—31no—
116#4095—64no—
117C2×#688—32no—
118C2×#686—32no—
119C2×#681—31no—
120C2×#677—34no—
121C2×#677—64no—
122#4041—34no—
123#4028—62no—
124#4021—61no—
125#4020—61no—
126C5×#103—32no—
127C5×#102—32no—
128#3952—34no—
129#3942—34no—
130#3010—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15—22no—
134C22×D15—42no—
135C22×D15—82no—
136C22×C3×D5C2×D412yes—
137C3×C5×Q8—21no—
138C3×C5×Q8C2×D412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C2×D412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2411yescharacteristic
148D60—22no—
149D60—22no—
150D60—42no—
151C2×C5×Dic3—22no—
152C3×C22⋊D5—28no—
153C3×C22⋊D5—24no—
154C2×C3×Dic5—28no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5C2×D412yes—
158C3×D20—22no—
159C3×C4×D5—28no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×Dic10—28no—
163C3×Dic10—22no—
164C3×Dic10—24no—
165C3×Dic10—22no—
166C3×Dic10C2×D414yes—
167#1202—84no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C3×2−1+4—104no—
171C3×2−1+4—104no—
172C2×C3×#41—51no—
173C2×C3×#41—52no—
174C2×C3×#41—101no—
175C2×C3×#41—102no—
176C2×C3×#41C2×D511yescharacteristic
177C22×C3×Q8—52no—
178C22×C3×Q8—51no—
179C22×C3×Q8—101no—
180C22×D12—51no—
181#949—104no—
182#947—101no—
183C2×#215—52no—
184C2×#215—54no—
185C2×#215—104no—
186#940—101no—
187#937—102no—
188C2×#213—52no—
189#930—54no—
190#926C2×D511yescharacteristic
191C2×#208—51no—
192C22×C3⋊C8C2×D511yescharacteristic
193#835—54no—
194#835C2×D512yescomplemented
195#832C2×D512yescomplemented
196#830—54no—
197C23×D5—61no—
198C5×#41—22no—
199C5×#41#6714yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—22no—
206C2×C22⋊D5#6712yes—
207C22×Dic5—21no—
208C22×Dic5—22no—
209Q8×D5—24no—
210Q8×D5—24no—
211#711—216no—
212#711—24no—
213#711—24no—
214#709—28no—
215#709—22no—
216#709—22no—
217C2×D20—32no—
218C2×D20—62no—
219C2×D20—62no—
220C2×D20—61no—
221C2×D20—64no—
222C2×D20#6711yescharacteristic
223C2×C4×D5—22no—
224C2×C4×D5C22×D312yes—
225C2×Dic10—28no—
226C2×Dic10—21no—
227C2×Dic10—22no—
228C2×Dic10—22no—
229C2×Dic10#6711yescharacteristic
230C2×Dic10#6714yescomplemented
231C2×Dic10C22×D312yes—
232C2×C5×C8—32no—
233C2×C5×C8—62no—
234C5×C4⋊C4—32no—
235C5×C22⋊C4—61no—
236C42×C5—61no—
237#688—64no—
238#686—64no—
239#685—64no—
240#681—62no—
241C2×#168—32no—
242#677—68no—
243C2×2−1+4—51no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—31no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—42no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—42no—
258C2×D15—44no—
259C2×D15—84no—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266C3×Dic5—22no—
267C3×Dic5—24no—
268C5×Dic3—42no—
269C23×D3—101no—
270C3×#41—22no—
271C3×#41—108no—
272C3×#41—104no—
273C3×#41—1016no—
274C3×#41—104no—
275C3×#41—102no—
276C3×#41—102no—
277C3×#41D2014yescomplemented
278C2×C3×Q8—51no—
279C2×C3×Q8—54no—
280C2×C3×Q8—52no—
281C2×C3×Q8—102no—
282C2×C3×Q8—108no—
283C2×C3×Q8—104no—
284C2×C3×Q8—104no—
285C2×C3×Q8—102no—
286C2×C3×Q8—101no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—52no—
290C2×C3×D4—51no—
291C2×C3×D4—102no—
292C2×C3×D4C22×D511yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—52no—
295C22×C3×C4—102no—
296C22×C3×C4—102no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—104no—
300C2×D12—52no—
301C2×D12—102no—
302C2×D12—102no—
303C2×D12—101no—
304#217—21no—
305#215—108no—
306#215—104no—
307#213—104no—
308(C2×D3)⋊C4—104no—
309C4⋊Dic3C22×D512yes—
310C4×Dic3—21no—
311#208—102no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8C22×D512yes—
315C23×C5—21no—
316C23×C5C2×#6711yescharacteristic
317C22×D5—62no—
318C22×D5—122no—
319C22×D5—242no—
320C22×D5C2×#6712yes—
321C5×Q8—21no—
322C5×Q8C2×#6712yes—
323C5×D4—24no—
324C5×D4—21no—
325C5×D4C2×#6712yes—
326C2×C4×C5—21no—
327C2×C4×C5—24no—
328C2×C4×C5—62no—
329C2×C4×C5C2×#6712yes—
330C2×C4×C5C2×#6711yescharacteristic
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—28no—
334C22⋊D5—24no—
335C2×Dic5—28no—
336C2×Dic5—24no—
337C2×Dic5—22no—
338C2×Dic5C2×#6712yes—
339D20—22no—
340D20—62no—
341D20—62no—
342D20—122no—
343D20—244no—
344C4×D5—28no—
345C4×D5—22no—
346C4×D5—22no—
347Dic10—28no—
348Dic10—22no—
349Dic10—24no—
350Dic10—22no—
351Dic10C2×#6714yes—
352C5×C8—62no—
353#168—62no—
3542−1+4—104no—
3552−1+4—104no—
356C2×#41—51no—
357C2×#41—52no—
358C2×#41—101no—
359C2×#41—102no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—52no—
362C22×Q8—51no—
363C22×Q8—101no—
364C22×D4—151no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8—31no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—31no—
377#103—32no—
378#103—154no—
379#102—32no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—82no—
386C3×D5—42no—
387C23×C3—21no—
388C23×C3—52no—
389C23×C3D4×D511yescharacteristic
390C22×D3—102no—
391C22×D3—202no—
392C22×D3—402no—
393C3×Q8—21no—
394C3×Q8—54no—
395C3×Q8—108no—
396C3×Q8—102no—
397C3×Q8—102no—
398C3×Q8—104no—
399C3×Q8C2×D2012yes—
400C3×D4—24no—
401C3×D4—21no—
402C3×D4—108no—
403C3×D4—104no—
404C3×D4—102no—
405C3×D4C2×D2012yes—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—52no—
409C2×C3×C4—108no—
410C2×C3×C4—108no—
411C2×C3×C4—102no—
412C2×C3×C4—104no—
413C2×C3×C4—102no—
414C2×C3×C4—102no—
415C2×C3×C4C2×D2012yes—
416C2×C3×C4D4×D512yes—
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4C23×D511yescharacteristic
419#67—404no—
420C2×Dic3—22no—
421D12—102no—
422D12—102no—
423D12—202no—
424C3⋊C8—22no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—42no—
429C22×C5#95312yes—
430C22×C5C22×#6711yescharacteristic
431C2×D5—24no—
432C2×D5—22no—
433C2×D5—124no—
434C2×D5—122no—
435C2×D5—244no—
436C4×C5—22no—
437C4×C5—122no—
438C4×C5#95312yes—
439C4×C5C22×#6711yescharacteristic
440C4×C5C22×#6711yescharacteristic
441Dic5—22no—
442Dic5—24no—
443C24—301no—
444#41—22no—
445#41—108no—
446#41—104no—
447#41—1016no—
448#41—104no—
449#41—102no—
450#41—102no—
451#41#120214yescomplemented
452C2×Q8—51no—
453C2×Q8—54no—
454C2×Q8—52no—
455C2×Q8—102no—
456C2×Q8—108no—
457C2×Q8—104no—
458C2×Q8—104no—
459C2×Q8—102no—
460C2×Q8—101no—
461C2×Q8C2×D3×D511yescharacteristic
462C2×D4—21no—
463C2×D4—52no—
464C2×D4—51no—
465C2×D4—102no—
466C2×D4—152no—
467C2×D4—304no—
468C2×D4—302no—
469C2×D4—302no—
470C2×D4—301no—
471C2×D4C2×D3×D511yescharacteristic
472C22×C4—21no—
473C22×C4—52no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—101no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—32no—
483C2×C8—62no—
484C2×C8—152no—
485C4⋊C4—32no—
486C22⋊C4—61no—
487C22⋊C4—304no—
488C42—61no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—42no—
493C22×C3—102no—
494C22×C3—104no—
495C22×C3#402812yes—
496C22×C3C2×D4×D511yescharacteristic
497C2×D3—202no—
498C2×D3—204no—
499C2×D3—404no—
500C3×C4—22no—
501C3×C4—102no—
502C3×C4—104no—
503C3×C4#402812yes—
504C3×C4C22×D2011yescharacteristic
505C3×C4C2×D4×D511yescharacteristic
506Dic3—42no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5#583712yes—
510C2×C5C2×#95311yescharacteristic
511D5—42no—
512D5—242no—
513C23—21no—
514C23—52no—
515C23—302no—
516C23—602no—
517C23—1202no—
518C23D5×#6711yescharacteristic
519Q8—21no—
520Q8—54no—
521Q8—108no—
522Q8—102no—
523Q8—102no—
524Q8—104no—
525Q8C2×#120212yes—
526D4—24no—
527D4—21no—
528D4—108no—
529D4—104no—
530D4—102no—
531D4—302no—
532D4—302no—
533D4—602no—
534D4—1204no—
535D4C2×#120212yes—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—52no—
539C2×C4—62no—
540C2×C4—108no—
541C2×C4—108no—
542C2×C4—102no—
543C2×C4—104no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4C2×#120212yes—
547C2×C4D5×#6712yes—
548C2×C4D5×#6711yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—202no—
555C2×C3C2×#402811yescharacteristic
556C2×C3#6610412yes—
557D3—402no—
558C5#8411311yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—42no—
562C22—104no—
563C22—102no—
564C22—604no—
565C22—602no—
566C22—1204no—
567C22#9156412yes—
568C22C2×D5×#6711yescharacteristic
569C4—22no—
570C4—102no—
571C4—104no—
572C4—122no—
573C4#9156412yes—
574C4C22×#120211yescharacteristic
575C4C2×D5×#6711yescharacteristic
576C3#1061056711yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—202no—
580C2—1202no—
581C2#1175531912yes—
582C2C2×#9156411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3010
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
1. C2×C3×#4150C2semidirect
2. C2×#91838C2semidirect
3. #11754609C2semidirect
4. C22×#6658C2semidirect
5. C5×#5233C2semidirect
6. #11749268C2semidirect
7. #11749026C2semidirect
8. #11748399C2semidirect
9. #11748342C2semidirect
15. C2×C3×Q8×D5C22semidirect
17. C2×C3×#711C22semidirect
34. C5×#835C22semidirect
35. C5×#832C22semidirect
36. #90970C22semidirect
37. #90955C22semidirect
39. C2×#4150D3semidirect
50. C3×C5×#41D4semidirect
80. C2×C3×Dic10D4semidirect
100. #5233D5semidirect
106. C2×Q8×D5C2×D3semidirect
108. C2×#711C2×D3semidirect
194. #835C2×D5semidirect
195. #832C2×D5semidirect
199. C5×#41#67semidirect
230. C2×Dic10#67semidirect
277. C3×#41D20semidirect
451. #41#1202semidirect
489. C3×C5#3010semidirect
558. C5#84113semidirect
576. C3#10610567semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×#918382
#117546092
C22×#66582
C5×#52332
#117492682
#117490262
#117483992
#117483422
#106105673
#841135