Finite Group Databasebeta

← #14439489

Subgroups — #14439489

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
1C2×#91838C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic, complemented
3C3×#66159C211yesmaximal, characteristic, complemented
4#11754610C211yesmaximal, characteristic, complemented
5C22×#6658C211yesmaximal, characteristic, complemented
6C2×#91309C211yesmaximal, characteristic, complemented
7#11749339C212yesmaximal, complemented
8#11749315C212yesmaximal, complemented
9#11749094C212yesmaximal, complemented
10#11749070C212yesmaximal, complemented
11#11748318C211yesmaximal, characteristic, complemented
12#10615636—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91838—24no—
18C2×#6717C2212yes—
19C2×#6715C2212yes—
20C2×#6710C2211yescharacteristic
21C5×#950—24no—
22C2×C5×#216C2211yescharacteristic, complemented
23C2×C5×#215C2211yescharacteristic, complemented
24C2×C5×#214C2211yescharacteristic, complemented
25C2×C5×#213C2211yescharacteristic, complemented
26C22×C5×C3⋊C8C2211yescharacteristic
27C3×#4090C2212yescomplemented
28C3×#4082C2212yescomplemented
29C3×#4081—22no—
30C3×#4072C2211yescharacteristic
31C3×#4070—22no—
32#91573—22no—
33#91460—22no—
34#91451C2212yes—
35#91375C2212yes—
36C2×#6661C2212yescomplemented
37C2×#6658—24no—
38C2×#6658C2212yes—
39C2×#6658C2212yes—
40#91309—24no—
41C2×#6656C2212yescomplemented
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83402—51nomaximal, Hall
45C2×C5×#135—31no—
46#66164—31no—
47#66159D311yescharacteristic, complemented
48C2×#4097—31no—
49C2×#4095—31no—
50C22×#677—31no—
51#65479—32no—
52#65464—32no—
53#65457—32no—
54#65443—32no—
55#65390—31no—
56C23×D15—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×D60—22no—
65C2×D60—22no—
66C2×D60—21no—
67C2×D60C2312yes—
68C2×C5×#67—21no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C22×C3×Dic5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79C2×#1203—24no—
80#6717—24no—
81#6715—24no—
82#6710D414yescomplemented
83C2×C3⋊#168C2312yes—
84C5×#216—22no—
85C5×#215—22no—
86C5×#214—22no—
87C5×#213—22no—
88C2×C5×C3⋊C8D414yescomplemented
89C2×C5×C3⋊C8C2311yescharacteristic
90C2×C5×C3⋊C8C2311yescharacteristic
91C3×C22⋊Dic5—24no—
92C3×C22⋊Dic5D412yes—
93C3×C4⋊Dic5D412yes—
94C3×#683—24no—
95C3×C4×Dic5C2312yes—
96#6667—24no—
97#6661—24no—
98#6658—24no—
99#6658—24no—
100#6656—24no—
101C3×#536—51no—
102C2×#950D511yescharacteristic, complemented
103C2×#949—51no—
104C2×#942—51no—
105C22×#215—51no—
106#5525—51no—
107#5086—52no—
108#5085—52no—
109#5059—52no—
110#5058—52no—
111#4997—51no—
112C2×C5×#41—31no—
113C2×C5×#41C2×D311yescharacteristic
114C22×D20—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×#135—64no—
117C2×C5×Q16—31no—
118C2×C5×SD16—31no—
119C2×C5×SD16—31no—
120C2×C5×D8—31no—
121C22×C5×C8—31no—
122#4097—64no—
123#4095—64no—
124#4093—32no—
125#4090C2×D312yescomplemented
126C2×#689—32no—
127C2×#688—32no—
128#4086—32no—
129#4083—62no—
130#4082C2×D312yescomplemented
131#4081—22no—
132C2×#687—32no—
133C2×#686—32no—
134#4076—62no—
135#4072C2×D311yescharacteristic
136#4070—22no—
137C2×#681—31no—
138C2×#677—32no—
139C2×#677—32no—
140C2×#677—64no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C5×D3—21no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161D60—22no—
162D60—22no—
163D60—42no—
164C5×#67—42no—
165C2×C5×Dic3—21no—
166C5×D12—21no—
167C5×D12—21no—
168C4×C5×D3—42no—
169C5×Dic6—21no—
170C5×Dic6—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C2×C3×Dic5C2×D414yes—
174C3×Dic10—22no—
175C3×Dic10—22no—
176C3×Dic10—42no—
177#1203—84no—
178C3⋊#168C2×D414yes—
179C5×C3⋊C8C2×D412yes—
180C5×C3⋊C8C2×D412yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8—51no—
183C2×#235C2×D511yescharacteristic
184C22×D12—51no—
185C3×C4⋊Q8—52no—
186C3×#124—52no—
187C3×#123—102no—
188C3×C22⋊Q8—102no—
189C3×#117—51no—
190#950—24no—
191#949—104no—
192C2×#216—52no—
193C2×#216C2×D511yescharacteristic, complemented
194#942—104no—
195C2×#215—52no—
196C2×#215—52no—
197C2×#215—52no—
198C2×#215—52no—
199C2×#215—104no—
200C2×#215C2×D511yescharacteristic, complemented
201C2×#214C2×D511yescharacteristic, complemented
202C2×#213—52no—
203C2×#213C2×D511yescharacteristic, complemented
204C2×#208—51no—
205C22×C3⋊C8C2×D511yescharacteristic
206#895—102no—
207#882—102no—
208#875—52no—
209#874—52no—
210#803—52no—
211C4×C3⋊C8—52no—
212C23×D5—61no—
213C5×#41—22no—
214C5×#41—22no—
215C5×#41—62no—
216C5×#41—62no—
217C2×C5×Q8—31no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—64no—
227C22×Dic5—21no—
228C2×D20—32no—
229C2×D20—62no—
230C2×D20—62no—
231C2×D20—61no—
232C2×Dic10—22no—
233C2×Dic10—22no—
234C2×Dic10—21no—
235C2×Dic10C22×D312yes—
236C5×Q16—62no—
237C5×SD16—62no—
238C5×SD16—62no—
239C5×D8—62no—
240C2×C5×C8—34no—
241C2×C5×C8—31no—
242C2×C5×C8—31no—
243C22⋊Dic5—24no—
244C22⋊Dic5#6712yes—
245#689—64no—
246#688—64no—
247#687—64no—
248#686—64no—
249#685—64no—
250C4⋊Dic5#6712yes—
251#683—24no—
252C4×Dic5C22×D312yes—
253#681—34no—
254C2×#168—32no—
255#677—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—31no—
260C22×SD16—151no—
261#536—51no—
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—41no—
270C22×C3×C5—42no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—42no—
274C2×D15—44no—
275C2×D15—84no—
276C2×C5×D3—41no—
277C2×C5×D3—42no—
278C3×C4×C5—41no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282C3×Dic5—24no—
283C3×Dic5—42no—
284C5×Dic3—41no—
285C23×D3—101no—
286C3×#41—22no—
287C3×#41—22no—
288C2×C3×Q8—52no—
289C2×C3×Q8—101no—
290C2×C3×Q8—102no—
291C2×C3×Q8—102no—
292C2×C3×Q8C22×D511yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4C22×D511yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299#235—22no—
300#235—22no—
301C2×D12—52no—
302C2×D12—102no—
303C2×D12—102no—
304C2×D12—101no—
305C2×D12—104no—
306C2×D12C22×D511yescharacteristic
307C2×C4×D3—21no—
308C2×Dic6C22×D511yescharacteristic
309C3×C4⋊C4—52no—
310C3×C4⋊C4—104no—
311C3×C22⋊C4—52no—
312C3×C22⋊C4—104no—
313C3×C42—52no—
314#216—22no—
315#216—104no—
316#215—22no—
317#215—104no—
318#215—104no—
319#215—104no—
320#215—104no—
321#214—22no—
322#213—22no—
323#213—104no—
324(C2×D3)⋊C4—104no—
325#208—54no—
326C2×C3⋊C8—52no—
327C2×C3⋊C8C22⋊D514yescomplemented
328C2×C3⋊C8C22×D511yescharacteristic
329C2×C3⋊C8C22×D511yescharacteristic
330C23×C5—21no—
331C23×C5—61no—
332C23×C5C2×#6711yescharacteristic
333C22×D5—62no—
334C22×D5—122no—
335C22×D5—242no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×Q8—61no—
339C5×Q8—61no—
340C5×D4—21no—
341C5×D4—21no—
342C5×D4—42no—
343C5×D4—61no—
344C5×D4—61no—
345C5×D4—122no—
346C2×C4×C5—21no—
347C2×C4×C5—42no—
348C2×C4×C5—61no—
349C2×C4×C5—122no—
350C2×C4×C5D3×D412yes—
351C2×C4×C5D3×D412yes—
352C2×C4×C5C2×#6711yescharacteristic
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—244no—
355C2×Dic5—22no—
356C2×Dic5—42no—
357C2×Dic5C2×#6714yes—
358D20—62no—
359D20—62no—
360D20—122no—
361Dic10—22no—
362Dic10—22no—
363Dic10—42no—
364C5×C8—32no—
365C5×C8—32no—
366#168—34no—
367C2×#41—31no—
368C2×#41D3×D511yescharacteristic
369C22×Q8—51no—
370C22×D4—151no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—64no—
374C2×Q16—31no—
375C2×Q16—152no—
376C2×SD16—31no—
377C2×SD16—31no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—31no—
384C2×D8—152no—
385C2×M16—151no—
386C22×C8—31no—
387C4⋊Q8—52no—
388#127—152no—
389#124—52no—
390#124—152no—
391#123—102no—
392C22⋊Q8—102no—
393#121—302no—
394#120—302no—
395#117—51no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—82no—
403C5×D3—81no—
404C23×C3—21no—
405C23×C3D4×D511yescharacteristic
406C22×D3—21no—
407C22×D3—102no—
408C22×D3—202no—
409C22×D3—402no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—102no—
413C3×Q8—102no—
414C3×Q8—202no—
415C3×D4—21no—
416C3×D4—21no—
417C3×D4—42no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
420C2×C3×C4—54no—
421C2×C3×C4—102no—
422C2×C3×C4—202no—
423C2×C3×C4D4×D511yescharacteristic
424C2×C3×C4D4×D512yes—
425C2×C3×C4C2×C22⋊D512yes—
426C2×C3×C4C23×D511yescharacteristic
427#67—42no—
428C2×Dic3—21no—
429D12—21no—
430D12—21no—
431D12—102no—
432D12—102no—
433D12—202no—
434D12—404no—
435C4×D3—42no—
436Dic6—21no—
437Dic6—21no—
438C3⋊C8—54no—
439C3⋊C8C2×C22⋊D512yes—
440C3⋊C8C2×C22⋊D512yes—
441C22×C5—22no—
442C22×C5—41no—
443C22×C5—42no—
444C22×C5—121no—
445C22×C5—122no—
446C22×C5#94012yes—
447C22×C5C22×#6711yescharacteristic
448C2×D5—122no—
449C2×D5—124no—
450C2×D5—244no—
451C4×C5—41no—
452C4×C5—121no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C2×D3×D411yescharacteristic
456Dic5—24no—
457Dic5—42no—
458C24—301no—
459#41—22no—
460#41—22no—
461#41—62no—
462#41—62no—
463C2×Q8—31no—
464C2×Q8—52no—
465C2×Q8—101no—
466C2×Q8—102no—
467C2×Q8—102no—
468C2×Q8C2×D3×D511yescharacteristic
469C2×D4—21no—
470C2×D4—31no—
471C2×D4—61no—
472C2×D4—152no—
473C2×D4—304no—
474C2×D4—301no—
475C2×D4—302no—
476C2×D4—302no—
477C2×D4C2×D3×D511yescharacteristic
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—62no—
483Q16—304no—
484SD16—62no—
485SD16—62no—
486SD16—304no—
487SD16—304no—
488SD16—304no—
489SD16—304no—
490D8—62no—
491D8—304no—
492M16—154no—
493C2×C8—34no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—152no—
497C4⋊C4—52no—
498C4⋊C4—104no—
499C22⋊C4—52no—
500C22⋊C4—104no—
501C22⋊C4—304no—
502C42—52no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—42no—
506C22×C3—41no—
507C22×C3#408612yes—
508C22×C3C2×D4×D511yescharacteristic
509C2×D3—42no—
510C2×D3—41no—
511C2×D3—204no—
512C2×D3—202no—
513C2×D3—404no—
514C3×C4—41no—
515C3×C4—104no—
516C3×C4—202no—
517C3×C4#408612yes—
518C3×C4C2×D4×D511yescharacteristic
519C3×C4C22×C22⋊D511yescharacteristic
520Dic3—41no—
521C2×C5—22no—
522C2×C5—81no—
523C2×C5—241no—
524C2×C5C2×#94011yescharacteristic
525C2×C5#583712yes—
526D5—242no—
527C23—21no—
528C23—61no—
529C23—302no—
530C23—602no—
531C23—1202no—
532C23D5×#6711yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—61no—
536Q8—61no—
537Q8—102no—
538Q8—102no—
539Q8—202no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—61no—
544D4—61no—
545D4—122no—
546D4—302no—
547D4—302no—
548D4—602no—
549D4—1204no—
550C2×C4—21no—
551C2×C4—42no—
552C2×C4—54no—
553C2×C4—61no—
554C2×C4—102no—
555C2×C4—122no—
556C2×C4—202no—
557C2×C4D5×#6711yescharacteristic
558C2×C4D3×C22⋊D512yes—
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—32no—
562C8—32no—
563C8—154no—
564C2×C3—22no—
565C2×C3—81no—
566C2×C3#6610412yes—
567C2×C3C2×#408611yescharacteristic
568D3—81no—
569D3—402no—
570C5#8340211yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—41no—
574C22—122no—
575C22—121no—
576C22—604no—
577C22—602no—
578C22—1204no—
579C22#9156712yes—
580C22C2×D5×#6711yescharacteristic
581C4—41no—
582C4—104no—
583C4—121no—
584C4—202no—
585C4#9156712yes—
586C4C2×D3×C22⋊D511yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061563611yescharacteristic, complemented, Sylow
589C2—22no—
590C2—81no—
591C2—241no—
592C2—1202no—
593C2#1175531912yes—
594C2C2×#9156711yescharacteristic
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#3154
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×#91838C2semidirect
2. C2×C5×#950C2semidirect
3. C3×#66159C2semidirect
4. #11754610C2semidirect
5. C22×#6658C2semidirect
6. C2×#91309C2semidirect
7. #11749339C2semidirect
8. #11749315C2semidirect
9. #11749094C2semidirect
10. #11749070C2semidirect
11. #11748318C2semidirect
22. C2×C5×#216C22semidirect
23. C2×C5×#215C22semidirect
24. C2×C5×#214C22semidirect
25. C2×C5×#213C22semidirect
27. C3×#4090C22semidirect
28. C3×#4082C22semidirect
36. C2×#6661C22semidirect
41. C2×#6656C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
47. #66159D3semidirect
82. #6710D4semidirect
88. C2×C5×C3⋊C8D4semidirect
102. C2×#950D5semidirect
125. #4090C2×D3semidirect
130. #4082C2×D3semidirect
193. C2×#216C2×D5semidirect
200. C2×#215C2×D5semidirect
201. C2×#214C2×D5semidirect
203. C2×#213C2×D5semidirect
327. C2×C3⋊C8C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83402semidirect
588. C3#10615636semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C2×C5×#9502
C3×#661592
#117546102
C22×#66582
C2×#913092
#117493392
#117493152
#117490942
#117490702
#117483182
#106156363
#834025