Finite Group Databasebeta

← #14439608

Subgroups — #14439608

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91839C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3C3×#66164C211yesmaximal, characteristic, complemented
4#11754606C211yesmaximal, characteristic, complemented
5C2×#91312C211yesmaximal, characteristic, complemented
6C22×#6652C211yesmaximal, characteristic, complemented
7#11749340C212yesmaximal, complemented
8#11749313C212yesmaximal, complemented
9#11749093C212yesmaximal, complemented
10#11749066C212yesmaximal, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10615671—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17#91839—24no—
18C2×#6718C2211yescharacteristic, complemented
19C2×#6717C2211yescharacteristic, complemented
20C2×#6716C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic, complemented
22C22×C3⋊#168C2211yescharacteristic
23C5×#949—24no—
24C2×C5×#215C2212yescomplemented
25C2×C5×#213C2212yescomplemented
26C2×C5×#208C2211yescharacteristic
27C3×#4093C2212yescomplemented
28C3×#4086C2212yescomplemented
29C3×#4083—22no—
30C3×#4076—22no—
31C3×#4072C2211yescharacteristic
32#91570—22no—
33#91466—22no—
34#91451C2212yescomplemented
35#91373C2212yescomplemented
36#91312—24no—
37C2×#6657C2212yescomplemented
38C2×#6653C2212yescomplemented
39C2×#6652—24no—
40C2×#6652C2212yes—
41C2×#6652C2212yes—
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83382—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66164D311yescharacteristic, complemented
47C2×#4096—31no—
48#66139—31no—
49C22×#686—31no—
50C2×#4054—31no—
51#65465—32no—
52#65457—32no—
53#65443—32no—
54#65440—32no—
55#65411—31no—
56C23×C5×D3—21no—
57C23×C3×D5—21no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×#1220—21no—
66#6817—22no—
67#6817—22no—
68C2×D60C2311yescharacteristic
69C2×C4×D15—21no—
70C2×Dic30C2311yescharacteristic
71C2×C5×D12—22no—
72C2×C5×D12—22no—
73C2×C5×D12—21no—
74C2×C5×D12C2312yes—
75C2×C3×C22⋊D5—24no—
76C2×C3×D20—22no—
77C2×C3×D20—22no—
78C2×C3×D20—21no—
79C2×C3×D20C2312yes—
80C2×#1203—24no—
81#6718—22no—
82#6717—22no—
83#6716—22no—
84#6715—22no—
85C2×C3⋊#168D414yescomplemented
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88C5×#215—24no—
89C5×#213—24no—
90C5×#208D414yescomplemented
91C2×C5×C3⋊C8C2312yes—
92C3×C22⋊Dic5D412yes—
93C3×#685—24no—
94C3×C4⋊Dic5D412yes—
95C3×C4×Dic5C2312yes—
96(C2×D3)⋊Dic5—24no—
97#6657—24no—
98#6653—24no—
99#6652—24no—
100#6652—24no—
101C3×#535—51no—
102C2×#950—51no—
103C2×#949D511yescharacteristic, complemented
104C2×#932—51no—
105C22×#213—51no—
106#5525—51no—
107#5074—52no—
108#5073—52no—
109#5059—52no—
110#5058—52no—
111#4997—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×D4—31no—
114C2×#709—31no—
115C22×D20C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
120#4099—62no—
121#4096—64no—
122#4093C2×D312yescomplemented
123C2×#689—31no—
124C2×#688—31no—
125#4086—32no—
126#4086C2×D312yescomplemented
127#4084—62no—
128#4083—22no—
129#4082—32no—
130C2×#687—31no—
131C2×#686—31no—
132C2×#686—32no—
133C2×#686—32no—
134C2×#686—64no—
135#4076—22no—
136#4072C2×D311yescharacteristic
137C22×#168—31no—
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C5×D3—22no—
148C22×C5×D3—42no—
149C22×C5×D3—82no—
150C22×C3×D5—22no—
151C22×C3×D5—42no—
152C22×C3×D5—82no—
153C3×C5×Q8—21no—
154C3×C5×Q8—21no—
155C3×C5×D4—21no—
156C3×C5×D4—21no—
157C3×C5×D4—42no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—42no—
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2411yescharacteristic
164#1220—42no—
165C2×Dic15—21no—
166D60—21no—
167D60—21no—
168C4×D15—42no—
169Dic30—21no—
170Dic30—21no—
171C5×D12—22no—
172C5×D12—22no—
173C5×D12—42no—
174C3×C22⋊D5—84no—
175C2×C3×Dic5C2×D414yes—
176C3×D20—22no—
177C3×D20—22no—
178C3×D20—42no—
179#1203—84no—
180C3⋊#168C2×D412yes—
181C3⋊#168C2×D412yes—
182C5×C3⋊C8C2×D414yes—
183C2×C3×#41C2×D511yescharacteristic
184C22×C3×D4—51no—
185C2×#235—51no—
186C22×D12C2×D511yescharacteristic
187C3×#127—52no—
188C3×#124—52no—
189C3×#121—102no—
190C3×#120—102no—
191C3×#117—51no—
192#950—104no—
193#949—24no—
194C2×#216—51no—
195C2×#215—51no—
196C2×#215C2×D512yescomplemented
197C2×#214—51no—
198C2×#214—52no—
199#932—104no—
200C2×#213—51no—
201C2×#213—52no—
202C2×#213—52no—
203C2×#213—52no—
204C2×#213—104no—
205C2×#213C2×D512yescomplemented
206C2×#208C2×D511yescharacteristic
207C22×C3⋊C8—51no—
208#895—102no—
209#882—102no—
210#875—52no—
211#874—52no—
212#803—52no—
213C4×C3⋊C8—52no—
214C24×C5—61no—
215C23×D5—21no—
216C5×#41—22no—
217C5×#41—22no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4—32no—
221C2×C5×D4—62no—
222C2×C5×D4—62no—
223C2×C5×D4—61no—
224C2×C5×D4C22×D311yescharacteristic
225C22×C4×C5—21no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—24no—
228C2×C22⋊D5—61no—
229C2×C22⋊D5—64no—
230#709—62no—
231#709—62no—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—21no—
235C2×D20—31no—
236C2×D20C22×D312yes—
237C2×C4×D5—61no—
238C2×Dic10—31no—
239C5×SD16—64no—
240C5×D8—64no—
241C5×M16—34no—
242C2×C5×C8—32no—
243C22⋊Dic5—64no—
244C22⋊Dic5#6712yes—
245#689—62no—
246#688—62no—
247#687—62no—
248#686—64no—
249#686—64no—
250#686—62no—
251#685—24no—
252C4⋊Dic5#6712yes—
253C4×Dic5C22×D312yes—
254C2×#168—34no—
255C2×#168—31no—
256C2×#168—31no—
257D40—64no—
258#677—64no—
259C2×AGL(1,ℤ/8)—31no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—151no—
262C22×D8—151no—
263#535—51no—
264#535—151no—
265#496—152no—
266#496—152no—
267#495—152no—
268#493—152no—
269#405—151no—
270C22×C3×C5—22no—
271C22×C3×C5—41no—
272C22×C3×C5—42no—
273C22×C3×C5#12712yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×D15—41no—
276C2×D15—42no—
277C2×C5×D3—42no—
278C2×C5×D3—44no—
279C2×C5×D3—84no—
280C2×C3×D5—42no—
281C2×C3×D5—44no—
282C2×C3×D5—84no—
283C3×C4×C5—41no—
284C3×C4×C5#12712yes—
285C3×C4×C5C22×D411yescharacteristic
286C3×C4×C5C22×D411yescharacteristic
287Dic15—41no—
288C3×Dic5—24no—
289C24×C3—101no—
290C23×D3—21no—
291C3×#41—22no—
292C3×#41—22no—
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—52no—
296C2×C3×D4—104no—
297C2×C3×D4—102no—
298C2×C3×D4—101no—
299C2×C3×D4—102no—
300C2×C3×D4C22×D511yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4C22×D511yescharacteristic
303C2×#67—101no—
304#235—102no—
305#235—102no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12—21no—
309C2×D12—51no—
310C2×D12—104no—
311C2×D12C22×D512yes—
312C2×C4×D3—101no—
313C2×Dic6—51no—
314C3×C4⋊C4—52no—
315C3×C22⋊C4—52no—
316C3×C22⋊C4—104no—
317C3×C42—52no—
318#216—102no—
319#215—24no—
320#215—102no—
321#214—102no—
322#214—104no—
323#213—24no—
324#213—104no—
325#213—104no—
326#213—102no—
327#213—104no—
328(C2×D3)⋊C4—104no—
329#208C22⋊D514yescomplemented
330C2×C3⋊C8—54no—
331C2×C3⋊C8—51no—
332C2×C3⋊C8—51no—
333C2×C3⋊C8C22×D512yes—
334C23×C5—21no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—242no—
338C23×C5C2×#6711yescharacteristic
339C22×D5—22no—
340C22×D5—42no—
341C22×D5—61no—
342C22×D5—82no—
343C5×Q8—21no—
344C5×Q8—21no—
345C5×D4—21no—
346C5×D4—21no—
347C5×D4—42no—
348C5×D4—62no—
349C5×D4—62no—
350C5×D4—122no—
351C2×C4×C5—21no—
352C2×C4×C5—42no—
353C2×C4×C5D3×D412yes—
354C2×C4×C5D3×D412yes—
355C2×C4×C5C2×#6711yescharacteristic
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—84no—
358C22⋊D5—122no—
359C22⋊D5—244no—
360C2×Dic5—61no—
361C2×Dic5C2×#6714yes—
362D20—22no—
363D20—22no—
364D20—42no—
365D20—61no—
366D20—61no—
367C4×D5—122no—
368Dic10—61no—
369Dic10—61no—
370C5×C8—34no—
371#168—32no—
372#168—32no—
373C2×#41—151no—
374C2×#41D3×D511yescharacteristic
375C22×D4—31no—
376C22×D4—51no—
377AGL(1,ℤ/8)—64no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—32no—
382C2×SD16—152no—
383C2×SD16—151no—
384C2×SD16—151no—
385C2×D8—32no—
386C2×D8—152no—
387C2×D8—152no—
388C2×D8—152no—
389C2×D8—151no—
390C2×D8—304no—
391C2×M16—31no—
392C22×C8—151no—
393#127—52no—
394#127—152no—
395#124—52no—
396#124—152no—
397#121—102no—
398#121—302no—
399#120—102no—
400#120—302no—
401#117—51no—
402#97—152no—
403C4×C8—152no—
404C2×C3×C5—22no—
405C2×C3×C5—81no—
406C2×C3×C5C2×#12711yescharacteristic
407C2×C3×C5#57612yes—
408D15—81no—
409C3×D5—82no—
410C5×D3—82no—
411C23×C3—21no—
412C23×C3—102no—
413C23×C3—202no—
414C23×C3—402no—
415C23×C3D4×D511yescharacteristic
416C22×D3—22no—
417C22×D3—42no—
418C22×D3—82no—
419C22×D3—101no—
420C3×Q8—21no—
421C3×Q8—21no—
422C3×D4—21no—
423C3×D4—21no—
424C3×D4—42no—
425C3×D4—102no—
426C3×D4—102no—
427C3×D4—202no—
428C3×D4—404no—
429C2×C3×C4—21no—
430C2×C3×C4—42no—
431C2×C3×C4—54no—
432C2×C3×C4D4×D511yescharacteristic
433C2×C3×C4D4×D512yes—
434C2×C3×C4C2×C22⋊D512yes—
435C2×C3×C4C23×D511yescharacteristic
436#67—202no—
437C2×Dic3—101no—
438D12—22no—
439D12—22no—
440D12—42no—
441D12—101no—
442D12—101no—
443D12—404no—
444C4×D3—202no—
445Dic6—101no—
446Dic6—101no—
447C3⋊C8—52no—
448C3⋊C8—52no—
449C3⋊C8C2×C22⋊D514yes—
450C22×C5—22no—
451C22×C5—41no—
452C22×C5—42no—
453C22×C5—122no—
454C22×C5—124no—
455C22×C5—244no—
456C22×C5#94012yes—
457C22×C5C22×#6711yescharacteristic
458C2×D5—42no—
459C2×D5—44no—
460C2×D5—84no—
461C2×D5—121no—
462C2×D5—122no—
463C4×C5—41no—
464C4×C5#94012yes—
465C4×C5C2×D3×D411yescharacteristic
466C4×C5C2×D3×D411yescharacteristic
467Dic5—24no—
468Dic5—121no—
469C24—61no—
470C24—101no—
471#41—22no—
472#41—22no—
473#41—302no—
474#41—302no—
475C2×Q8—151no—
476C2×Q8C2×D3×D511yescharacteristic
477C2×D4—21no—
478C2×D4—32no—
479C2×D4—52no—
480C2×D4—61no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—104no—
484C2×D4—101no—
485C2×D4—102no—
486C2×D4—102no—
487C2×D4—151no—
488C2×D4—304no—
489C2×D4—301no—
490C2×D4C2×D3×D511yescharacteristic
491C22×C4—21no—
492C22×C4—301no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—64no—
496SD16—304no—
497SD16—302no—
498SD16—302no—
499D8—64no—
500D8—304no—
501D8—302no—
502D8—304no—
503D8—304no—
504M16—34no—
505C2×C8—32no—
506C2×C8—154no—
507C2×C8—151no—
508C2×C8—151no—
509C4⋊C4—52no—
510C22⋊C4—52no—
511C22⋊C4—104no—
512C22⋊C4—304no—
513C42—52no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—204no—
519C22×C3—202no—
520C22×C3—404no—
521C22×C3#408612yes—
522C22×C3C2×D4×D511yescharacteristic
523C2×D3—44no—
524C2×D3—42no—
525C2×D3—84no—
526C2×D3—202no—
527C2×D3—201no—
528C3×C4—41no—
529C3×C4—104no—
530C3×C4#408612yes—
531C3×C4C2×D4×D511yescharacteristic
532C3×C4C22×C22⋊D511yescharacteristic
533Dic3—201no—
534C2×C5—22no—
535C2×C5—81no—
536C2×C5—242no—
537C2×C5C2×#94011yescharacteristic
538C2×C5#583512yes—
539D5—82no—
540D5—241no—
541C23—21no—
542C23—62no—
543C23—102no—
544C23—122no—
545C23—202no—
546C23—242no—
547C23—301no—
548C23—402no—
549C23D5×#6711yescharacteristic
550Q8—21no—
551Q8—21no—
552Q8—301no—
553Q8—301no—
554D4—21no—
555D4—21no—
556D4—42no—
557D4—62no—
558D4—62no—
559D4—102no—
560D4—102no—
561D4—122no—
562D4—202no—
563D4—301no—
564D4—301no—
565D4—404no—
566D4—602no—
567D4—1204no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—54no—
571C2×C4—301no—
572C2×C4—602no—
573C2×C4D5×#6711yescharacteristic
574C2×C4D3×C22⋊D512yes—
575C2×C4#679012yes—
576C2×C4C22×D3×D511yescharacteristic
577C8—34no—
578C8—152no—
579C8—152no—
580C2×C3—22no—
581C2×C3—81no—
582C2×C3—402no—
583C2×C3#6610812yes—
584C2×C3C2×#408611yescharacteristic
585D3—82no—
586D3—401no—
587C5#8338211yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—41no—
591C22—124no—
592C22—122no—
593C22—204no—
594C22—202no—
595C22—244no—
596C22—404no—
597C22—602no—
598C22—601no—
599C22#9156712yes—
600C22C2×D5×#6711yescharacteristic
601C4—41no—
602C4—104no—
603C4—601no—
604C4#9156712yes—
605C4C2×D3×C22⋊D511yescharacteristic
606C4C2×#679011yescharacteristic
607C3#1061567111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—81no—
610C2—242no—
611C2—402no—
612C2—1201no—
613C2#1175531612yes—
614C2C2×#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#3155
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×#91839C2semidirect
2. C2×C5×#949C2semidirect
3. C3×#66164C2semidirect
4. #11754606C2semidirect
5. C2×#91312C2semidirect
6. C22×#6652C2semidirect
7. #11749340C2semidirect
8. #11749313C2semidirect
9. #11749093C2semidirect
10. #11749066C2semidirect
11. #11748320C2semidirect
18. C2×#6718C22semidirect
19. C2×#6717C22semidirect
20. C2×#6716C22semidirect
21. C2×#6715C22semidirect
24. C2×C5×#215C22semidirect
25. C2×C5×#213C22semidirect
27. C3×#4093C22semidirect
28. C3×#4086C22semidirect
34. #91451C22semidirect
35. #91373C22semidirect
37. C2×#6657C22semidirect
38. C2×#6653C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
46. #66164D3semidirect
85. C2×C3⋊#168D4semidirect
90. C5×#208D4semidirect
103. C2×#949D5semidirect
122. #4093C2×D3semidirect
126. #4086C2×D3semidirect
196. C2×#215C2×D5semidirect
205. C2×#213C2×D5semidirect
329. #208C22⋊D5semidirect
514. C3×C5#3155semidirect
587. C5#83382semidirect
607. C3#10615671semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C2×C5×#9492
C3×#661642
#117546062
C2×#913122
C22×#66522
#117493402
#117493132
#117490932
#117490662
#117483202
#106156713
#833825