Finite Group Databasebeta

← #14439588

Subgroups — #14439588

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×#91821C211yesmaximal, characteristic, complemented
2C22×C5×#213C211yesmaximal, characteristic, complemented
3C3×#66139C211yesmaximal, characteristic, complemented
4#11754606C211yesmaximal, characteristic, complemented
5C2×#91311C211yesmaximal, characteristic, complemented
6C2×#91299C211yesmaximal, characteristic, complemented
7#11749094C212yesmaximal, complemented
8#11749093C212yesmaximal, complemented
9#11749067C212yesmaximal, complemented
10#11749066C212yesmaximal, complemented
11#11748318C211yesmaximal, characteristic, complemented
12#10615561—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6716C2212yescomplemented
18#91821—24no—
19C2×#6715C2212yescomplemented
20C2×#6710C2211yescharacteristic
21C2×C5×#213—24no—
22C2×C5×#213C2212yes—
23C2×C5×#213C2212yes—
24C22×C5×C3⋊C8C2211yescharacteristic
25C3×#4099—22no—
26C3×#4086C2212yescomplemented
27C3×#4084—22no—
28C3×#4082C2212yescomplemented
29C3×#4072C2211yescharacteristic
30#91570—22no—
31#91466—22no—
32#91451C2212yescomplemented
33#91373C2212yescomplemented
34C2×#6662C2211yescharacteristic, complemented
35C2×#6658C2211yescharacteristic, complemented
36#91311—24no—
37C2×#6657C2211yescharacteristic, complemented
38C2×#6656C2212yescomplemented
39C2×#6653C2211yescharacteristic, complemented
40#91299—24no—
41C2×#6652C2212yescomplemented
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83382—51nomaximal, Hall
45C22×C5×D8—31no—
46#66139—31no—
47#66139D311yescharacteristic, complemented
48C2×#4078—31no—
49C2×#4078—31no—
50C2×#4050—31no—
51#65444—32no—
52#65443—32no—
53#65443—32no—
54#65440—32no—
55#65390—31no—
56C24×C3×C5—21no—
57C23×C5×D3—21no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×D12—22no—
70C2×C5×D12—22no—
71C2×C5×D12—21no—
72C2×C5×D12C2312yes—
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—24no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1203—24no—
81#6716—24no—
82#6715—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#213—24no—
86C5×#213—24no—
87C2×C5×C3⋊C8D414yescomplemented
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C5×C3⋊C8C2311yescharacteristic
90C3×C22⋊Dic5—24no—
91C3×C22⋊Dic5D412yes—
92C3×C4⋊Dic5D412yes—
93C3×C4×Dic5C2312yes—
94(C2×D3)⋊Dic5—24no—
95#6662—22no—
96#6658—22no—
97#6657—22no—
98#6656—24no—
99#6653—22no—
100#6652—24no—
101C3×#535—51no—
102C2×#950—51no—
103C2×#949—51no—
104C2×#932—51no—
105C22×#213D511yescharacteristic, complemented
106#5525—51no—
107#5074—52no—
108#5073—52no—
109#5059—52no—
110#5058—52no—
111#4997—51no—
112C22×C5×D4—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C2×#709C2×D311yescharacteristic
116C2×C5×D8—32no—
117C2×C5×D8—32no—
118C2×C5×D8—64no—
119C22×C5×C8—31no—
120#4099—22no—
121#4099—62no—
122#4086—32no—
123#4086C2×D312yescomplemented
124#4084—22no—
125#4084—62no—
126#4082—32no—
127#4082C2×D312yescomplemented
128C2×#687—32no—
129C2×#687—32no—
130#4078—64no—
131#4078—64no—
132C2×#686—32no—
133C2×#686—32no—
134#4072C2×D311yescharacteristic
135C2×#681—31no—
136C2×Dic20—31no—
137#4050—64no—
138C2×D40—31no—
139C2×#677—31no—
140C2×#677—31no—
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—21no—
149C22×C5×D3—22no—
150C22×C5×D3—42no—
151C22×C5×D3—82no—
152C22×C3×D5—21no—
153C3×C5×D4—22no—
154C3×C5×D4—22no—
155C3×C5×D4—42no—
156C2×C3×C4×C5C2×D411yescharacteristic
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2411yescharacteristic
160#1220—42no—
161C2×Dic15—21no—
162D60—21no—
163D60—21no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C5×D12—22no—
168C5×D12—22no—
169C5×D12—42no—
170C3×C22⋊D5—42no—
171C3×C22⋊D5—84no—
172C2×C3×Dic5—21no—
173C2×C3×Dic5C2×D414yes—
174C3×D20—21no—
175C3×D20—21no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10—21no—
179#1203—84no—
180C3⋊#168C2×D414yes—
181C5×C3⋊C8C2×D412yes—
182C5×C3⋊C8C2×D412yes—
183C2×C3×#41—51no—
184C22×C3×D4C2×D511yescharacteristic
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—104no—
194C2×#216—51no—
195C2×#215—52no—
196C2×#215—51no—
197C2×#214—52no—
198C2×#214—51no—
199#932—104no—
200C2×#213—24no—
201C2×#213—52no—
202C2×#213—52no—
203C2×#213—51no—
204C2×#213C2×D512yes—
205C2×#213C2×D512yes—
206C2×#208—51no—
207C22×C3⋊C8C2×D511yescharacteristic
208#895—102no—
209#882—102no—
210#875—52no—
211#874—52no—
212#803—52no—
213C4×C3⋊C8—52no—
214C24×C5—21no—
215C24×C5—61no—
216C2×C5×D4—22no—
217C2×C5×D4—22no—
218C2×C5×D4—21no—
219C2×C5×D4—32no—
220C2×C5×D4—62no—
221C2×C5×D4—62no—
222C2×C5×D4—61no—
223C2×C5×D4C22×D312yes—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—61no—
228C2×C22⋊D5—64no—
229#709—22no—
230#709—22no—
231#709—62no—
232#709—62no—
233C2×D20—31no—
234C2×D20C22×D311yescharacteristic
235C2×C4×D5—21no—
236C2×C4×D5—61no—
237C2×Dic10—31no—
238C2×Dic10C22×D311yescharacteristic
239C5×D8—64no—
240C5×D8—64no—
241C2×C5×C8—34no—
242C2×C5×C8—31no—
243C2×C5×C8—31no—
244C22⋊Dic5—24no—
245C22⋊Dic5—64no—
246C22⋊Dic5#6712yes—
247#687—64no—
248#687—64no—
249#686—64no—
250#686—64no—
251C4⋊Dic5#6712yes—
252C4×Dic5C22×D312yes—
253#681—34no—
254C2×#168—32no—
255Dic20—62no—
256D40—62no—
257#677—62no—
258#677—62no—
259C2×AGL(1,ℤ/8)—151no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—151no—
262C22×D8—31no—
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—42no—
272C22×C3×C5—44no—
273C22×C3×C5—84no—
274C22×C3×C5#12712yes—
275C22×C3×C5C22×D411yescharacteristic
276C2×D15—41no—
277C2×D15—42no—
278C2×C5×D3—42no—
279C2×C5×D3—44no—
280C2×C5×D3—84no—
281C2×C3×D5—41no—
282C2×C3×D5—42no—
283C3×C4×C5#12712yes—
284C3×C4×C5C22×D411yescharacteristic
285C3×C4×C5C22×D411yescharacteristic
286Dic15—41no—
287C3×Dic5—24no—
288C3×Dic5—41no—
289C24×C3—21no—
290C23×D3—21no—
291C3×#41—102no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—22no—
295C2×C3×D4—21no—
296C2×C3×D4—22no—
297C2×C3×D4—51no—
298C2×C3×D4—104no—
299C2×C3×D4—101no—
300C2×C3×D4C22×D512yes—
301C22×C3×C4—101no—
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—104no—
320#215—102no—
321#214—104no—
322#214—102no—
323#213—24no—
324#213—24no—
325#213—104no—
326#213—104no—
327#213—102no—
328(C2×D3)⋊C4—104no—
329#208—54no—
330C2×C3⋊C8—52no—
331C2×C3⋊C8C22⋊D514yescomplemented
332C2×C3⋊C8C22×D511yescharacteristic
333C2×C3⋊C8C22×D511yescharacteristic
334C23×C5—22no—
335C23×C5—42no—
336C23×C5—62no—
337C23×C5—82no—
338C23×C5—122no—
339C23×C5—242no—
340C23×C5C2×#6711yescharacteristic
341C22×D5—21no—
342C22×D5—61no—
343C5×D4—22no—
344C5×D4—22no—
345C5×D4—42no—
346C5×D4—62no—
347C5×D4—62no—
348C5×D4—122no—
349C2×C4×C5D3×D412yes—
350C2×C4×C5D3×D412yes—
351C2×C4×C5C2×#6711yescharacteristic
352C2×C4×C5C23×D311yescharacteristic
353C22⋊D5—42no—
354C22⋊D5—84no—
355C22⋊D5—122no—
356C22⋊D5—244no—
357C2×Dic5—21no—
358C2×Dic5—61no—
359C2×Dic5C2×#6714yes—
360D20—21no—
361D20—21no—
362D20—61no—
363D20—61no—
364C4×D5—42no—
365C4×D5—122no—
366Dic10—21no—
367Dic10—21no—
368Dic10—61no—
369Dic10—61no—
370C5×C8—32no—
371C5×C8—32no—
372#168—34no—
373C2×#41—51no—
374C2×#41—151no—
375C22×D4—31no—
376C22×D4D3×D511yescharacteristic
377AGL(1,ℤ/8)—304no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—151no—
382C2×SD16—151no—
383C2×SD16—152no—
384C2×SD16—152no—
385C2×D8—32no—
386C2×D8—32no—
387C2×D8—64no—
388C2×D8—151no—
389C2×D8—152no—
390C2×D8—152no—
391C2×M16—151no—
392C22×C8—31no—
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—82no—
406C2×C3×C5C2×#12711yescharacteristic
407C2×C3×C5#57612yes—
408D15—81no—
409C3×D5—81no—
410C5×D3—82no—
411C23×C3—22no—
412C23×C3—42no—
413C23×C3—82no—
414C23×C3—101no—
415C23×C3D4×D511yescharacteristic
416C22×D3—22no—
417C22×D3—42no—
418C22×D3—82no—
419C22×D3—101no—
420C3×Q8—101no—
421C3×Q8—101no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—42no—
425C3×D4—101no—
426C3×D4—101no—
427C3×D4—202no—
428C3×D4—404no—
429C2×C3×C4—54no—
430C2×C3×C4—101no—
431C2×C3×C4—202no—
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—54no—
448C3⋊C8C2×C22⋊D512yes—
449C3⋊C8C2×C22⋊D512yes—
450C22×C5—22no—
451C22×C5—42no—
452C22×C5—44no—
453C22×C5—84no—
454C22×C5—122no—
455C22×C5—124no—
456C22×C5—244no—
457C22×C5#94012yes—
458C22×C5C22×#6711yescharacteristic
459C2×D5—41no—
460C2×D5—42no—
461C2×D5—121no—
462C2×D5—122no—
463C4×C5#94012yes—
464C4×C5C2×D3×D411yescharacteristic
465C4×C5C2×D3×D411yescharacteristic
466Dic5—24no—
467Dic5—41no—
468Dic5—121no—
469C24—21no—
470C24—61no—
471#41—102no—
472#41—102no—
473#41—302no—
474#41—302no—
475C2×Q8—51no—
476C2×Q8—151no—
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—32no—
481C2×D4—51no—
482C2×D4—61no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—104no—
486C2×D4—101no—
487C2×D4—151no—
488C2×D4—304no—
489C2×D4—301no—
490C2×D4C2×D3×D512yes—
491C22×C4—101no—
492C22×C4—301no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—302no—
496SD16—302no—
497SD16—304no—
498SD16—304no—
499D8—64no—
500D8—64no—
501D8—302no—
502D8—304no—
503D8—304no—
504M16—154no—
505C2×C8—34no—
506C2×C8—31no—
507C2×C8—31no—
508C2×C8—152no—
509C4⋊C4—52no—
510C22⋊C4—52no—
511C22⋊C4—104no—
512C22⋊C4—304no—
513C42—52no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—84no—
519C22×C3—202no—
520C22×C3—201no—
521C22×C3#408612yes—
522C22×C3C2×D4×D511yescharacteristic
523C2×D3—44no—
524C2×D3—42no—
525C2×D3—84no—
526C2×D3—202no—
527C2×D3—201no—
528C3×C4—104no—
529C3×C4—201no—
530C3×C4#408612yes—
531C3×C4C2×D4×D511yescharacteristic
532C3×C4C22×C22⋊D511yescharacteristic
533Dic3—201no—
534C2×C5—22no—
535C2×C5—82no—
536C2×C5—242no—
537C2×C5C2×#94011yescharacteristic
538C2×C5#583512yes—
539D5—81no—
540D5—241no—
541C23—22no—
542C23—42no—
543C23—62no—
544C23—82no—
545C23—101no—
546C23—122no—
547C23—242no—
548C23—301no—
549C23D5×#6711yescharacteristic
550Q8—101no—
551Q8—101no—
552Q8—301no—
553Q8—301no—
554D4—22no—
555D4—22no—
556D4—42no—
557D4—62no—
558D4—62no—
559D4—101no—
560D4—101no—
561D4—122no—
562D4—202no—
563D4—301no—
564D4—301no—
565D4—404no—
566D4—602no—
567D4—1204no—
568C2×C4—54no—
569C2×C4—101no—
570C2×C4—202no—
571C2×C4—301no—
572C2×C4—602no—
573C2×C4D5×#6711yescharacteristic
574C2×C4D3×C22⋊D512yes—
575C2×C4#679012yes—
576C2×C4C22×D3×D511yescharacteristic
577C8—32no—
578C8—32no—
579C8—154no—
580C2×C3—22no—
581C2×C3—82no—
582C2×C3—401no—
583C2×C3#6609112yes—
584C2×C3C2×#408611yescharacteristic
585D3—82no—
586D3—401no—
587C5#8338211yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—44no—
591C22—84no—
592C22—122no—
593C22—124no—
594C22—201no—
595C22—202no—
596C22—244no—
597C22—601no—
598C22—602no—
599C22#9156712yes—
600C22C2×D5×#6711yescharacteristic
601C4—104no—
602C4—201no—
603C4—601no—
604C4#9156712yes—
605C4C2×D3×C22⋊D511yescharacteristic
606C4C2×#679011yescharacteristic
607C3#1061556111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—82no—
610C2—242no—
611C2—401no—
612C2—1201no—
613C2#1175469112yes—
614C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3155
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91821C2semidirect
2. C22×C5×#213C2semidirect
3. C3×#66139C2semidirect
4. #11754606C2semidirect
5. C2×#91311C2semidirect
6. C2×#91299C2semidirect
7. #11749094C2semidirect
8. #11749093C2semidirect
9. #11749067C2semidirect
10. #11749066C2semidirect
11. #11748318C2semidirect
17. C2×#6716C22semidirect
19. C2×#6715C22semidirect
26. C3×#4086C22semidirect
28. C3×#4082C22semidirect
32. #91451C22semidirect
33. #91373C22semidirect
34. C2×#6662C22semidirect
35. C2×#6658C22semidirect
37. C2×#6657C22semidirect
38. C2×#6656C22semidirect
39. C2×#6653C22semidirect
41. C2×#6652C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
47. #66139D3semidirect
83. #6710D4semidirect
87. C2×C5×C3⋊C8D4semidirect
105. C22×#213D5semidirect
123. #4086C2×D3semidirect
127. #4082C2×D3semidirect
331. C2×C3⋊C8C22⋊D5semidirect
514. C3×C5#3155semidirect
587. C5#83382semidirect
607. C3#10615561semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C22×C5×#2132
C3×#661392
#117546062
C2×#913112
C2×#912992
#117490942
#117490932
#117490672
#117490662
#117483182
#106155613
#833825