Finite Group Databasebeta

← #14413422

Subgroups — #14413422

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D15C211yesmaximal, characteristic
2#11754461C211yesmaximal, characteristic
3C2×#91347C211yesmaximal, characteristic
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6#11748472C211yesmaximal, characteristic, complemented
7#11748470C211yesmaximal, characteristic, complemented
8#11747690C212yesmaximal, complemented
9#11747687C212yesmaximal, complemented
10#11747640C212yesmaximal, complemented
11#11747638C212yesmaximal, complemented
12#10610939—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16M16×D15C418yescomplemented
17C2×#6705C2212yes—
18C2×C8×D15C2212yes—
19C5×#926C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C3×#4072C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23#91561—21no—
24C2×#6667—21no—
25#91532—21no—
26C2×Dic3×Dic5—21no—
27#91437C2211yescharacteristic
28#91437C2211yescharacteristic
29C4×#1200—21no—
30#91386—21no—
31#91347—21no—
32#91347—21no—
33#91347C2212yes—
34#91347C2211yescharacteristic
35#91347C2212yes—
36#91347C2211yescharacteristic
37C5×#818C2212yescomplemented
38C5×#817C2212yescomplemented
39C3×#3950C2212yescomplemented
40C3×#3949C2212yescomplemented
41#90989C2212yescomplemented
42#90989C2212yescomplemented
43#90986C2212yescomplemented
44#90986C2212yescomplemented
45#79208—51nomaximal, Hall
46C2×D5×M16—31no—
47D5×#117—31no—
48C2×#4038—31no—
49C5×#428—31no—
50#65410D311yescharacteristic, complemented
51#65284—31no—
52#65253—31no—
53#65170—32no—
54#65169—32no—
55#65150—32no—
56#65149—32no—
57C23×D15D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15D411yescharacteristic
60C2×C4×D15C2×C414yes—
61C2×C4×D15D411yescharacteristic
62C2×C4×D15D411yescharacteristic
63C2×C4×D15Q814yes—
64C2×C4×D15C2311yescharacteristic
65C2×C4×D15C2311yescharacteristic
66C22×C5×Dic3—21no—
67C22×C3×Dic5—21no—
68C2×#1200—21no—
69C2×#1200—21no—
70C3×C5×M16C2×C414yescomplemented
71C2×C3×C5×C8C2312yes—
72#6710C2×C414yescomplemented
73C2×C3⋊#168C2312yes—
74#6705C2×C418yescomplemented
75C8×D15C2×C418yescomplemented
76C5×#217—21no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2312yes—
81C4×C5×Dic3—21no—
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2312yes—
87C3×C4×Dic5—21no—
88#6669—21no—
89#6669—21no—
90#6667—22no—
91#6667—22no—
92#6667—21no—
93#6667—21no—
94Dic3×Dic5—21no—
95Dic3×Dic5—21no—
96Dic3×Dic5—22no—
97Dic3×Dic5—22no—
98C2×D3×M16—51no—
99D3×#117—51no—
100C2×#892—51no—
101C3×#428—51no—
102#5121D511yescharacteristic, complemented
103#4995—51no—
104#4964—51no—
105#4881—52no—
106#4880—52no—
107#4861—52no—
108#4860—52no—
109C22×C4×D5—31no—
110C2×C5×M16C2×D311yescharacteristic
111C5×#117—31no—
112C2×C5×C4⋊C4—31no—
113C2×#685—61no—
114#4072C2×D311yescharacteristic
115C2×C4⋊Dic5C2×D311yescharacteristic
116C2×C4×Dic5—61no—
117C2×#681—31no—
118D5×M16—38no—
119C2×#676—32no—
120C2×C8×D5—32no—
121#4038—32no—
122#4038—32no—
123#4038—31no—
124#4038—31no—
125#4038—61no—
126#4038—61no—
127D5×C4⋊C4—31no—
128D5×C4⋊C4—31no—
129D5×C22⋊C4—61no—
130#4023—61no—
131#4018—61no—
132C42×D5—61no—
133C5×#107—32no—
134C5×#106—32no—
135#3950C2×D312yescomplemented
136#3949C2×D312yescomplemented
137#3940—32no—
138#3940—32no—
139#3939—32no—
140#3939—32no—
141#2911—151noSylow
142C23×C3×C5C2×D411yescharacteristic
143C22×D15—41no—
144C22×D15—41no—
145C22×D15C4⋊C414yes—
146C22×D15C2×D411yescharacteristic
147C22×D15C2×D411yescharacteristic
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×Q812yes—
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15C4⋊C414yes—
153C2×Dic15C2×D411yescharacteristic
154C2×Dic15C2×D411yescharacteristic
155C4×D15C4⋊C414yes—
156C4×D15C4⋊C414yes—
157C4×D15C22×C412yes—
158C4×D15C22×C412yes—
159C4×D15C2×Q812yes—
160C4×D15C2×Q812yes—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—21no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—42no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—42no—
169#1200—42no—
170#1200—42no—
171C3×C5×C8C22×C414yes—
172C3⋊#168C22×C414yes—
173C22×C4×D3—51no—
174C2×C3×M16C2×D511yescharacteristic
175C3×#117—51no—
176C2×C3×C4⋊C4—51no—
177C2×(C2×D3)⋊C4—101no—
178#926C2×D511yescharacteristic
179C2×C4⋊Dic3C2×D511yescharacteristic
180C2×C4×Dic3—101no—
181C2×#208—51no—
182D3×M16—58no—
183C2×ΓL(1,𝔽25)—52no—
184C2×D3×C8—52no—
185#892—51no—
186#892—52no—
187#892—52no—
188#892—51no—
189#892—101no—
190#892—101no—
191D3×C4⋊C4—51no—
192D3×C4⋊C4—51no—
193D3×C22⋊C4—101no—
194#877—101no—
195#872—101no—
196C42×D3—101no—
197C3×#107—52no—
198C3×#106—52no—
199#818C2×D512yescomplemented
200#817C2×D512yescomplemented
201#808—52no—
202#808—52no—
203#807—52no—
204#807—52no—
205C23×D5—31no—
206C22×C4×C5—61no—
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5—21no—
209C22×Dic5—31no—
210C2×C4×D5—34no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—34no—
214C2×C4×D5—31no—
215C2×C4×D5—31no—
216C2×C4×D5—61no—
217C2×C4×D5—61no—
218C5×M16C4×D314yescomplemented
219C2×C5×C8C22×D312yes—
220C5×C4⋊C4—32no—
221C5×C4⋊C4—31no—
222C5×C4⋊C4—31no—
223C5×C4⋊C4—61no—
224C5×C22⋊C4—61no—
225C42×C5—61no—
226C22⋊Dic5—21no—
227#685—61no—
228#685—61no—
229#685—62no—
230#685—62no—
231C4⋊Dic5—21no—
232C4⋊Dic5C22×D311yescharacteristic
233C4⋊Dic5C22×D312yes—
234C4⋊Dic5C22×D311yescharacteristic
235#683—61no—
236#683—61no—
237C4×Dic5—21no—
238C4×Dic5—61no—
239C4×Dic5—61no—
240C4×Dic5—62no—
241C4×Dic5—62no—
242#681—34no—
243C2×#168—32no—
244#676—38no—
245C8×D5—38no—
246C22×M16—151no—
247C2×#117—151no—
248C2×#117—151no—
249#428—31no—
250#428—51no—
251#428—152no—
252#428—152no—
253#428—151no—
254#428—151no—
255#427—152no—
256#427—152no—
257C22×C3×C5—21no—
258C22×C3×C5—21no—
259C22×C3×C5C2×C4⋊C412yes—
260C22×C3×C5C22×D411yescharacteristic
261C2×D15—21no—
262C2×D15—21no—
263C2×D15—21no—
264C2×D15—21no—
265C2×D15—44no—
266C2×D15C2×C4⋊C412yes—
267C2×D15C2×C4⋊C412yes—
268C3×C4×C5C2×C4⋊C412yes—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×Q811yescharacteristic
271Dic15C2×C4⋊C412yes—
272Dic15C2×C4⋊C412yes—
273C3×Dic5—41no—
274C3×Dic5—41no—
275C3×Dic5—42no—
276C5×Dic3—41no—
277C5×Dic3—41no—
278C5×Dic3—42no—
279C23×D3—51no—
280C22×C3×C4—101no—
281C22×C3×C4C22×D511yescharacteristic
282C22×Dic3—21no—
283C22×Dic3—51no—
284C2×C4×D3—54no—
285C2×C4×D3—51no—
286C2×C4×D3—51no—
287C2×C4×D3—54no—
288C2×C4×D3—51no—
289C2×C4×D3—51no—
290C2×C4×D3—101no—
291C2×C4×D3—101no—
292C3×M16C4×D514yescomplemented
293C2×C3×C8C22×D512yes—
294C3×C4⋊C4—51no—
295C3×C4⋊C4—52no—
296C3×C4⋊C4—51no—
297C3×C4⋊C4—101no—
298C3×C22⋊C4—101no—
299C3×C42—101no—
300#217—21no—
301(C2×D3)⋊C4—101no—
302(C2×D3)⋊C4—101no—
303(C2×D3)⋊C4—102no—
304(C2×D3)⋊C4—102no—
305C4⋊Dic3—21no—
306C4⋊Dic3C22×D511yescharacteristic
307C4⋊Dic3C22×D512yes—
308C4⋊Dic3C22×D511yescharacteristic
309Dic3⋊C4—101no—
310Dic3⋊C4—101no—
311C4×Dic3—21no—
312C4×Dic3—101no—
313C4×Dic3—101no—
314C4×Dic3—102no—
315C4×Dic3—102no—
316#208—54no—
317C2×C3⋊C8—52no—
318ΓL(1,𝔽25)—58no—
319D3×C8—58no—
320C23×C5D3×D411yescharacteristic
321C22×D5—31no—
322C22×D5—31no—
323C22×D5—34no—
324C22×D5—121no—
325C22×D5—121no—
326C2×C4×C5—62no—
327C2×C4×C5—61no—
328C2×C4×C5—61no—
329C2×C4×C5—122no—
330C2×C4×C5C2×C4×D312yes—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5D3×Q812yes—
333C2×C4×C5C23×D311yescharacteristic
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—22no—
337C2×Dic5—34no—
338C2×Dic5—31no—
339C2×Dic5—31no—
340C2×Dic5—42no—
341C4×D5—34no—
342C4×D5—34no—
343C4×D5—32no—
344C4×D5—32no—
345C4×D5—32no—
346C4×D5—32no—
347C4×D5—122no—
348C4×D5—122no—
349C5×C8C2×C4×D314yes—
350#168—34no—
351C23×C4—151no—
352C2×M16—151no—
353C2×M16—158no—
354C2×M16—152no—
355C2×M16D3×D511yescharacteristic
356C22×C8—152no—
357#117—31no—
358#117—51no—
359#117—151no—
360#117—152no—
361#117—151no—
362#117—152no—
363#117—301no—
364#117—301no—
365#117—301no—
366#117—301no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C22⋊C4—301no—
372C2×C22⋊C4—301no—
373C2×C42—301no—
374C2×C42—301no—
375#107—32no—
376#107—52no—
377#107—152no—
378#107—152no—
379#106—32no—
380#106—52no—
381#106—152no—
382#106—152no—
383C2×C3×C5—22no—
384C2×C3×C5C22×C4⋊C411yescharacteristic
385C2×C3×C5#57511yescharacteristic
386C2×C3×C5#57511yescharacteristic
387D15—22no—
388D15—22no—
389C23×C3D4×D511yescharacteristic
390C22×D3—51no—
391C22×D3—51no—
392C22×D3—54no—
393C22×D3—201no—
394C22×D3—201no—
395C2×C3×C4—102no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—202no—
399C2×C3×C4C2×C4×D512yes—
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4Q8×D512yes—
402C2×C3×C4C23×D511yescharacteristic
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—42no—
407C2×Dic3—51no—
408C2×Dic3—51no—
409C2×Dic3—54no—
410C4×D3—52no—
411C4×D3—52no—
412C4×D3—52no—
413C4×D3—52no—
414C4×D3—54no—
415C4×D3—54no—
416C4×D3—202no—
417C4×D3—202no—
418C3×C8C2×C4×D514yes—
419C3⋊C8—54no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5D3×C4⋊C412yes—
423C22×C5C2×D3×D411yescharacteristic
424C2×D5—32no—
425C2×D5—32no—
426C2×D5—61no—
427C2×D5—61no—
428C2×D5—61no—
429C2×D5—61no—
430C2×D5—124no—
431C4×C5—121no—
432C4×C5—121no—
433C4×C5—122no—
434C4×C5D3×C4⋊C412yes—
435C4×C5C22×C4×D311yescharacteristic
436C4×C5C2×D3×Q811yescharacteristic
437Dic5—32no—
438Dic5—32no—
439Dic5—41no—
440Dic5—42no—
441Dic5—41no—
442C24—151no—
443C22×C4—61no—
444C22×C4—101no—
445C22×C4—151no—
446C22×C4—154no—
447C22×C4—151no—
448C22×C4—151no—
449C22×C4—154no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—301no—
453C22×C4—301no—
454C22×C4C2×D3×D511yescharacteristic
455M16—154no—
456M16—158no—
457M16#120014yescomplemented
458C2×C8—152no—
459C2×C8—158no—
460C2×C8C2×D3×D512yes—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—31no—
464C4⋊C4—51no—
465C4⋊C4—52no—
466C4⋊C4—51no—
467C4⋊C4—61no—
468C4⋊C4—101no—
469C4⋊C4—301no—
470C4⋊C4—301no—
471C22⋊C4—61no—
472C22⋊C4—101no—
473C22⋊C4—301no—
474C22⋊C4—301no—
475C22⋊C4—302no—
476C22⋊C4—302no—
477C42—61no—
478C42—101no—
479C42—301no—
480C42—301no—
481C42—302no—
482C42—302no—
483C3×C5#291111yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3D5×C4⋊C412yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—52no—
489C2×D3—52no—
490C2×D3—101no—
491C2×D3—101no—
492C2×D3—101no—
493C2×D3—101no—
494C2×D3—204no—
495C3×C4—201no—
496C3×C4—201no—
497C3×C4—202no—
498C3×C4D5×C4⋊C412yes—
499C3×C4C22×C4×D511yescharacteristic
500C3×C4C2×Q8×D511yescharacteristic
501Dic3—41no—
502Dic3—42no—
503Dic3—41no—
504Dic3—52no—
505Dic3—52no—
506C2×C5—22no—
507C2×C5C2×D3×C4⋊C411yescharacteristic
508C2×C5#577311yescharacteristic
509C2×C5#577711yescharacteristic
510D5—62no—
511D5—62no—
512C23—151no—
513C23—151no—
514C23—154no—
515C23—601no—
516C23—601no—
517C23#677711yescharacteristic
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—102no—
524C2×C4—122no—
525C2×C4—154no—
526C2×C4—151no—
527C2×C4—151no—
528C2×C4—154no—
529C2×C4—154no—
530C2×C4—152no—
531C2×C4—152no—
532C2×C4—152no—
533C2×C4—152no—
534C2×C4—202no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4D15⋊Q812yes—
538C2×C4#677711yescharacteristic
539C2×C4C2×#120012yes—
540C2×C4C22×D3×D511yescharacteristic
541C8—154no—
542C8C2×#120014yes—
543C2×C3—22no—
544C2×C3C2×D5×C4⋊C411yescharacteristic
545C2×C3#6610711yescharacteristic
546C2×C3#6611111yescharacteristic
547D3—102no—
548D3—102no—
549C5#7920811yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—152no—
553C22—152no—
554C22—301no—
555C22—301no—
556C22—301no—
557C22—301no—
558C22—604no—
559C22#9143712yes—
560C22C2×#677711yescharacteristic
561C4—122no—
562C4—121no—
563C4—121no—
564C4—152no—
565C4—152no—
566C4—201no—
567C4—202no—
568C4—201no—
569C4#9143712yes—
570C4C2×D15⋊Q811yescharacteristic
571C4C22×#120011yescharacteristic
572C3#1061093911yescharacteristic, complemented, Sylow
573C2—22no—
574C2—302no—
575C2—302no—
576C2#1175403511yescharacteristic
577C2#1175403611yescharacteristic
578C2C2×#9143711yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC23×D15D4
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2911
LCSG ▷ 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
4. C5×#5121C2semidirect
5. C3×#65410C2semidirect
6. #11748472C2semidirect
7. #11748470C2semidirect
8. #11747690C2semidirect
9. #11747687C2semidirect
10. #11747640C2semidirect
11. #11747638C2semidirect
16. M16×D15C4semidirect
37. C5×#818C22semidirect
38. C5×#817C22semidirect
39. C3×#3950C22semidirect
40. C3×#3949C22semidirect
41. #90989C22semidirect
42. #90989C22semidirect
43. #90986C22semidirect
44. #90986C22semidirect
50. #65410D3semidirect
70. C3×C5×M16C2×C4semidirect
72. #6710C2×C4semidirect
74. #6705C2×C4semidirect
75. C8×D15C2×C4semidirect
102. #5121D5semidirect
135. #3950C2×D3semidirect
136. #3949C2×D3semidirect
199. #818C2×D5semidirect
200. #817C2×D5semidirect
218. C5×M16C4×D3semidirect
292. C3×M16C4×D5semidirect
457. M16#1200semidirect
483. C3×C5#2911semidirect
549. C5#79208semidirect
572. C3#10610939semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D152
#117544612
C2×#913472
C5×#51212
C3×#654102
#117484722
#117484702
#117476902
#117476872
#117476402
#117476382
#106109393
#792085