Finite Group Databasebeta

← #14413419

Subgroups — #14413419

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×#91781C211yesmaximal, characteristic
2#11754461C211yesmaximal, characteristic
3C2×#91292C211yesmaximal, characteristic
4C5×#4964C211yesmaximal, characteristic, complemented
5C3×#65253C211yesmaximal, characteristic, complemented
6#11748460C211yesmaximal, characteristic, complemented
7#11748455C211yesmaximal, characteristic, complemented
8#11747459C212yesmaximal, complemented
9#11747456C212yesmaximal, complemented
10#11747440C212yesmaximal, complemented
11#11747439C212yesmaximal, complemented
12#10610939—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×#6714—21no—
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15—21no—
18#91781—21no—
19#91781—21no—
20#91781C2212yes—
21#91781C2212yes—
22C5×#926C2211yescharacteristic
23C2×C5×#208C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91561—21no—
27#91532—21no—
28#91437C2211yescharacteristic
29#91437C2211yescharacteristic
30C4×#1200—21no—
31#91386—21no—
32#91347C2211yescharacteristic
33#91347C2211yescharacteristic
34C2×#6651C2212yes—
35#91292C418yescomplemented
36C2×#6648C2212yes—
37C5×#808C2212yescomplemented
38C5×#807C2212yescomplemented
39C3×#3940C2212yescomplemented
40C3×#3939C2212yescomplemented
41#90990C2212yescomplemented
42#90988C2212yescomplemented
43#90987C2212yescomplemented
44#90985C2212yescomplemented
45#79208—51nomaximal, Hall
46C2×D5×M16—31no—
47D5×#117—31no—
48C2×#4038—31no—
49C5×#428—31no—
50#65410—31no—
51#65284—31no—
52#65253D311yescharacteristic, complemented
53#65170—32no—
54#65169—32no—
55#65150—32no—
56#65149—32no—
57C23×D15D411yescharacteristic
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×Dic15—21no—
61C22×Dic15D411yescharacteristic
62C2×C4×D15C2×C414yes—
63C2×C4×D15D411yescharacteristic
64C2×C4×D15D411yescharacteristic
65C2×C4×D15Q814yes—
66C2×C4×D15C2311yescharacteristic
67C2×C4×D15C2311yescharacteristic
68C2×#1200—21no—
69C2×#1200—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72#6714—22no—
73#6714—22no—
74C4⋊Dic15—21no—
75C4⋊Dic15C2312yes—
76C4×Dic15—22no—
77C4×Dic15—22no—
78C5×#217—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C4×C5×Dic3—21no—
82C5×#208C2×C414yescomplemented
83C2×C5×C3⋊C8C2312yes—
84C3×C22⋊Dic5—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2311yescharacteristic
87C3×C4×Dic5—21no—
88C3×#681C2×C414yescomplemented
89C2×C3×#168C2312yes—
90#6669—21no—
91#6669—21no—
92#6667—21no—
93#6667—21no—
94Dic3×Dic5—21no—
95Dic3×Dic5—21no—
96#6651C2×C418yescomplemented
97#6648C2×C418yescomplemented
98C2×D3×M16—51no—
99D3×#117—51no—
100C2×#892—51no—
101C3×#428—51no—
102#5121—51no—
103#4995—51no—
104#4964D511yescharacteristic, complemented
105#4881—52no—
106#4880—52no—
107#4861—52no—
108#4860—52no—
109C22×C4×D5—31no—
110C2×C5×M16—31no—
111C5×#117—31no—
112C2×C5×C4⋊C4C2×D311yescharacteristic
113C2×#685—61no—
114#4072C2×D311yescharacteristic
115C2×C4⋊Dic5—31no—
116C2×C4×Dic5—61no—
117C2×#681C2×D311yescharacteristic
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#3950—32no—
136#3949—32no—
137#3940—32no—
138#3940C2×D312yescomplemented
139#3939—32no—
140#3939C2×D312yescomplemented
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×C5—22no—
149C2×C3×C4×C5—42no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×Q812yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15—22no—
155C2×Dic15—42no—
156C2×Dic15C4⋊C414yes—
157C2×Dic15C2×D411yescharacteristic
158C2×Dic15C2×D411yescharacteristic
159C4×D15C4⋊C414yes—
160C4×D15C4⋊C414yes—
161C4×D15C22×C412yes—
162C4×D15C22×C412yes—
163C4×D15C2×Q812yes—
164C4×D15C2×Q812yes—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—21no—
169#1200—42no—
170#1200—42no—
171C3×#168C22×C414yes—
172C5×C3⋊C8C22×C414yes—
173C22×C4×D3—51no—
174C2×C3×M16—51no—
175C3×#117—51no—
176C2×C3×C4⋊C4C2×D511yescharacteristic
177C2×(C2×D3)⋊C4—101no—
178#926C2×D511yescharacteristic
179C2×C4⋊Dic3—51no—
180C2×C4×Dic3—101no—
181C2×#208C2×D511yescharacteristic
182D3×M16—58no—
183C2×ΓL(1,𝔽25)—52no—
184C2×D3×C8—52no—
185#892—52no—
186#892—52no—
187#892—51no—
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#818—52no—
200#817—52no—
201#808—52no—
202#808C2×D512yescomplemented
203#807—52no—
204#807C2×D512yescomplemented
205C23×D5—31no—
206C22×C4×C5—21no—
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5—31no—
209C22×Dic5—61no—
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×M16—34no—
219C2×C5×C8—32no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—31no—
222C5×C4⋊C4—31no—
223C5×C4⋊C4C22×D312yes—
224C5×C22⋊C4—61no—
225C42×C5—61no—
226C22⋊Dic5—21no—
227#685—61no—
228#685—61no—
229#685—62no—
230#685—62no—
231C4⋊Dic5—32no—
232C4⋊Dic5—61no—
233C4⋊Dic5C22×D311yescharacteristic
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#681C4×D314yescomplemented
243C2×#168C22×D312yes—
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×C5—42no—
269C3×C4×C5C2×C4⋊C412yes—
270C3×C4×C5C23×C411yescharacteristic
271C3×C4×C5C22×Q811yescharacteristic
272Dic15—42no—
273Dic15C2×C4⋊C412yes—
274Dic15C2×C4⋊C412yes—
275C3×Dic5—41no—
276C3×Dic5—41no—
277C5×Dic3—41no—
278C5×Dic3—41no—
279C23×D3—51no—
280C22×C3×C4—21no—
281C22×C3×C4C22×D511yescharacteristic
282C22×Dic3—51no—
283C22×Dic3—101no—
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×M16—54no—
293C2×C3×C8—52no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—51no—
296C3×C4⋊C4—51no—
297C3×C4⋊C4C22×D512yes—
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—52no—
306C4⋊Dic3—101no—
307C4⋊Dic3C22×D511yescharacteristic
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#208C4×D514yescomplemented
317C2×C3⋊C8C22×D512yes—
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—22no—
327C2×C4×C5—42no—
328C2×C4×C5—61no—
329C2×C4×C5—61no—
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—34no—
337C2×Dic5—31no—
338C2×Dic5—31no—
339C2×Dic5—62no—
340C2×Dic5—122no—
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×C8—34no—
350#168C2×C4×D314yes—
351C23×C4—151no—
352C2×M16—31no—
353C2×M16—51no—
354C2×M16—152no—
355C2×M16—158no—
356C22×C8—152no—
357#117—31no—
358#117—51no—
359#117—151no—
360#117—151no—
361#117—152no—
362#117—152no—
363#117—301no—
364#117—301no—
365#117—301no—
366#117—301no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—151no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4D3×D511yescharacteristic
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—22no—
396C2×C3×C4—42no—
397C2×C3×C4—101no—
398C2×C3×C4—101no—
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—51no—
406C2×Dic3—51no—
407C2×Dic3—54no—
408C2×Dic3—102no—
409C2×Dic3—202no—
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×C8—54no—
419C3⋊C8C2×C4×D514yes—
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—42no—
432C4×C5—121no—
433C4×C5—121no—
434C4×C5D3×C4⋊C412yes—
435C4×C5C22×C4×D311yescharacteristic
436C4×C5C2×D3×Q811yescharacteristic
437Dic5—32no—
438Dic5—32no—
439Dic5—41no—
440Dic5—41no—
441Dic5—122no—
442C24—151no—
443C22×C4—21no—
444C22×C4—151no—
445C22×C4—154no—
446C22×C4—154no—
447C22×C4—151no—
448C22×C4—151no—
449C22×C4—151no—
450C22×C4—151no—
451C22×C4—301no—
452C22×C4—301no—
453C22×C4—301no—
454C22×C4C2×D3×D511yescharacteristic
455M16—34no—
456M16—54no—
457M16—158no—
458C2×C8—32no—
459C2×C8—52no—
460C2×C8—158no—
461C4⋊C4—21no—
462C4⋊C4—31no—
463C4⋊C4—31no—
464C4⋊C4—51no—
465C4⋊C4—51no—
466C4⋊C4—152no—
467C4⋊C4—301no—
468C4⋊C4—301no—
469C4⋊C4—301no—
470C4⋊C4C2×D3×D512yes—
471C22⋊C4—61no—
472C22⋊C4—101no—
473C22⋊C4—302no—
474C22⋊C4—302no—
475C22⋊C4—301no—
476C22⋊C4—301no—
477C42—61no—
478C42—101no—
479C42—302no—
480C42—302no—
481C42—301no—
482C42—301no—
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—42no—
496C3×C4—201no—
497C3×C4—201no—
498C3×C4D5×C4⋊C412yes—
499C3×C4C22×C4×D511yescharacteristic
500C3×C4C2×Q8×D511yescharacteristic
501Dic3—41no—
502Dic3—41no—
503Dic3—52no—
504Dic3—52no—
505Dic3—202no—
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#679011yescharacteristic
518C2×C4—22no—
519C2×C4—42no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—154no—
525C2×C4—151no—
526C2×C4—151no—
527C2×C4—154no—
528C2×C4—154no—
529C2×C4—152no—
530C2×C4—152no—
531C2×C4—152no—
532C2×C4—152no—
533C2×C4—302no—
534C2×C4—602no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4D15⋊Q812yes—
538C2×C4C4×D3×D512yes—
539C2×C4#679011yescharacteristic
540C2×C4C22×D3×D511yescharacteristic
541C8—34no—
542C8—54no—
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#9140412yes—
560C22C2×#679011yescharacteristic
561C4—42no—
562C4—121no—
563C4—121no—
564C4—152no—
565C4—152no—
566C4—201no—
567C4—201no—
568C4—602no—
569C4#9140412yes—
570C4C2×D15⋊Q811yescharacteristic
571C4C2×C4×D3×D511yescharacteristic
572C3#1061093911yescharacteristic, complemented, Sylow
573C2—22no—
574C2—302no—
575C2—302no—
576C2C2×#9140411yescharacteristic
577C2#1175470211yescharacteristic
578C2#1175509611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC23×D15D4
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2911
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C5×#4964C2semidirect
5. C3×#65253C2semidirect
6. #11748460C2semidirect
7. #11748455C2semidirect
8. #11747459C2semidirect
9. #11747456C2semidirect
10. #11747440C2semidirect
11. #11747439C2semidirect
35. #91292C4semidirect
37. C5×#808C22semidirect
38. C5×#807C22semidirect
39. C3×#3940C22semidirect
40. C3×#3939C22semidirect
41. #90990C22semidirect
42. #90988C22semidirect
43. #90987C22semidirect
44. #90985C22semidirect
52. #65253D3semidirect
82. C5×#208C2×C4semidirect
88. C3×#681C2×C4semidirect
96. #6651C2×C4semidirect
97. #6648C2×C4semidirect
104. #4964D5semidirect
138. #3940C2×D3semidirect
140. #3939C2×D3semidirect
202. #808C2×D5semidirect
204. #807C2×D5semidirect
242. #681C4×D3semidirect
316. #208C4×D5semidirect
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×#917812
#117544612
C2×#912922
C5×#49642
C3×#652532
#117484602
#117484552
#117474592
#117474562
#117474402
#117474392
#106109393
#792085