Finite Group Databasebeta

← #14413421

Subgroups — #14413421

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×C3×D5×M16C211yesmaximal, characteristic
2D5×#926C211yesmaximal, characteristic
3C2×#91358C211yesmaximal, characteristic
4#11751222C211yesmaximal, characteristic, complemented
5C5×#5121C211yesmaximal, characteristic, complemented
6#11748460C211yesmaximal, characteristic, complemented
7#11748459C211yesmaximal, characteristic, complemented
8#11747672C212yesmaximal, complemented
9#11747671C212yesmaximal, complemented
10#11747619C212yesmaximal, complemented
11#11747618C212yesmaximal, complemented
12#10610939—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×D5×M16C418yescomplemented
21C2×C3×#676C2212yes—
22C2×C3×C8×D5C2212yes—
23D5×#217—21no—
24C2×#6665—21no—
25#91528—21no—
26C2×Dic3×Dic5—21no—
27D5×C4⋊Dic3C2211yescharacteristic
28D5×C4⋊Dic3C2211yescharacteristic
29C4×D5×Dic3—21no—
30#91358—21no—
31#91358—21no—
32#91358C2212yes—
33#91358C2211yescharacteristic
34#91358C2212yes—
35#91358C2211yescharacteristic
36#91357—21no—
37#91102C2212yescomplemented
38#91101C2212yescomplemented
39C5×#818C2212yescomplemented
40C5×#817C2212yescomplemented
41#90988C2212yescomplemented
42#90988C2212yescomplemented
43#90985C2212yescomplemented
44#90985C2212yescomplemented
45#83752—51nomaximal, Hall
46C2×D5×M16D311yescharacteristic
47D5×#117—31no—
48C2×#4038—31no—
49C5×#428—31no—
50#65410—31no—
51#65284—31no—
52#65253—31no—
53#65170—32no—
54#65169—32no—
55#65150—32no—
56#65149—32no—
57C23×C3×D5D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C22×C5×Dic3—21no—
61C22×C3×Dic5D411yescharacteristic
62C2×C3×C4×D5C2×C414yes—
63C2×C3×C4×D5D411yescharacteristic
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5Q814yes—
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×D5×Dic3—21no—
69C2×D5×Dic3—21no—
70C3×C5×M16C2×C414yescomplemented
71C2×C3×C5×C8C2312yes—
72#6719—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2311yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C4⋊Dic15C2312yes—
77C4×Dic15—21no—
78C5×#217—21no—
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2311yescharacteristic
81C5×C4⋊Dic3C2311yescharacteristic
82C5×C4⋊Dic3C2312yes—
83C4×C5×Dic3—21no—
84C3×#681C2×C414yescomplemented
85C2×C3×#168C2312yes—
86C3×#676C2×C418yescomplemented
87C3×C8×D5C2×C418yescomplemented
88#6668—21no—
89#6668—21no—
90#6665—22no—
91#6665—22no—
92#6665—21no—
93#6665—21no—
94Dic3×Dic5—22no—
95Dic3×Dic5—22no—
96Dic3×Dic5—21no—
97Dic3×Dic5—21no—
98C22×C3×M16—51no—
99C2×#926—51no—
100C2×#926—51no—
101#5121—51no—
102#5121—51no—
103#5121—51no—
104#5121—52no—
105#5121—52no—
106#5121D511yescharacteristic, complemented
107#5106—52no—
108#5106—52no—
109C22×C4×D5C2×D311yescharacteristic
110C2×C5×M16C2×D311yescharacteristic
111C5×#117—31no—
112C2×C5×C4⋊C4—31no—
113C2×#685—61no—
114#4072—31no—
115C2×C4⋊Dic5—31no—
116C2×C4×Dic5—61no—
117C2×#681C2×D311yescharacteristic
118D5×M16Dic318yescomplemented
119C2×#676C2×D312yes—
120C2×C8×D5C2×D312yes—
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#3940—32no—
139#3939—32no—
140#3939—32no—
141#2911—151noSylow
142C23×C3×C5C2×D411yescharacteristic
143C22×C3×D5—41no—
144C22×C3×D5—41no—
145C22×C3×D5C4⋊C414yes—
146C22×C3×D5C2×D411yescharacteristic
147C22×C3×D5C2×D411yescharacteristic
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×Q812yes—
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15—42no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C2×C5×Dic3—42no—
160C2×C3×Dic5C4⋊C414yes—
161C2×C3×Dic5C2×D411yescharacteristic
162C2×C3×Dic5C2×D411yescharacteristic
163C3×C4×D5C4⋊C414yes—
164C3×C4×D5C4⋊C414yes—
165C3×C4×D5C22×C412yes—
166C3×C4×D5C22×C412yes—
167C3×C4×D5C2×Q812yes—
168C3×C4×D5C2×Q812yes—
169D5×Dic3—42no—
170D5×Dic3—42no—
171C3×C5×C8C22×C414yes—
172C3×#168C22×C414yes—
173C23×C3×C4—51no—
174C2×C3×M16—51no—
175C2×C3×M16—58no—
176C2×C3×M16—52no—
177C2×C3×M16C2×D511yescharacteristic
178C22×C3×C8—52no—
179C2×#217—101no—
180C2×#217—101no—
181#926—51no—
182#926—52no—
183#926—51no—
184#926—52no—
185#926—51no—
186#926—101no—
187#926—101no—
188#926—101no—
189#926—101no—
190#926C2×D511yescharacteristic
191C2×C4⋊Dic3—51no—
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3—51no—
194C2×C4⋊Dic3C2×D511yescharacteristic
195C2×C4×Dic3—101no—
196C2×C4×Dic3—101no—
197#818—52no—
198#818—52no—
199#818—52no—
200#818C2×D512yescomplemented
201#817—52no—
202#817—52no—
203#817—52no—
204#817C2×D512yescomplemented
205C23×D5D1211yescharacteristic
206C22×C4×C5—61no—
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5—61no—
209C22×Dic5D1211yescharacteristic
210C2×C4×D5—61no—
211C2×C4×D5—61no—
212C2×C4×D5Dic614yes—
213C2×C4×D5D1211yescharacteristic
214C2×C4×D5D1211yescharacteristic
215C2×C4×D5C2×Dic314yes—
216C2×C4×D5C22×D311yescharacteristic
217C2×C4×D5C22×D311yescharacteristic
218C5×M16C2×Dic314yescomplemented
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—61no—
227#685—61no—
228#685—61no—
229#685—62no—
230#685—62no—
231C4⋊Dic5—31no—
232C4⋊Dic5—32no—
233C4⋊Dic5—31no—
234C4⋊Dic5—61no—
235#683—61no—
236#683—61no—
237C4×Dic5—61no—
238C4×Dic5—61no—
239C4×Dic5—61no—
240C4×Dic5—62no—
241C4×Dic5—62no—
242#681C2×Dic314yescomplemented
243C2×#168C22×D312yes—
244#676C2×Dic318yescomplemented
245C8×D5C2×Dic318yescomplemented
246C22×M16—51no—
247C2×#117—151no—
248C2×#117—151no—
249#428—31no—
250#428—152no—
251#428—152no—
252#428—151no—
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×C3×D5—21no—
262C2×C3×D5—21no—
263C2×C3×D5—21no—
264C2×C3×D5—21no—
265C2×C3×D5—44no—
266C2×C3×D5C2×C4⋊C412yes—
267C2×C3×D5C2×C4⋊C412yes—
268C3×C4×C5C2×C4⋊C412yes—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×Q811yescharacteristic
271Dic15—41no—
272Dic15—41no—
273Dic15—42no—
274C3×Dic5C2×C4⋊C412yes—
275C3×Dic5C2×C4⋊C412yes—
276C5×Dic3—41no—
277C5×Dic3—41no—
278C5×Dic3—42no—
279C24×C3—51no—
280C22×C3×C4—51no—
281C22×C3×C4—54no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—54no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4C22×D511yescharacteristic
288C22×Dic3—21no—
289C22×Dic3—101no—
290C22×Dic3—101no—
291C22×Dic3—101no—
292C3×M16—54no—
293C3×M16—58no—
294C3×M16C4×D514yescomplemented
295C2×C3×C8—52no—
296C2×C3×C8—58no—
297C2×C3×C8C22×D512yes—
298#217—21no—
299#217—101no—
300#217—101no—
301#217—102no—
302#217—102no—
303#217—101no—
304C4⋊Dic3—21no—
305C4⋊Dic3—51no—
306C4⋊Dic3—52no—
307C4⋊Dic3—51no—
308C4⋊Dic3—101no—
309C4⋊Dic3—101no—
310C4⋊Dic3—101no—
311C4⋊Dic3C22×D511yescharacteristic
312C4⋊Dic3C22×D512yes—
313C4⋊Dic3C22×D511yescharacteristic
314C4×Dic3—21no—
315C4×Dic3—101no—
316C4×Dic3—101no—
317C4×Dic3—102no—
318C4×Dic3—102no—
319C4×Dic3—101no—
320C23×C5C2×D1211yescharacteristic
321C22×D5—41no—
322C22×D5—41no—
323C22×D5C4⋊Dic314yes—
324C22×D5C2×D1211yescharacteristic
325C22×D5C2×D1211yescharacteristic
326C2×C4×C5—62no—
327C2×C4×C5—61no—
328C2×C4×C5—61no—
329C2×C4×C5—122no—
330C2×C4×C5C2×Dic612yes—
331C2×C4×C5C2×D1211yescharacteristic
332C2×C4×C5C22×Dic312yes—
333C2×C4×C5C23×D311yescharacteristic
334C2×Dic5—61no—
335C2×Dic5—61no—
336C2×Dic5—62no—
337C2×Dic5—122no—
338C2×Dic5C4⋊Dic314yes—
339C2×Dic5C2×D1211yescharacteristic
340C2×Dic5C2×D1211yescharacteristic
341C4×D5—122no—
342C4×D5—122no—
343C4×D5C4⋊Dic314yes—
344C4×D5C4⋊Dic314yes—
345C4×D5C2×Dic612yes—
346C4×D5C2×Dic612yes—
347C4×D5C22×Dic312yes—
348C4×D5C22×Dic312yes—
349C5×C8C22×Dic314yes—
350#168C22×Dic314yes—
351C23×C4—51no—
352C2×M16—51no—
353C2×M16—58no—
354C2×M16—52no—
355C2×M16D3×D511yescharacteristic
356C22×C8—52no—
357#117—31no—
358#117—151no—
359#117—152no—
360#117—151no—
361#117—152no—
362#117—151no—
363#117—301no—
364#117—301no—
365#117—301no—
366#117—301no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—151no—
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—152no—
377#107—152no—
378#107—152no—
379#106—32no—
380#106—152no—
381#106—152no—
382#106—152no—
383C2×C3×C5—22no—
384C2×C3×C5C22×C4⋊C411yescharacteristic
385C2×C3×C5#57511yescharacteristic
386C2×C3×C5#57511yescharacteristic
387C3×D5—22no—
388C3×D5—22no—
389C23×C3—51no—
390C23×C3—51no—
391C23×C3—54no—
392C23×C3—201no—
393C23×C3—201no—
394C23×C3D4×D511yescharacteristic
395C2×C3×C4—51no—
396C2×C3×C4—51no—
397C2×C3×C4—54no—
398C2×C3×C4—52no—
399C2×C3×C4—52no—
400C2×C3×C4—52no—
401C2×C3×C4—52no—
402C2×C3×C4—54no—
403C2×C3×C4—54no—
404C2×C3×C4C2×C4×D512yes—
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4Q8×D512yes—
407C2×C3×C4C23×D511yescharacteristic
408C2×Dic3—21no—
409C2×Dic3—21no—
410C2×Dic3—22no—
411C2×Dic3—42no—
412C2×Dic3—101no—
413C2×Dic3—102no—
414C2×Dic3—101no—
415C2×Dic3—202no—
416C2×Dic3—202no—
417C2×Dic3—202no—
418C3×C8—54no—
419C3×C8C2×C4×D514yes—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5C2×C4⋊Dic312yes—
423C22×C5C22×D1211yescharacteristic
424C2×D5—21no—
425C2×D5—21no—
426C2×D5—21no—
427C2×D5—21no—
428C2×D5—44no—
429C2×D5C2×C4⋊Dic312yes—
430C2×D5C2×C4⋊Dic312yes—
431C4×C5—121no—
432C4×C5—121no—
433C4×C5—122no—
434C4×C5C2×C4⋊Dic312yes—
435C4×C5C22×Dic611yescharacteristic
436C4×C5C23×Dic311yescharacteristic
437Dic5—121no—
438Dic5—121no—
439Dic5—122no—
440Dic5C2×C4⋊Dic312yes—
441Dic5C2×C4⋊Dic312yes—
442C24—51no—
443C22×C4—51no—
444C22×C4—54no—
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—54no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—61no—
451C22×C4—301no—
452C22×C4—301no—
453C22×C4—301no—
454C22×C4C2×D3×D511yescharacteristic
455M16—54no—
456M16—58no—
457M16D5×Dic314yescomplemented
458C2×C8—52no—
459C2×C8—58no—
460C2×C8C2×D3×D512yes—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—31no—
464C4⋊C4—61no—
465C4⋊C4—151no—
466C4⋊C4—152no—
467C4⋊C4—151no—
468C4⋊C4—301no—
469C4⋊C4—301no—
470C4⋊C4—301no—
471C22⋊C4—61no—
472C22⋊C4—301no—
473C22⋊C4—301no—
474C22⋊C4—302no—
475C22⋊C4—302no—
476C22⋊C4—301no—
477C42—61no—
478C42—301no—
479C42—301no—
480C42—302no—
481C42—302no—
482C42—301no—
483C3×C5#291111yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—52no—
487C22×C3—52no—
488C22×C3—101no—
489C22×C3—101no—
490C22×C3—101no—
491C22×C3—101no—
492C22×C3—204no—
493C22×C3D5×C4⋊C412yes—
494C22×C3C2×D4×D511yescharacteristic
495C3×C4—52no—
496C3×C4—52no—
497C3×C4D5×C4⋊C412yes—
498C3×C4C22×C4×D511yescharacteristic
499C3×C4C2×Q8×D511yescharacteristic
500Dic3—42no—
501Dic3—41no—
502Dic3—41no—
503Dic3—201no—
504Dic3—201no—
505Dic3—202no—
506C2×C5—22no—
507C2×C5#574811yescharacteristic
508C2×C5#574811yescharacteristic
509C2×C5C22×C4⋊Dic311yescharacteristic
510D5—22no—
511D5—22no—
512C23—51no—
513C23—51no—
514C23—54no—
515C23—201no—
516C23—201no—
517C23D5×D1211yescharacteristic
518C2×C4—54no—
519C2×C4—51no—
520C2×C4—51no—
521C2×C4—54no—
522C2×C4—54no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—52no—
526C2×C4—52no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—122no—
531C2×C4—302no—
532C2×C4—301no—
533C2×C4—301no—
534C2×C4—602no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4D5×Dic612yes—
538C2×C4D5×D1211yescharacteristic
539C2×C4C2×D5×Dic312yes—
540C2×C4C22×D3×D511yescharacteristic
541C8—54no—
542C8C2×D5×Dic314yes—
543C2×C3—22no—
544C2×C3—102no—
545C2×C3—102no—
546C2×C3C2×D5×C4⋊C411yescharacteristic
547C2×C3#6610711yescharacteristic
548C2×C3#6611111yescharacteristic
549C5#8375211yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—52no—
553C22—52no—
554C22—101no—
555C22—101no—
556C22—101no—
557C22—101no—
558C22—204no—
559C22D5×C4⋊Dic312yes—
560C22C2×D5×D1211yescharacteristic
561C4—52no—
562C4—52no—
563C4—121no—
564C4—122no—
565C4—121no—
566C4—601no—
567C4—602no—
568C4—601no—
569C4D5×C4⋊Dic312yes—
570C4C2×D5×Dic611yescharacteristic
571C4C22×D5×Dic311yescharacteristic
572C3#1061093911yescharacteristic, complemented, Sylow
573C2—22no—
574C2—102no—
575C2—102no—
576C2#1175402111yescharacteristic
577C2#1175402211yescharacteristic
578C2C2×D5×C4⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
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. #11751222C2semidirect
5. C5×#5121C2semidirect
6. #11748460C2semidirect
7. #11748459C2semidirect
8. #11747672C2semidirect
9. #11747671C2semidirect
10. #11747619C2semidirect
11. #11747618C2semidirect
20. C3×D5×M16C4semidirect
37. #91102C22semidirect
38. #91101C22semidirect
39. C5×#818C22semidirect
40. C5×#817C22semidirect
41. #90988C22semidirect
42. #90988C22semidirect
43. #90985C22semidirect
44. #90985C22semidirect
70. C3×C5×M16C2×C4semidirect
84. C3×#681C2×C4semidirect
86. C3×#676C2×C4semidirect
87. C3×C8×D5C2×C4semidirect
106. #5121D5semidirect
118. D5×M16Dic3semidirect
200. #818C2×D5semidirect
204. #817C2×D5semidirect
218. C5×M16C2×Dic3semidirect
242. #681C2×Dic3semidirect
244. #676C2×Dic3semidirect
245. C8×D5C2×Dic3semidirect
294. C3×M16C4×D5semidirect
457. M16D5×Dic3semidirect
483. C3×C5#2911semidirect
549. C5#83752semidirect
572. C3#10610939semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×M162
D5×#9262
C2×#913582
#117512222
C5×#51212
#117484602
#117484592
#117476722
#117476712
#117476192
#117476182
#106109393
#837525