Finite Group Databasebeta

← #14297022

Subgroups — #14297022

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic
2C2×#91094C211yesmaximal, characteristic, complemented
3C2×C5×#810C211yesmaximal, characteristic, complemented
4C3×#65276C211yesmaximal, characteristic
5C2×#90974C211yesmaximal, characteristic, complemented
6C2×#90972C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic
8#10601059—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C22×#1204—21no—
13C22×D5×Dic3—21no—
14C2×D5×Dic6—22no—
15C2×D5×Dic6—22no—
16C2×D5×Dic6—22no—
17C2×D5×Dic6—22no—
18C2×D5×Dic6—22no—
19C2×D5×Dic6C414yescomplemented
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×#685—21no—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25#91094—22no—
26C5×#810—22no—
27C3×#3963—21no—
28#90974—22no—
29#90972—22no—
30#90955—22no—
31#69525—51nomaximal, Hall
32C22×Q8×D5—31no—
33C2×C5×#103—31no—
34C2×#3967—31no—
35C2×#3952—31no—
36C2×#3948—31no—
37#65276D311yescharacteristic
38C2×#3942—31no—
39C23×C3×D5D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30C2×C412yes—
47C2×Dic30D412yes—
48C2×Dic30D412yes—
49C22×C5×Dic3—21no—
50C2×C5×Dic6—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—21no—
53C2×C5×Dic6C2×C412yes—
54C2×C5×Dic6D412yes—
55C2×C5×Dic6D412yes—
56C22×C3×Dic5—21no—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×C4×D5—21no—
60C2×C3×C4×D5—21no—
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5C2×C412yes—
63C2×C3×C4×D5D412yes—
64C2×#1204—24no—
65C2×#1204—24no—
66C2×#1204—24no—
67C2×D5×Dic3—24no—
68C2×D5×Dic3—24no—
69C2×D5×Dic3—24no—
70D5×Dic6—28no—
71D5×Dic6—28no—
72D5×Dic6—28no—
73D5×Dic6—28no—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4—21no—
76C2×C3⋊#168—21no—
77C2×C3⋊#168—21no—
78C2×C3⋊#168—21no—
79C2×C5×C3⋊C8—21no—
80C2×C5×C3⋊C8—21no—
81C2×C5×C3⋊C8—21no—
82C3×#685—42no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—21no—
85C23×Dic6—51no—
86C3×#380—51no—
87C2×#830—51no—
88C2×#810—51no—
89C2×#810—51no—
90C2×#810—51no—
91C2×#810D511yescharacteristic, complemented
92C22×C5×Q8—31no—
93C2×Q8×D5—34no—
94C2×Q8×D5—62no—
95C2×Q8×D5—62no—
96C2×Q8×D5—62no—
97C2×Q8×D5—62no—
98C2×Q8×D5—62no—
99C22×C4×D5—61no—
100C22×C4×D5C2×D311yescharacteristic
101C22×Dic10—31no—
102C22×Dic10—61no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#685—21no—
106C2×C4⋊Dic5C2×D311yescharacteristic
107C22×#168—31no—
108C5×#103—62no—
109#3967—62no—
110#3963—21no—
111#3952—62no—
112#3948—62no—
113#3942—62no—
114#1787—151noSylow
115C23×C3×C5C2×D411yescharacteristic
116C22×C3×D5—21no—
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5C22⋊C412yes—
121C22×C3×D5SD1612yes—
122C22×C3×D5Q1612yes—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5C22×C411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135Dic30—22no—
136Dic30—22no—
137Dic30—22no—
138Dic30C22⋊C414yescomplemented
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C5×Dic6—22no—
143C5×Dic6—22no—
144C5×Dic6—22no—
145C5×Dic6C22⋊C414yescomplemented
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—41no—
149C2×C3×Dic5—41no—
150C2×C3×Dic5—41no—
151C2×C3×Dic5C22⋊C412yes—
152C3×C4×D5—22no—
153C3×C4×D5—22no—
154C3×C4×D5—22no—
155C3×C4×D5—22no—
156#1204—216no—
157D5×Dic3—216no—
158C3⋊#168—41no—
159C5×C3⋊C8—41no—
160C23×C3×C4—51no—
161C23×Dic3—101no—
162C22×Dic6—51no—
163C22×Dic6—54no—
164C22×Dic6—102no—
165C22×Dic6—102no—
166C22×Dic6—102no—
167C22×Dic6—101no—
168C22×Dic6—102no—
169C22×Dic6—102no—
170C22×Dic6C2×D511yescharacteristic
171C2×C3×C4⋊C4—51no—
172C2×C3×C4⋊C4C2×D511yescharacteristic
173C2×C3×C22⋊C4—101no—
174C22×C3⋊C8—51no—
175C22×C3⋊C8C2×D511yescharacteristic
176C3×#95—101no—
177#830—102no—
178#810—22no—
179#810—102no—
180#810—102no—
181#810—102no—
182C23×D5#6711yescharacteristic
183C2×C5×Q8—32no—
184C2×C5×Q8—32no—
185C2×C5×Q8—32no—
186C2×C5×Q8—61no—
187C2×C5×Q8—61no—
188C2×C5×Q8—61no—
189C22×C4×C5—21no—
190C22×C4×C5—61no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—21no—
193C22×Dic5—61no—
194C22×Dic5#6711yescharacteristic
195Q8×D5—68no—
196Q8×D5—68no—
197Q8×D5—68no—
198Q8×D5—68no—
199C2×C4×D5—21no—
200C2×C4×D5—21no—
201C2×C4×D5—21no—
202C2×C4×D5—21no—
203C2×C4×D5—64no—
204C2×C4×D5—64no—
205C2×C4×D5—64no—
206C2×C4×D5C4×D312yes—
207C2×C4×D5D1212yes—
208C2×Dic10—32no—
209C2×Dic10—32no—
210C2×Dic10—32no—
211C2×Dic10—64no—
212C2×Dic10—64no—
213C2×Dic10—61no—
214C2×Dic10—61no—
215C2×Dic10—61no—
216C2×Dic10—64no—
217C2×C5×C8—61no—
218C2×C5×C8—61no—
219C2×C5×C8—61no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222#685—42no—
223C4⋊Dic5—21no—
224C4⋊Dic5—21no—
225C2×#168—61no—
226C2×#168—61no—
227C2×#168—61no—
228C23×Q8—151no—
229C2×#103—31no—
230C2×#103—151no—
231C2×#103—151no—
232C2×#103—151no—
233C2×C22⋊C8—151no—
234#380—51no—
235C22×C3×C5C2×C22⋊C411yescharacteristic
236C22×C3×C5#12011yescharacteristic
237C22×C3×C5#12011yescharacteristic
238C22×C3×C5C2×SD1611yescharacteristic
239C22×C3×C5C2×Q1611yescharacteristic
240C22×C3×C5#13711yescharacteristic
241C22×C3×C5#13711yescharacteristic
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C2×C3×D5—22no—
245C2×C3×D5—22no—
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5#10314yescomplemented
249C3×C4×C5—81no—
250C3×C4×C5C2×C22⋊C411yescharacteristic
251C3×C4×C5C2×C22⋊C411yescharacteristic
252C3×C4×C5#12011yescharacteristic
253C3×C4×C5#12011yescharacteristic
254Dic15—24no—
255C3×Dic5—22no—
256C3×Dic5—81no—
257C5×Dic3—24no—
258C24×C3—51no—
259C22×C3×C4—21no—
260C22×C3×C4—51no—
261C22×C3×C4—52no—
262C22×C3×C4—52no—
263C22×C3×C4—101no—
264C22×C3×C4—101no—
265C22×C3×C4—101no—
266C22×C3×C4—101no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—104no—
271C22×Dic3—104no—
272C22×Dic3—104no—
273C22×Dic3—101no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—52no—
278C2×Dic6—52no—
279C2×Dic6—52no—
280C2×Dic6—108no—
281C2×Dic6—108no—
282C2×Dic6—108no—
283C2×Dic6—104no—
284C2×Dic6—104no—
285C2×Dic6—104no—
286C2×Dic6—101no—
287C2×Dic6—101no—
288C2×Dic6—101no—
289C2×Dic6—108no—
290C2×Dic6C4×D512yes—
291C2×Dic6D2012yes—
292C2×Dic6C22⋊D512yes—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—101no—
296C3×C4⋊C4—101no—
297C3×C22⋊C4—202no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—101no—
302C2×C3⋊C8—101no—
303C2×C3⋊C8—101no—
304C23×C5C2×#6711yescharacteristic
305C22×D5—21no—
306C22×D5—21no—
307C22×D5—21no—
308C22×D5—21no—
309C22×D5(C2×D3)⋊C412yes—
310C22×D5#21412yes—
311C22×D5#21612yes—
312C5×Q8—34no—
313C5×Q8—62no—
314C5×Q8—62no—
315C5×Q8—62no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—62no—
320C2×C4×C5—62no—
321C2×C4×C5—62no—
322C2×C4×C5C2×C4×D311yescharacteristic
323C2×C4×C5C2×D1211yescharacteristic
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5D3×D411yescharacteristic
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5D3×D411yescharacteristic
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—41no—
331C2×Dic5—41no—
332C2×Dic5—41no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5(C2×D3)⋊C412yes—
337C4×D5—22no—
338C4×D5—22no—
339C4×D5—22no—
340C4×D5—22no—
341C4×D5—616no—
342Dic10—34no—
343Dic10—616no—
344Dic10—62no—
345Dic10—62no—
346Dic10—62no—
347C5×C8—121no—
348#168—121no—
349C22×Q8—31no—
350C22×Q8—154no—
351C22×Q8—151no—
352C22×Q8—301no—
353C22×Q8—302no—
354C22×Q8—302no—
355C22×Q8—302no—
356C22×Q8—302no—
357C22×Q8—302no—
358C23×C4—51no—
359C23×C4—301no—
360C22×C8—31no—
361C22×C8—151no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4D3×D511yescharacteristic
364C2×C22⋊C4—101no—
365#103—62no—
366#103—302no—
367#103—302no—
368#103—302no—
369C22⋊C8—302no—
370#95—101no—
371C2×C3×C5#37911yescharacteristic
372C2×C3×C5C2×#10311yescharacteristic
373C2×C3×C5#41911yescharacteristic
374C2×C3×C5#44811yescharacteristic
375C2×C3×C5#44811yescharacteristic
376C2×C3×C5#45111yescharacteristic
377C2×C3×C5#45111yescharacteristic
378C3×D5—24no—
379C23×C3—52no—
380C23×C3—52no—
381C23×C3—52no—
382C23×C3—101no—
383C23×C3—101no—
384C23×C3—101no—
385C23×C3—101no—
386C23×C3D4×D511yescharacteristic
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—52no—
391C2×C3×C4—101no—
392C2×C3×C4—101no—
393C2×C3×C4—102no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—201no—
398C2×C3×C4—201no—
399C2×C3×C4—201no—
400C2×C3×C4C2×C4×D511yescharacteristic
401C2×C3×C4C2×D2011yescharacteristic
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4D4×D511yescharacteristic
404C2×C3×C4D4×D511yescharacteristic
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—1016no—
410C2×Dic3—102no—
411C2×Dic3—102no—
412C2×Dic3—102no—
413Dic6—22no—
414Dic6—22no—
415Dic6—22no—
416Dic6—54no—
417Dic6—1016no—
418Dic6—102no—
419Dic6—102no—
420Dic6—102no—
421Dic6#68514yescomplemented
422C3⋊C8—41no—
423C3⋊C8—201no—
424C22×C5C2×(C2×D3)⋊C411yescharacteristic
425C22×C5C2×#21411yescharacteristic
426C22×C5#93711yescharacteristic
427C22×C5#93711yescharacteristic
428C22×C5C2×#21611yescharacteristic
429C22×C5#95111yescharacteristic
430C22×C5#95111yescharacteristic
431C2×D5—22no—
432C2×D5—22no—
433C2×D5—22no—
434C2×D5—22no—
435C2×D5—22no—
436C2×D5—22no—
437C2×D5#81014yescomplemented
438C4×C5—64no—
439C4×C5—81no—
440C4×C5D3×C22⋊C411yescharacteristic
441C4×C5D3×C22⋊C411yescharacteristic
442C4×C5#88211yescharacteristic
443C4×C5#88211yescharacteristic
444Dic5—22no—
445Dic5—64no—
446Dic5—81no—
447C24—51no—
448C2×Q8—32no—
449C2×Q8—32no—
450C2×Q8—32no—
451C2×Q8—61no—
452C2×Q8—61no—
453C2×Q8—61no—
454C2×Q8—152no—
455C2×Q8—152no—
456C2×Q8—152no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—304no—
460C2×Q8—308no—
461C2×Q8—308no—
462C2×Q8—308no—
463C2×Q8—308no—
464C2×Q8—301no—
465C2×Q8—301no—
466C2×Q8—301no—
467C22×C4—21no—
468C22×C4—51no—
469C22×C4—52no—
470C22×C4—52no—
471C22×C4—61no—
472C22×C4—101no—
473C22×C4—101no—
474C22×C4—101no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—304no—
478C22×C4—304no—
479C22×C4—304no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482C2×C8—61no—
483C2×C8—61no—
484C2×C8—61no—
485C2×C8—301no—
486C2×C8—301no—
487C2×C8—301no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C22⋊C4—202no—
493C3×C5#178711yescharacteristic, complemented, Hall
494C22×C3—54no—
495C22×C3—102no—
496C22×C3—102no—
497C22×C3—102no—
498C22×C3—102no—
499C22×C3—102no—
500C22×C3—102no—
501C22×C3D5×C22⋊C411yescharacteristic
502C22×C3#402811yescharacteristic
503C22×C3D5×SD1611yescharacteristic
504C22×C3#406111yescharacteristic
505C22×C3D5×Q1611yescharacteristic
506C22×C3#406411yescharacteristic
507C22×C3#408311yescharacteristic
508C3×C4—81no—
509C3×C4—102no—
510C3×C4—401no—
511C3×C4D5×C22⋊C411yescharacteristic
512C3×C4#402811yescharacteristic
513C3×C4C2×#68511yescharacteristic
514C3×C4#408311yescharacteristic
515Dic3—24no—
516Dic3—104no—
517C2×C5#495511yescharacteristic
518C2×C5C2×#81011yescharacteristic
519C2×C5#500411yescharacteristic
520C2×C5#504011yescharacteristic
521C2×C5#504011yescharacteristic
522C2×C5#505011yescharacteristic
523C2×C5#505011yescharacteristic
524D5—24no—
525C23—52no—
526C23—52no—
527C23—52no—
528C23—101no—
529C23—101no—
530C23—101no—
531C23—101no—
532C23D5×#6711yescharacteristic
533Q8—34no—
534Q8—62no—
535Q8—62no—
536Q8—62no—
537Q8—154no—
538Q8—3016no—
539Q8—302no—
540Q8—302no—
541Q8—302no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—52no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—101no—
550C2×C4—101no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—3016no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4—302no—
562C2×C4C4×D3×D511yescharacteristic
563C2×C4D5×D1211yescharacteristic
564C2×C4D3×D2011yescharacteristic
565C2×C4#677711yescharacteristic
566C2×C4D3×C22⋊D511yescharacteristic
567C2×C4#679011yescharacteristic
568C8—121no—
569C8—601no—
570C2×C3—104no—
571C2×C3D5×#10311yescharacteristic
572C2×C3#6509111yescharacteristic
573C2×C3#6509511yescharacteristic
574C2×C3#6509711yescharacteristic
575C2×C3#6524411yescharacteristic
576C2×C3#6545911yescharacteristic
577C2×C3#6547511yescharacteristic
578C5#6952511yescharacteristic, complemented, Sylow
579C22—54no—
580C22—102no—
581C22—102no—
582C22—102no—
583C22—102no—
584C22—102no—
585C22—102no—
586C22D5×(C2×D3)⋊C411yescharacteristic
587C22#9147411yescharacteristic
588C22D5×#21411yescharacteristic
589C22#9148411yescharacteristic
590C22D5×#21611yescharacteristic
591C22#9150811yescharacteristic
592C22#9157711yescharacteristic
593C4—64no—
594C4—81no—
595C4—102no—
596C4—304no—
597C4—401no—
598C4D3×#68511yescharacteristic
599C4#9147311yescharacteristic
600C4#9147511yescharacteristic
601C4#9147611yescharacteristic
602C3#1060105911yescharacteristic, complemented, Sylow
603C2—104no—
604C2D5×#81011yescharacteristic
605C2#1174748711yescharacteristic
606C2#1174749211yescharacteristic
607C2#1174749311yescharacteristic
608C2#1174894011yescharacteristic
609C2#1174915411yescharacteristic
610C2#1174940011yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1787
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91094C2semidirect
3. C2×C5×#810C2semidirect
5. C2×#90974C2semidirect
6. C2×#90972C2semidirect
19. C2×D5×Dic6C4semidirect
91. C2×#810D5semidirect
138. Dic30C22⋊C4semidirect
145. C5×Dic6C22⋊C4semidirect
248. C2×C3×D5#103semidirect
421. Dic6#685semidirect
437. C2×D5#810semidirect
493. C3×C5#1787semidirect
578. C5#69525semidirect
602. C3#10601059semidirect

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×#910942
C2×C5×#8102
C3×#652762
C2×#909742
C2×#909722
C2×#909552
#106010593
#695255