Finite Group Databasebeta

← #14300504

Subgroups — #14300504

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2C22×#6649C211yesmaximal, characteristic, complemented
3C2×#90955C211yesmaximal, characteristic, complemented
4C2×#90955C211yesmaximal, characteristic, complemented
5C2×#90955C211yesmaximal, characteristic, complemented
6#11746345C211yesmaximal, characteristic, complemented
7C5×#4524C211yesmaximal, characteristic, complemented
8#10599462—31nomaximal, Hall
9C22×C3×D20C411yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×#685C411yescharacteristic
18C2×C3×#685C411yescharacteristic
19C2×C3×C4⋊Dic5C411yescharacteristic
20C3×C4×D20—22no—
21C3×C4×D20—22no—
22C2×#6649—22no—
23C2×#6649—22no—
24C2×#6649—22no—
25#90955—22no—
26#90955—22no—
27#90955—22no—
28#71611—51nomaximal, Hall
29C22×#676—31no—
30C2×C4×D20D311yescharacteristic
31C2×#3952—31no—
32C2×#3952—31no—
33C2×#3952—31no—
34C5×#336—31no—
35#64744—31no—
36C23×C3×D5C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C22×C3×C4×C5C2×C411yescharacteristic
39C22×C3×C4×C5C2×C411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C22×C3×Dic5C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×D20—22no—
44C2×C3×D20—22no—
45C2×C3×D20—22no—
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5D412yes—
57C2×C3×C4×D5D412yes—
58C3×C42×C5—21no—
59C3×C42×C5—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65C2×C3⋊#168D412yescomplemented
66C2×C5×C3⋊C8—21no—
67C2×C5×C3⋊C8—21no—
68C2×C5×C3⋊C8—21no—
69C2×C5×C3⋊C8—21no—
70C2×C5×C3⋊C8—21no—
71C2×C5×C3⋊C8D412yescomplemented
72C3×#685—22no—
73C3×#685—22no—
74C3×C4⋊Dic5—22no—
75#6649—28no—
76C2×C3×C4×D4—51no—
77C22×#208—51no—
78C2×#830—51no—
79C2×#830—51no—
80C2×#830—51no—
81#4524—51no—
82#4524D511yescharacteristic, complemented
83C22×D20Dic311yescharacteristic
84C22×C4×D5C2×D311yescharacteristic
85C22×C4×D5C2×D311yescharacteristic
86C22×C5×C8—31no—
87C22×C5×C8—31no—
88C2×C42×C5C2×D311yescharacteristic
89C2×#685Dic311yescharacteristic
90C2×#685Dic311yescharacteristic
91C2×C4⋊Dic5Dic311yescharacteristic
92C22×#168—31no—
93C22×#168—31no—
94C2×#676—62no—
95C2×#676—62no—
96C2×#676—62no—
97C4×D20—22no—
98C4×D20—22no—
99#3952—62no—
100#3952—62no—
101#3952—62no—
102#1870—151noSylow
103C23×C3×C5C22×C411yescharacteristic
104C22×C3×D5—21no—
105C22×C3×D5—21no—
106C22×C3×D5—21no—
107C22×C3×D5—21no—
108C22×C3×D5—21no—
109C22×C3×D5—21no—
110C22×C3×D5—21no—
111C22×C3×D5—21no—
112C22×C3×D5—21no—
113C22×C3×D5—21no—
114C22×C3×D5—21no—
115C22×C3×D5—21no—
116C22×C3×D5C22⋊C412yes—
117C22×C3×D5M1612yescomplemented
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5M1612yescomplemented
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5#4111yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×Dic5—21no—
131C2×C3×Dic5—21no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—21no—
135C2×C3×Dic5C22⋊C412yes—
136C3×D20—28no—
137C3×C4×D5—22no—
138C3×C4×D5—22no—
139C3×C4×D5—22no—
140C3×C4×D5—22no—
141C3×C4×D5—41no—
142C3×C4×D5—41no—
143C3×C4×D5—41no—
144C3×C4×D5—41no—
145C3⋊#168—22no—
146C3⋊#168—41no—
147C5×C3⋊C8—22no—
148C5×C3⋊C8—41no—
149C22×C3×D4—51no—
150C23×C3×C4—51no—
151C23×C3×C4—51no—
152C3×C4×D4—102no—
153C3×C4×D4—102no—
154C2×C3×C4⋊C4—51no—
155C2×C3×C22⋊C4—51no—
156C2×C3×C22⋊C4—51no—
157C2×C3×C42C2×D511yescharacteristic
158C2×#208—102no—
159C2×#208—102no—
160C2×#208—102no—
161C22×C3⋊C8—51no—
162C22×C3⋊C8—51no—
163C22×C3⋊C8C2×D511yescharacteristic
164C22×C3⋊C8C2×D511yescharacteristic
165#830—102no—
166#830—102no—
167#830—102no—
168C23×D5C2×Dic311yescharacteristic
169C23×D5C2×Dic311yescharacteristic
170C22×C4×C5C2×Dic311yescharacteristic
171C22×C4×C5C2×Dic311yescharacteristic
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5C2×Dic311yescharacteristic
174C22×Dic5C2×Dic311yescharacteristic
175C2×D20—22no—
176C2×D20—22no—
177C2×D20—22no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5—21no—
181C2×C4×D5—21no—
182C2×C4×D5—21no—
183C2×C4×D5—21no—
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×C4×D5—21no—
187C2×C4×D5—21no—
188C2×C4×D5#6712yes—
189C2×C4×D5#6712yes—
190C2×C5×C8—32no—
191C2×C5×C8—61no—
192C2×C5×C8—61no—
193C2×C5×C8—61no—
194C2×C5×C8—61no—
195C2×C5×C8—61no—
196C42×C5—21no—
197C42×C5—21no—
198#685—22no—
199#685—22no—
200C4⋊Dic5—22no—
201C2×#168—32no—
202C2×#168—61no—
203C2×#168—61no—
204C2×#168—61no—
205C2×#168—61no—
206C2×#168—61no—
207#676—68no—
208C22×M16—151no—
209C2×C4×D4—51no—
210C2×C22⋊C8—151no—
211C2×C22⋊C8—151no—
212C2×C22⋊C8—151no—
213#336—31no—
214#336—151no—
215C22×C3×C5C2×C22⋊C411yescharacteristic
216C22×C3×C5C4×D411yescharacteristic
217C22×C3×C5C4×D411yescharacteristic
218C22×C3×C5C2×M1611yescharacteristic
219C22×C3×C5C2×M1611yescharacteristic
220C22×C3×C5#13111yescharacteristic
221C22×C3×C5#13111yescharacteristic
222C2×C3×D5—22no—
223C2×C3×D5—22no—
224C2×C3×D5—22no—
225C2×C3×D5—22no—
226C2×C3×D5—22no—
227C2×C3×D5—22no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C2×C3×D5—41no—
232C2×C3×D5—41no—
233C2×C3×D5—41no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C3×C4×C5—22no—
237C3×C4×C5—41no—
238C3×C4×C5#12011yescharacteristic
239C3×C4×C5#12111yescharacteristic
240C3×C4×C5#12111yescharacteristic
241C3×C4×C5#12311yescharacteristic
242C3×Dic5—22no—
243C3×Dic5—41no—
244C24×C3—51no—
245C24×C3—51no—
246C2×C3×D4—102no—
247C2×C3×D4—102no—
248C2×C3×D4—102no—
249C22×C3×C4—51no—
250C22×C3×C4—52no—
251C22×C3×C4—52no—
252C22×C3×C4—51no—
253C22×C3×C4—101no—
254C22×C3×C4—101no—
255C22×C3×C4—101no—
256C22×C3×C4—101no—
257C22×C3×C4—101no—
258C22×C3×C4—101no—
259C22×C3×C4—101no—
260C22×C3×C4—101no—
261C22×C3×C4—101no—
262C22×C3×C4—101no—
263C22×C3×C4C4×D511yescharacteristic
264C22×C3×C4C4×D511yescharacteristic
265C22×C3×C4C22×D511yescharacteristic
266C3×C4⋊C4—102no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4—102no—
269C3×C42—21no—
270C3×C42—21no—
271#208—108no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—101no—
279C2×C3⋊C8—101no—
280C2×C3⋊C8—101no—
281C2×C3⋊C8—101no—
282C2×C3⋊C8—101no—
283C2×C3⋊C8D2012yescomplemented
284C23×C5C22×Dic311yescharacteristic
285C22×D5—21no—
286C22×D5—21no—
287C22×D5—21no—
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C22×D5—21no—
292C22×D5—21no—
293C22×D5—21no—
294C22×D5—21no—
295C22×D5—21no—
296C22×D5—21no—
297C22×D5#20812yescomplemented
298C22×D5#21712yes—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5#20812yescomplemented
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5D3×D411yescharacteristic
307C2×C4×C5#23711yescharacteristic
308C2×C4×C5#23711yescharacteristic
309C2×C4×C5C2×#6711yescharacteristic
310C2×C4×C5C2×#6711yescharacteristic
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5#21712yes—
317D20—28no—
318C4×D5—22no—
319C4×D5—22no—
320C4×D5—22no—
321C4×D5—22no—
322C4×D5—41no—
323C4×D5—41no—
324C4×D5—41no—
325C4×D5—41no—
326C5×C8—62no—
327C5×C8—121no—
328#168—62no—
329#168—121no—
330C22×D4—51no—
331C23×C4—51no—
332C23×C4—51no—
333C2×M16—302no—
334C2×M16—302no—
335C2×M16—302no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8—151no—
339C22×C8—151no—
340C4×D4—102no—
341C4×D4—102no—
342C2×C4⋊C4—51no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—51no—
345C2×C42D3×D511yescharacteristic
346C22⋊C8—302no—
347C22⋊C8—302no—
348C22⋊C8—302no—
349C2×C3×C5#38611yescharacteristic
350C2×C3×C5#40711yescharacteristic
351C2×C3×C5#40811yescharacteristic
352C2×C3×C5#43511yescharacteristic
353C2×C3×C5#43511yescharacteristic
354C2×C3×C5#43611yescharacteristic
355C2×C3×C5#43611yescharacteristic
356C3×D5—42no—
357C3×D5—42no—
358C23×C3—52no—
359C23×C3—52no—
360C23×C3—101no—
361C23×C3—101no—
362C23×C3—101no—
363C23×C3—101no—
364C23×C3—101no—
365C23×C3—101no—
366C23×C3—101no—
367C23×C3—101no—
368C23×C3—101no—
369C23×C3—101no—
370C23×C3—101no—
371C23×C3—101no—
372C23×C3C2×C4×D511yescharacteristic
373C3×D4—108no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—52no—
380C2×C3×C4—101no—
381C2×C3×C4—101no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—101no—
387C2×C3×C4—101no—
388C2×C3×C4—101no—
389C2×C3×C4—201no—
390C2×C3×C4—201no—
391C2×C3×C4—201no—
392C2×C3×C4—201no—
393C2×C3×C4#67612yescomplemented
394C2×C3×C4C2×D2011yescharacteristic
395C2×C3×C4#70911yescharacteristic
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4D4×D511yescharacteristic
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4#71311yescharacteristic
400C3⋊C8—22no—
401C3⋊C8—41no—
402C3⋊C8—102no—
403C3⋊C8—201no—
404C22×C5C2×#20811yescharacteristic
405C22×C5C2×#20811yescharacteristic
406C22×C5D4×Dic311yescharacteristic
407C22×C5D4×Dic311yescharacteristic
408C22×C5#94811yescharacteristic
409C22×C5#94811yescharacteristic
410C22×C5C2×#21711yescharacteristic
411C2×D5—22no—
412C2×D5—22no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—41no—
418C2×D5—41no—
419C2×D5—41no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—41no—
424C2×D5—41no—
425C4×C5—22no—
426C4×C5—41no—
427C4×C5#93511yescharacteristic
428C4×C5#93711yescharacteristic
429C4×C5#93911yescharacteristic
430C4×C5#93911yescharacteristic
431Dic5—22no—
432Dic5—41no—
433C24—51no—
434C24—51no—
435C2×D4—102no—
436C2×D4—102no—
437C2×D4—102no—
438C22×C4—51no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—51no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4D5×Dic311yescharacteristic
453C22×C4D5×Dic311yescharacteristic
454C22×C4C2×D3×D511yescharacteristic
455M16—308no—
456C2×C8—32no—
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8—61no—
461C2×C8—61no—
462C2×C8—152no—
463C2×C8—301no—
464C2×C8—301no—
465C2×C8—301no—
466C2×C8—301no—
467C2×C8—301no—
468C4⋊C4—102no—
469C22⋊C4—102no—
470C22⋊C4—102no—
471C42—21no—
472C42—21no—
473C3×C5#187011yescharacteristic, complemented, Hall
474C22×C3—102no—
475C22×C3—102no—
476C22×C3—102no—
477C22×C3—102no—
478C22×C3—102no—
479C22×C3—102no—
480C22×C3—201no—
481C22×C3—201no—
482C22×C3—201no—
483C22×C3—201no—
484C22×C3—201no—
485C22×C3—201no—
486C22×C3—201no—
487C22×C3—201no—
488C22×C3C4×D2011yescharacteristic
489C22×C3D5×C22⋊C411yescharacteristic
490C22×C3#403911yescharacteristic
491C22×C3C2×#67611yescharacteristic
492C22×C3#404711yescharacteristic
493C22×C3D5×M1611yescharacteristic
494C22×C3#405311yescharacteristic
495C3×C4—22no—
496C3×C4—41no—
497C3×C4—102no—
498C3×C4—201no—
499C3×C4#402811yescharacteristic
500C3×C4#403011yescharacteristic
501C3×C4#404011yescharacteristic
502C3×C4#404111yescharacteristic
503C2×C5#501111yescharacteristic
504C2×C5#501111yescharacteristic
505C2×C5#501211yescharacteristic
506C2×C5#501211yescharacteristic
507C2×C5#520711yescharacteristic
508C2×C5#522011yescharacteristic
509C2×C5#523411yescharacteristic
510D5—42no—
511D5—42no—
512C23—52no—
513C23—52no—
514C23—101no—
515C23—101no—
516C23—101no—
517C23—101no—
518C23—101no—
519C23—101no—
520C23—101no—
521C23—101no—
522C23—101no—
523C23—101no—
524C23—101no—
525C23—101no—
526C23C2×D5×Dic311yescharacteristic
527D4—108no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—52no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—102no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—101no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4#664912yescomplemented
548C2×C4#676511yescharacteristic
549C2×C4#676611yescharacteristic
550C2×C4D3×D2011yescharacteristic
551C2×C4#677711yescharacteristic
552C2×C4D5×#6711yescharacteristic
553C2×C4D5×#6711yescharacteristic
554C8—62no—
555C8—121no—
556C8—302no—
557C8—601no—
558C2×C3—202no—
559C2×C3—202no—
560C2×C3#6495411yescharacteristic
561C2×C3#6497711yescharacteristic
562C2×C3#6499511yescharacteristic
563C2×C3#6501511yescharacteristic
564C2×C3#6501611yescharacteristic
565C2×C3#6512511yescharacteristic
566C2×C3#6512711yescharacteristic
567C5#7161111yescharacteristic, complemented, Sylow
568C22—102no—
569C22—102no—
570C22—102no—
571C22—102no—
572C22—102no—
573C22—102no—
574C22—201no—
575C22—201no—
576C22—201no—
577C22—201no—
578C22—201no—
579C22—201no—
580C22—201no—
581C22—201no—
582C22D5×#20811yescharacteristic
583C22#9128311yescharacteristic
584C22#9128411yescharacteristic
585C22C2×#664911yescharacteristic
586C22Dic3×D2011yescharacteristic
587C22#9143411yescharacteristic
588C22D5×#21711yescharacteristic
589C4—22no—
590C4—41no—
591C4—102no—
592C4—201no—
593C4#9140711yescharacteristic
594C4#9140811yescharacteristic
595C4#9140911yescharacteristic
596C4#9147411yescharacteristic
597C3#1059946211yescharacteristic, complemented, Sylow
598C2—202no—
599C2—202no—
600C2#1174699111yescharacteristic
601C2#1174699711yescharacteristic
602C2#1174701011yescharacteristic
603C2#1174701311yescharacteristic
604C2#1174848211yescharacteristic
605C2#1174849911yescharacteristic
606C2#1174889611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D3×D5
commutator, socleC23×C3×C5C22×C4
FittingC2×C3×C42×C5C22
prime radicalC22×C3×D20C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1870
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C22×#6649C2semidirect
3. C2×#90955C2semidirect
4. C2×#90955C2semidirect
5. C2×#90955C2semidirect
6. #11746345C2semidirect
7. C5×#4524C2semidirect
65. C2×C3⋊#168D4semidirect
71. C2×C5×C3⋊C8D4semidirect
82. #4524D5semidirect
117. C22×C3×D5M16semidirect
123. C2×C3×C4×C5M16semidirect
283. C2×C3⋊C8D20semidirect
297. C22×D5#208semidirect
304. C2×C4×C5#208semidirect
393. C2×C3×C4#676semidirect
473. C3×C5#1870semidirect
547. C2×C4#6649semidirect
567. C5#71611semidirect
597. C3#10599462semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C22×#66492
C2×#909552
#117463452
C5×#45242
#105994623
#716115