Finite Group Databasebeta

← #14430711

Subgroups — #14430711

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#711C211yesmaximal, characteristic
2D5×#870C211yesmaximal, characteristic, complemented
3#11751110C211yesmaximal, characteristic, complemented
4C5×#5009C211yesmaximal, characteristic, complemented
5#11749086C211yesmaximal, characteristic, complemented
6#11749083C211yesmaximal, characteristic, complemented
7#11748951C211yesmaximal, characteristic
8#11748951C211yesmaximal, characteristic
9#11747391C211yesmaximal, characteristic, complemented
10#11747390C211yesmaximal, characteristic, complemented
11#11747189C211yesmaximal, characteristic, complemented
12#11747188C211yesmaximal, characteristic, complemented
13#11747007C211yesmaximal, characteristic, complemented
14#11746944C211yesmaximal, characteristic, complemented
15#11746919C211yesmaximal, characteristic, complemented
16#10612898—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19#91759C2211yescharacteristic
20C5×#870C2211yescharacteristic
21C3×D4×Dic5C2211yescharacteristic
22C3×C4×C22⋊D5—21no—
23C2×C3×C4×Dic5—21no—
24C3×#4038C2211yescharacteristic
25C3×#4033C2211yescharacteristic
26C3×#4027—21no—
27C3×#4023—21no—
28C3×C42×D5C2211yescharacteristic
29C3×C4×Dic10C2211yescharacteristic
30D5×C4⋊Dic3C2211yescharacteristic
31D5×C4⋊Dic3C2211yescharacteristic
32D5×Dic3⋊C4—21no—
33D5×Dic3⋊C4—21no—
34#91388C2211yescharacteristic
35#91388C2211yescharacteristic
36#91378—21no—
37#91378—21no—
38C2×#6649C2211yescharacteristic
39C2×#6649C2211yescharacteristic
40#91116C2211yescharacteristic
41#91116C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#832C2211yescharacteristic
46C5×#832C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90990C2211yescharacteristic
51#90989C2211yescharacteristic
52#90987C2211yescharacteristic
53#90986C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90971C2211yescharacteristic
57#90971C2211yescharacteristic
58#90970C2211yescharacteristic
59#90970C2211yescharacteristic
60#82509—51nomaximal, Hall
61D5×#125—31no—
62C4×#711D311yescharacteristic
63C5×#478—31no—
64#65352—31no—
65#65298—31no—
66#65170—31no—
67#65166—31no—
68#65150—31no—
69#65146—31no—
70#65126—31no—
71#65118—31no—
72#65060—31no—
73#65060—31no—
74#65055—31no—
75#65052—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×C3×C22⋊D5—21no—
79C22×C3×Dic5—21no—
80C22×C3×Dic5—21no—
81C3×#711—22no—
82C3×#711Q814yes—
83C2×C3×C4×D5D411yescharacteristic
84C2×C3×C4×D5D411yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×Dic10C2311yescharacteristic
87C2×D5×Dic3—21no—
88C2×D5×Dic3—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95#6712—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×C4⋊Dic3C2311yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C5×Dic3⋊C4—21no—
102C2×C5×C3⋊C8C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C3×C22⋊Dic5—21no—
105C3×#685—21no—
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×C4×Dic5—21no—
110C3×C4×Dic5—21no—
111C3×C4×Dic5—21no—
112C3×C4×Dic5D411yescharacteristic
113C3×C4×Dic5D411yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5—21no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6669—21no—
119#6668—21no—
120#6668—21no—
121#6649—22no—
122#6649—22no—
123C3×C4×#41—51no—
124C2×#870—51no—
125#5232—51no—
126#5232—51no—
127#5022—51no—
128#5022—51no—
129#5022—51no—
130#5022—51no—
131#5009—51no—
132#5009—51no—
133#5009—51no—
134#5009D511yescharacteristic, complemented
135#4995—51no—
136#4995—51no—
137#4924—51no—
138C2×#711C2×D311yescharacteristic
139C5×#125—31no—
140C4×C5×D4C2×D311yescharacteristic
141D4×Dic5C2×D311yescharacteristic
142C4×C22⋊D5—21no—
143C2×C4×Dic5—21no—
144C2×#676—31no—
145C2×#676—31no—
146#4038C2×D311yescharacteristic
147D5×C4⋊C4—31no—
148D5×C4⋊C4—31no—
149D5×C4⋊C4—61no—
150D5×C4⋊C4—61no—
151#4036—31no—
152#4036—31no—
153#4035—61no—
154#4035—61no—
155#4033C2×D311yescharacteristic
156#4027—21no—
157#4023—21no—
158C42×D5C2×D311yescharacteristic
159#4016—31no—
160C4×Dic10C2×D311yescharacteristic
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102—31no—
166#3964—31no—
167#3964—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3080—151noSylow
182C23×C3×C5—21no—
183C22×C3×D5C2×D411yescharacteristic
184C3×C5×D4—21no—
185C3×C5×D4C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—42no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C3×C22⋊D5—24no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—24no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—42no—
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C2×C3×Dic5C2×D411yescharacteristic
203C3×C4×D5—41no—
204C3×C4×D5—41no—
205C3×C4×D5C2×Q812yes—
206C3×C4×D5#4112yes—
207C3×Dic10—21no—
208C3×Dic10C2×Q812yes—
209D5×Dic3—42no—
210D5×Dic3—42no—
211C3⋊#168—21no—
212C3⋊#168—21no—
213C5×C3⋊C8—21no—
214C5×C3⋊C8—21no—
215C2×C3×#41—51no—
216C3×C4×Q8—51no—
217C3×C4×Q8—51no—
218C3×C4×D4—51no—
219C3×C4×D4—101no—
220C3×C4×D4—101no—
221C3×C4×D4C2×D511yescharacteristic
222C3×#117—51no—
223C3×#117—101no—
224C2×C3×C42—51no—
225C2×C3×C42—101no—
226C2×C4⋊Dic3—51no—
227C2×C4⋊Dic3—51no—
228C2×Dic3⋊C4—101no—
229C2×Dic3⋊C4—101no—
230C2×#208—51no—
231C2×#208—51no—
232#870—51no—
233#870—51no—
234#870—51no—
235#870—101no—
236#870—101no—
237#870C2×D511yescharacteristic
238#835—51no—
239#835—51no—
240#835—51no—
241#835—51no—
242#832—51no—
243#832—51no—
244#832C2×D511yescharacteristic
245#832C2×D511yescharacteristic
246#808—51no—
247#808—51no—
248#808—51no—
249#808C2×D511yescharacteristic
250#807—51no—
251#807—51no—
252#807—51no—
253#807C2×D511yescharacteristic
254C4⋊(C3⋊C8)—51no—
255C4⋊(C3⋊C8)—51no—
256C4⋊(C3⋊C8)—51no—
257C4⋊(C3⋊C8)C2×D511yescharacteristic
258C2×C5×D4C22×D311yescharacteristic
259C22×C4×C5—21no—
260C2×C22⋊D5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263#711—22no—
264#711Dic614yes—
265C2×C4×D5—61no—
266C2×C4×D5—61no—
267C2×C4×D5#6711yescharacteristic
268C2×C4×D5#6711yescharacteristic
269C2×C4×D5C22×D311yescharacteristic
270C2×Dic10C22×D311yescharacteristic
271C2×C5×C8—31no—
272C2×C5×C8—31no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—21no—
279C42×C5C22×D311yescharacteristic
280C22⋊Dic5—21no—
281#685—21no—
282C4⋊Dic5—31no—
283C4⋊Dic5—31no—
284C4⋊Dic5—61no—
285C4⋊Dic5—61no—
286C4⋊Dic5C22×D311yescharacteristic
287#683—21no—
288#683—21no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294#683—61no—
295C4×Dic5—21no—
296C4×Dic5—21no—
297C4×Dic5—21no—
298C4×Dic5#6711yescharacteristic
299C4×Dic5#6711yescharacteristic
300C4×Dic5C22×D311yescharacteristic
301C2×#168—31no—
302C2×#168—31no—
303#676—62no—
304#676—62no—
305C2×#125—151no—
306C4×#41—51no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#478—31no—
312#478—151no—
313#478—151no—
314#478—151no—
315#428—151no—
316#428—151no—
317#423—151no—
318#417—151no—
319#417—151no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5C22×D411yescharacteristic
324C2×C3×D5—21no—
325C2×C3×D5—21no—
326C2×C3×D5C22⋊Q812yes—
327C3×C4×C5—21no—
328C3×C4×C5—21no—
329C3×C4×C5—41no—
330C3×C4×C5C22×Q811yescharacteristic
331C3×C4×C5C2×#4111yescharacteristic
332Dic15—41no—
333Dic15—41no—
334C3×Dic5—22no—
335C3×Dic5—21no—
336C3×Dic5—21no—
337C3×Dic5—41no—
338C3×Dic5C22⋊Q812yes—
339C5×Dic3—41no—
340C5×Dic3—41no—
341C3×#41—54no—
342C3×#41—102no—
343C2×C3×Q8—51no—
344C2×C3×D4—101no—
345C2×C3×D4C22×D511yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—101no—
351C22×C3×C4—101no—
352C22×Dic3—101no—
353C22×Dic3—101no—
354C3×C4⋊C4—51no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—101no—
360C3×C22⋊C4—101no—
361C3×C42—51no—
362C3×C42—51no—
363C3×C42—51no—
364C3×C42—101no—
365C3×C42—101no—
366C3×C42—101no—
367C3×C42C22×D511yescharacteristic
368C4⋊Dic3—51no—
369C4⋊Dic3—51no—
370C4⋊Dic3—101no—
371C4⋊Dic3—101no—
372C4⋊Dic3C22×D511yescharacteristic
373C4⋊Dic3C22×D511yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382#208—102no—
383#208—102no—
384C2×C3⋊C8—51no—
385C2×C3⋊C8—51no—
386C2×C3⋊C8C22×D511yescharacteristic
387C2×C3⋊C8C22×D511yescharacteristic
388C23×C5—21no—
389C22×D5C2×#6711yescharacteristic
390C5×D4—21no—
391C5×D4C2×Dic612yes—
392C2×C4×C5—21no—
393C2×C4×C5—42no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5C2×#6711yescharacteristic
397C2×C4×C5C2×#6711yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—24no—
400C2×Dic5—21no—
401C2×Dic5—24no—
402C2×Dic5—21no—
403C2×Dic5—42no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5C2×#6711yescharacteristic
407C2×Dic5C2×#6711yescharacteristic
408C2×Dic5C2×#6711yescharacteristic
409C4×D5—41no—
410C4×D5—41no—
411C4×D5—122no—
412C4×D5—122no—
413C4×D5C2×Dic612yes—
414C4×D5#23512yes—
415Dic10—21no—
416Dic10C2×Dic612yes—
417C5×C8—61no—
418C5×C8—61no—
419#168—61no—
420#168—61no—
421C2×#41—51no—
422C2×M16—151no—
423C2×M16—151no—
424#125—31no—
425#125—151no—
426#125—151no—
427#125—151no—
428#125—301no—
429#125—301no—
430C4×Q8—51no—
431C4×Q8—51no—
432C4×D4—51no—
433C4×D4—101no—
434C4×D4—101no—
435C4×D4D3×D511yescharacteristic
436#117—51no—
437#117—101no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—301no—
441C2×C4⋊C4—301no—
442C2×C42—51no—
443C2×C42—101no—
444#107—31no—
445#107—151no—
446#107—151no—
447#107—151no—
448#106—31no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—31no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460#102—31no—
461#102—31no—
462#102—151no—
463#102—151no—
464C2×C3×C5—42no—
465C2×C3×C5C2×C22⋊Q811yescharacteristic
466C2×C3×C5#57511yescharacteristic
467C2×C3×C5#57511yescharacteristic
468C3×D5—22no—
469C23×C3—21no—
470C23×C3—51no—
471C3×Q8—52no—
472C3×Q8—101no—
473C3×D4—21no—
474C3×D4—104no—
475C3×D4Q8×D512yes—
476C2×C3×C4—21no—
477C2×C3×C4—42no—
478C2×C3×C4—51no—
479C2×C3×C4—52no—
480C2×C3×C4—52no—
481C2×C3×C4—51no—
482C2×C3×C4—51no—
483C2×C3×C4—104no—
484C2×C3×C4—101no—
485C2×C3×C4—101no—
486C2×C3×C4—201no—
487C2×C3×C4—201no—
488C2×C3×C4—202no—
489C2×C3×C4D4×D511yescharacteristic
490C2×C3×C4D4×D511yescharacteristic
491C2×C3×C4C23×D511yescharacteristic
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—101no—
495C2×Dic3—101no—
496C2×Dic3—202no—
497C2×Dic3—202no—
498C3⋊C8—21no—
499C3⋊C8—21no—
500C3⋊C8—101no—
501C3⋊C8—101no—
502C22×C5—22no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5C22×#6711yescharacteristic
506C2×D5—21no—
507C2×D5—21no—
508C2×D5#92412yes—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—41no—
512C4×C5—121no—
513C4×C5—121no—
514C4×C5C22×Dic611yescharacteristic
515C4×C5C2×#23511yescharacteristic
516Dic5—22no—
517Dic5—21no—
518Dic5—21no—
519Dic5—41no—
520Dic5—121no—
521Dic5—121no—
522Dic5#92412yes—
523#41—54no—
524#41—102no—
525C2×Q8—51no—
526C2×D4—101no—
527C2×D4C2×D3×D511yescharacteristic
528C22×C4—21no—
529C22×C4—51no—
530C22×C4—51no—
531C22×C4—51no—
532C22×C4—101no—
533C22×C4—101no—
534C22×C4—301no—
535C22×C4—301no—
536M16—302no—
537M16—302no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8—151no—
541C2×C8—151no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—51no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—151no—
550C4⋊C4—151no—
551C4⋊C4—301no—
552C4⋊C4—301no—
553C4⋊C4—301no—
554C4⋊C4—301no—
555C4⋊C4—301no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4C2×D3×D511yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—101no—
562C22⋊C4—101no—
563C42—51no—
564C42—51no—
565C42—51no—
566C42—101no—
567C42—101no—
568C42—101no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308011yescharacteristic, complemented, Hall
571C22×C3—22no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—52no—
575C22×C3—101no—
576C22×C3—101no—
577C22×C3C2×D4×D511yescharacteristic
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—41no—
581C3×C4—52no—
582C3×C4—101no—
583C3×C4—101no—
584C3×C4—102no—
585C3×C4—201no—
586C3×C4C2×Q8×D511yescharacteristic
587C3×C4D5×#4111yescharacteristic
588Dic3—41no—
589Dic3—41no—
590Dic3—201no—
591Dic3—201no—
592C2×C5—42no—
593C2×C5C2×#92411yescharacteristic
594C2×C5#582211yescharacteristic
595C2×C5#582211yescharacteristic
596D5—22no—
597C23—21no—
598C23—51no—
599Q8—52no—
600Q8—101no—
601D4—21no—
602D4—104no—
603D4D5×Dic612yes—
604C2×C4—21no—
605C2×C4—42no—
606C2×C4—51no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—51no—
610C2×C4—51no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—104no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—201no—
617C2×C4—201no—
618C2×C4—202no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—602no—
622C2×C4—602no—
623C2×C4D5×#6711yescharacteristic
624C2×C4D5×#6711yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—61no—
627C8—61no—
628C8—301no—
629C8—301no—
630C2×C3—42no—
631C2×C3—102no—
632C2×C3D5×C22⋊Q811yescharacteristic
633C2×C3#6610211yescharacteristic
634C2×C3#6610711yescharacteristic
635C5#8250911yescharacteristic, complemented, Sylow
636C22—22no—
637C22—41no—
638C22—41no—
639C22—52no—
640C22—101no—
641C22—101no—
642C22C2×D5×#6711yescharacteristic
643C4—21no—
644C4—21no—
645C4—41no—
646C4—52no—
647C4—101no—
648C4—102no—
649C4—101no—
650C4—121no—
651C4—121no—
652C4—201no—
653C4—601no—
654C4—601no—
655C4C2×D5×Dic611yescharacteristic
656C4D5×#23511yescharacteristic
657C3#1061289811yescharacteristic, complemented, Sylow
658C2—42no—
659C2—102no—
660C2D5×#92411yescharacteristic
661C2#1175469011yescharacteristic
662C2#1175531511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#711C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. D5×#870C2semidirect
3. #11751110C2semidirect
4. C5×#5009C2semidirect
5. #11749086C2semidirect
6. #11749083C2semidirect
9. #11747391C2semidirect
10. #11747390C2semidirect
11. #11747189C2semidirect
12. #11747188C2semidirect
13. #11747007C2semidirect
14. #11746944C2semidirect
15. #11746919C2semidirect
134. #5009D5semidirect
570. C3×C5#3080semidirect
635. C5#82509semidirect
657. C3#10612898semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7112
D5×#8702
#117511102
C5×#50092
#117490862
#117490832
#117489512
#117473912
#117473902
#117471892
#117471882
#117470072
#117469442
#117469192
#106128983
#825095