Finite Group Databasebeta

← #14431385

Subgroups — #14431385

Order 1920.

752 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×#65908C211yesmaximal, characteristic
2#11752647C211yesmaximal, characteristic, complemented
3#11751121C211yesmaximal, characteristic, complemented
4C5×#5022C211yesmaximal, characteristic, complemented
5#11749348C211yesmaximal, characteristic, complemented
6#11749332C211yesmaximal, characteristic, complemented
7#11749207C211yesmaximal, characteristic
8#11749198C211yesmaximal, characteristic
9#11747452C211yesmaximal, characteristic, complemented
10D5×#808C211yesmaximal, characteristic, complemented
11#11747415C211yesmaximal, characteristic, complemented
12#11747389C211yesmaximal, characteristic, complemented
13#11746985C211yesmaximal, characteristic, complemented
14#11746887C211yesmaximal, characteristic, complemented
15#11746881C211yesmaximal, characteristic, complemented
16#10612966—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19#91758C2211yescharacteristic
20C5×#870C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C3×#4039—21no—
23C3×#4039C2211yescharacteristic
24C3×D5×C4⋊C4—21no—
25C3×D5×C4⋊C4C2211yescharacteristic
26C3×C4×D20—21no—
27C3×C4×D20C2211yescharacteristic
28C3×#4018—21no—
29C3×#4018C2211yescharacteristic
30#91468C2211yescharacteristic
31#91431—21no—
32#91422—21no—
33D5×C4⋊Dic3C2211yescharacteristic
34#91388C2211yescharacteristic
35#91358C2211yescharacteristic
36#91334—21no—
37#91328—21no—
38C2×#6649C2211yescharacteristic
39C2×D5×C3⋊C8C2211yescharacteristic
40#91119C2211yescharacteristic
41#91119C2211yescharacteristic
42#91092C2211yescharacteristic
43#91092C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90989C2211yescharacteristic
51#90987C2211yescharacteristic
52#90987C2211yescharacteristic
53#90986C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90965C2211yescharacteristic
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic
60#82560—51nomaximal, Hall
61#66023—31no—
62#65908D311yescharacteristic
63C5×#479—31no—
64#65355—31no—
65#65309—31no—
66#65180—31no—
67#65170—31no—
68#65159—31no—
69D5×#106—31no—
70#65131—31no—
71#65128—31no—
72#65093—31no—
73#65092—31no—
74#65088—31no—
75#65080—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30—21no—
78C3×#713—22no—
79C3×#713Q814yescomplemented
80C2×C3×D20—21no—
81C2×C3×D20C2311yescharacteristic
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1204—21no—
88C2×D5×Dic3—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C42×C5—21no—
92C3×C42×C5C2311yescharacteristic
93C4⋊Dic15—21no—
94C4⋊Dic15C2311yescharacteristic
95C4⋊Dic15C2311yescharacteristic
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×#685—21no—
105C3×#685—21no—
106C3×#685D411yescharacteristic
107C3×#685D411yescharacteristic
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×#683D411yescharacteristic
112C3×#683D411yescharacteristic
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119#6665—21no—
120Dic3×Dic5—21no—
121#6649—22no—
122D5×C3⋊C8—22no—
123C3×#520—51no—
124#5519—51no—
125#5233—51no—
126#5232—51no—
127#5022—51no—
128#5022D511yescharacteristic, complemented
129#5020—51no—
130#5020—51no—
131#5009—51no—
132#5009—51no—
133#5008—51no—
134#5008—51no—
135#4999—51no—
136#4964—51no—
137C2×#808—51no—
138C2×#713C2×D311yescharacteristic
139C5×#125—31no—
140C4×C5×Q8C2×D311yescharacteristic
141Q8×Dic5C2×D311yescharacteristic
142C2×#676—31no—
143C2×C8×D5—31no—
144#4043—61no—
145#4042—61no—
146#4039—21no—
147#4039C2×D311yescharacteristic
148#4038—31no—
149D5×C4⋊C4—21no—
150D5×C4⋊C4—31no—
151D5×C4⋊C4C2×D311yescharacteristic
152#4036—31no—
153#4035—61no—
154#4034—31no—
155#4034—61no—
156C4×D20—21no—
157C4×D20C2×D311yescharacteristic
158#4018—21no—
159#4018C2×D311yescharacteristic
160#4015—31no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3953—31no—
169#3953—31no—
170#3949—31no—
171#3949—31no—
172#3946—31no—
173#3946—31no—
174#3941—31no—
175#3941—31no—
176#3940—31no—
177#3940—31no—
178#3940—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3084—151noSylow
182C22×C3×D5—21no—
183C22×C3×D5C2×D411yescharacteristic
184C3×C5×Q8—21no—
185C3×C5×Q8C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192C2×Dic15—21no—
193Dic30—81no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5C2×D411yescharacteristic
198C2×C3×Dic5C2×D411yescharacteristic
199C2×C3×Dic5C2×D411yescharacteristic
200C3×D20—24no—
201C3×D20—21no—
202C3×D20C2×Q812yes—
203C3×C4×D5—24no—
204C3×C4×D5—81no—
205C3×C4×D5—81no—
206C3×C4×D5—81no—
207C3×C4×D5C2×Q812yes—
208C3×C4×D5#4112yes—
209#1204—81no—
210D5×Dic3—81no—
211C3⋊#168—21no—
212C3⋊#168—21no—
213C5×C3⋊C8—21no—
214C5×C3⋊C8—21no—
215C2×C3×#41—51no—
216C3×C4×Q8—51no—
217C3×C4×Q8C2×D511yescharacteristic
218C3×C4×D4—51no—
219C3×C4×D4—51no—
220C3×C4×D4—101no—
221C3×C4×D4—101no—
222C3×#117—51no—
223C3×#117—101no—
224C2×C3×C4⋊C4—51no—
225C2×C3×C4⋊C4—101no—
226#926—51no—
227C2×C4⋊Dic3—51no—
228C2×#208—51no—
229C22×C3⋊C8—51no—
230#890—101no—
231#888—101no—
232#878—101no—
233#878—101no—
234#870—51no—
235#870C2×D511yescharacteristic
236#869—51no—
237#869—51no—
238#835—51no—
239#835—51no—
240#835C2×D511yescharacteristic
241#835C2×D511yescharacteristic
242#832—51no—
243#832—51no—
244#832—51no—
245#832—51no—
246#808—51no—
247#808—51no—
248#808—51no—
249#808—51no—
250#808—51no—
251#808C2×D511yescharacteristic
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×Q8C22×D311yescharacteristic
259#713—22no—
260#713Dic614yescomplemented
261C2×D20—21no—
262C2×D20C22×D311yescharacteristic
263C2×C4×D5—21no—
264C2×C4×D5—21no—
265C2×C4×D5—21no—
266C2×C4×D5—21no—
267C2×C4×D5—61no—
268C2×C4×D5C22×D311yescharacteristic
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×C5×C8—31no—
272C2×C5×C8—31no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4C22×D311yescharacteristic
279C42×C5—21no—
280C42×C5C22×D311yescharacteristic
281#685—21no—
282#685—21no—
283#685—61no—
284#685#6711yescharacteristic
285#685#6711yescharacteristic
286C4⋊Dic5—21no—
287C4⋊Dic5—31no—
288C4⋊Dic5—31no—
289C4⋊Dic5—61no—
290C4⋊Dic5—61no—
291C4⋊Dic5C22×D311yescharacteristic
292#683—21no—
293#683—61no—
294#683—61no—
295#683—61no—
296#683#6711yescharacteristic
297#683#6711yescharacteristic
298C4×Dic5—21no—
299C4×Dic5—61no—
300C4×Dic5C22×D311yescharacteristic
301C2×#168—31no—
302C2×#168—31no—
303#676—62no—
304C8×D5—62no—
305#544—151no—
306#520—51no—
307#479—31no—
308#479—151no—
309#478—151no—
310#478—151no—
311#476—151no—
312#476—151no—
313#475—151no—
314#475—151no—
315#428—151no—
316C2×#106—151no—
317#424—151no—
318#417—151no—
319#416—151no—
320C22×C3×C5C22×D411yescharacteristic
321C2×C3×D5—21no—
322C2×C3×D5—21no—
323C2×C3×D5—22no—
324C2×C3×D5—41no—
325C2×C3×D5—41no—
326C2×C3×D5C22⋊Q812yes—
327C3×C4×C5—22no—
328C3×C4×C5—21no—
329C3×C4×C5—21no—
330C3×C4×C5—41no—
331C3×C4×C5C22×Q811yescharacteristic
332C3×C4×C5C2×#4111yescharacteristic
333Dic15—41no—
334Dic15—41no—
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×Q8C22×D511yescharacteristic
344C2×C3×D4—51no—
345C2×C3×D4—101no—
346C22×C3×C4—51no—
347C22×C3×C4—101no—
348C22×C3×C4—101no—
349C22×C3×C4—101no—
350C22×C3×C4—101no—
351C22×Dic3—101no—
352C2×Dic6—101no—
353C2×Dic6—101no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—51no—
356C3×C4⋊C4—51no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4C22×D511yescharacteristic
361C3×C22⋊C4—51no—
362C3×C22⋊C4—51no—
363C3×C22⋊C4—101no—
364C3×C22⋊C4—101no—
365C3×C42—21no—
366C3×C42—51no—
367C3×C42—101no—
368C3×C42C22×D511yescharacteristic
369#217—101no—
370C4⋊Dic3—51no—
371C4⋊Dic3—51no—
372C4⋊Dic3—101no—
373C4⋊Dic3—101no—
374C4⋊Dic3—101no—
375C4⋊Dic3C22×D511yescharacteristic
376C4⋊Dic3C22×D511yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381C4×Dic3—101no—
382#208—102no—
383C2×C3⋊C8—51no—
384C2×C3⋊C8—51no—
385C2×C3⋊C8—102no—
386C2×C3⋊C8C22×D511yescharacteristic
387C2×C3⋊C8C22×D511yescharacteristic
388C22×D5—21no—
389C22×D5C2×#6711yescharacteristic
390C5×Q8—21no—
391C5×Q8C2×Dic612yes—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5C2×#6711yescharacteristic
397C2×C4×C5C2×#6711yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C2×Dic5—21no—
400C2×Dic5—61no—
401C2×Dic5—61no—
402C2×Dic5C2×#6711yescharacteristic
403C2×Dic5C2×#6711yescharacteristic
404C2×Dic5C2×#6711yescharacteristic
405D20—24no—
406D20—21no—
407D20C2×Dic612yes—
408C4×D5—24no—
409C4×D5—81no—
410C4×D5—81no—
411C4×D5—81no—
412C4×D5—241no—
413C4×D5C2×Dic612yes—
414C4×D5#23512yes—
415Dic10—241no—
416Dic10—241no—
417C5×C8—61no—
418C5×C8—61no—
419#168—61no—
420#168—61no—
421C2×#41—51no—
422C2×M16—151no—
423C22×C8—151no—
424C4⋊Q8—151no—
425C4⋊Q8—151no—
426C4⋊Q8—301no—
427#125—31no—
428#125—151no—
429#125—301no—
430C22⋊Q8—301no—
431C22⋊Q8—301no—
432C4×Q8—51no—
433C4×Q8D3×D511yescharacteristic
434C4×D4—51no—
435C4×D4—51no—
436C4×D4—101no—
437C4×D4—101no—
438#117—51no—
439#117—101no—
440#117—151no—
441C2×C4⋊C4—51no—
442C2×C4⋊C4—101no—
443C2×C4⋊C4—151no—
444#107—31no—
445#107—151no—
446#106—31no—
447#106—151no—
448#106—151no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—31no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—31no—
457#103—31no—
458#103—151no—
459#103—151no—
460#102—151no—
461#102—151no—
462#102—151no—
463#102—151no—
464C2×C3×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57711yescharacteristic
466C2×C3×C5#57711yescharacteristic
467C3×D5—22no—
468C3×D5—42no—
469C23×C3—51no—
470C23×C3—101no—
471C3×Q8—21no—
472C3×Q8Q8×D512yes—
473C3×D4—52no—
474C3×D4—104no—
475C3×D4—101no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
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—401no—
486C2×C3×C4—401no—
487C2×C3×C4—401no—
488C2×C3×C4D4×D511yescharacteristic
489C2×C3×C4D4×D511yescharacteristic
490C2×C3×C4C23×D511yescharacteristic
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—101no—
494C2×Dic3—101no—
495C2×Dic3—401no—
496Dic6—401no—
497Dic6—401no—
498C3⋊C8—21no—
499C3⋊C8—21no—
500C3⋊C8—101no—
501C3⋊C8—101no—
502C22×C5C22×#6711yescharacteristic
503C2×D5—21no—
504C2×D5—21no—
505C2×D5—22no—
506C2×D5—41no—
507C2×D5—41no—
508C2×D5#92412yes—
509C4×C5—22no—
510C4×C5—21no—
511C4×C5—21no—
512C4×C5—41no—
513C4×C5—121no—
514C4×C5—121no—
515C4×C5C22×Dic611yescharacteristic
516C4×C5C2×#23511yescharacteristic
517Dic5—21no—
518Dic5—21no—
519Dic5—41no—
520Dic5—121no—
521Dic5—121no—
522Dic5#92412yes—
523#41—54no—
524#41—102no—
525C2×Q8—301no—
526C2×Q8—301no—
527C2×Q8C2×D3×D511yescharacteristic
528C2×D4—51no—
529C2×D4—101no—
530C22×C4—51no—
531C22×C4—101no—
532C22×C4—101no—
533C22×C4—101no—
534C22×C4—101no—
535C22×C4—301no—
536M16—302no—
537C2×C8—31no—
538C2×C8—31no—
539C2×C8—151no—
540C2×C8—151no—
541C2×C8—302no—
542C4⋊C4—21no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—51no—
546C4⋊C4—51no—
547C4⋊C4—51no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—101no—
551C4⋊C4—101no—
552C4⋊C4—151no—
553C4⋊C4—151no—
554C4⋊C4—301no—
555C4⋊C4—301no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4C2×D3×D511yescharacteristic
560C22⋊C4—51no—
561C22⋊C4—51no—
562C22⋊C4—101no—
563C22⋊C4—101no—
564C22⋊C4—301no—
565C42—21no—
566C42—51no—
567C42—101no—
568C42—301no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308411yescharacteristic, complemented, Hall
571C22×C3—52no—
572C22×C3—101no—
573C22×C3—101no—
574C22×C3—102no—
575C22×C3—201no—
576C22×C3—201no—
577C22×C3C2×D4×D511yescharacteristic
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—41no—
582C3×C4—52no—
583C3×C4—101no—
584C3×C4—101no—
585C3×C4—201no—
586C3×C4C2×Q8×D511yescharacteristic
587C3×C4D5×#4111yescharacteristic
588Dic3—41no—
589Dic3—41no—
590Dic3—201no—
591Dic3—201no—
592C2×C5C2×#92411yescharacteristic
593C2×C5#583611yescharacteristic
594C2×C5#583711yescharacteristic
595D5—22no—
596D5—42no—
597C23—51no—
598C23—101no—
599Q8—21no—
600Q8—1201no—
601Q8—1201no—
602Q8D5×Dic612yes—
603D4—52no—
604D4—104no—
605D4—101no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—51no—
609C2×C4—52no—
610C2×C4—52no—
611C2×C4—51no—
612C2×C4—51no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—104no—
616C2×C4—101no—
617C2×C4—301no—
618C2×C4—301no—
619C2×C4—401no—
620C2×C4—401no—
621C2×C4—401no—
622C2×C4—1201no—
623C2×C4D5×#6711yescharacteristic
624C2×C4D5×#6711yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—61no—
627C8—61no—
628C8—301no—
629C8—301no—
630C2×C3—102no—
631C2×C3—202no—
632C2×C3D5×C22⋊Q811yescharacteristic
633C2×C3#6610411yescharacteristic
634C2×C3#6611211yescharacteristic
635C5#8256011yescharacteristic, complemented, Sylow
636C22—52no—
637C22—101no—
638C22—101no—
639C22—102no—
640C22—201no—
641C22—201no—
642C22C2×D5×#6711yescharacteristic
643C4—22no—
644C4—21no—
645C4—21no—
646C4—41no—
647C4—52no—
648C4—101no—
649C4—101no—
650C4—121no—
651C4—121no—
652C4—201no—
653C4—601no—
654C4—601no—
655C4C2×D5×Dic611yescharacteristic
656C4D5×#23511yescharacteristic
657C3#1061296611yescharacteristic, complemented, Sylow
658C2—102no—
659C2—202no—
660C2D5×#92411yescharacteristic
661C2#1175508611yescharacteristic
662C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#713C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11752647C2semidirect
3. #11751121C2semidirect
4. C5×#5022C2semidirect
5. #11749348C2semidirect
6. #11749332C2semidirect
9. #11747452C2semidirect
10. D5×#808C2semidirect
11. #11747415C2semidirect
12. #11747389C2semidirect
13. #11746985C2semidirect
14. #11746887C2semidirect
15. #11746881C2semidirect
79. C3×#713Q8semidirect
128. #5022D5semidirect
260. #713Dic6semidirect
570. C3×C5#3084semidirect
635. C5#82560semidirect
657. C3#10612966semidirect

Maximal subgroups

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

subgroupindex
C3×#659082
#117526472
#117511212
C5×#50222
#117493482
#117493322
#117492072
#117491982
#117474522
D5×#8082
#117474152
#117473892
#117469852
#117468872
#117468812
#106129663
#825605