Finite Group Databasebeta

← #14430756

Subgroups — #14430756

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×#713C211yesmaximal, characteristic
2D5×#870C211yesmaximal, characteristic, complemented
3#11751123C211yesmaximal, characteristic, complemented
4C5×#5022C211yesmaximal, characteristic, complemented
5#11749332C211yesmaximal, characteristic, complemented
6#11749329C211yesmaximal, characteristic, complemented
7#11749198C211yesmaximal, characteristic
8#11749198C211yesmaximal, characteristic
9#11747392C211yesmaximal, characteristic, complemented
10#11747389C211yesmaximal, characteristic, complemented
11#11747189C211yesmaximal, characteristic, complemented
12#11747188C211yesmaximal, characteristic, complemented
13#11747007C211yesmaximal, characteristic, complemented
14#11746888C211yesmaximal, characteristic, complemented
15#11746887C211yesmaximal, characteristic, complemented
16#10612962—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19#91759C2211yescharacteristic
20C5×#870C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C3×#4039—21no—
23C3×#4039C2211yescharacteristic
24C3×#4038—21no—
25C3×#4038C2211yescharacteristic
26C3×C4×D20—21no—
27C3×C4×D20C2211yescharacteristic
28C3×C42×D5—21no—
29C3×C42×D5C2211yescharacteristic
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#91119C2211yescharacteristic
41#91119C2211yescharacteristic
42#91092C2211yescharacteristic
43#91091C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90990C2211yescharacteristic
51#90989C2211yescharacteristic
52#90987C2211yescharacteristic
53#90986C2211yescharacteristic
54#90982C2211yescharacteristic
55#90982C2211yescharacteristic
56#90965C2211yescharacteristic
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic
60#82509—51nomaximal, Hall
61D5×#125—31no—
62C4×#713D311yescharacteristic
63C5×#479—31no—
64#65355—31no—
65#65311—31no—
66#65180—31no—
67#65170—31no—
68#65160—31no—
69#65150—31no—
70#65136—31no—
71#65126—31no—
72#65092—31no—
73#65092—31no—
74#65088—31no—
75#65085—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C3×#713—22no—
78C3×#713Q814yes—
79C2×C3×D20—21no—
80C2×C3×D20C2311yescharacteristic
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5D411yescharacteristic
85C2×C3×C4×D5D411yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×D5×Dic3—21no—
88C2×D5×Dic3—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C42×C5—21no—
92C3×C42×C5C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96#6712—21no—
97C2×C3⋊#168C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C2×C5×C3⋊C8C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C3×#685—21no—
106C3×#685—21no—
107C3×#685—21no—
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5C2311yescharacteristic
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#5022D511yescharacteristic, complemented
131#5009—51no—
132#5009—51no—
133#5009—51no—
134#5009—51no—
135#4995—51no—
136#4995—51no—
137#4924—51no—
138C2×#713C2×D311yescharacteristic
139C5×#125—31no—
140C4×C5×Q8C2×D311yescharacteristic
141Q8×Dic5C2×D311yescharacteristic
142C2×#676—31no—
143C2×#676—31no—
144#4039—21no—
145#4039C2×D311yescharacteristic
146#4038—21no—
147#4038C2×D311yescharacteristic
148D5×C4⋊C4—31no—
149D5×C4⋊C4—31no—
150D5×C4⋊C4—61no—
151D5×C4⋊C4—61no—
152#4036—31no—
153#4036—31no—
154#4035—61no—
155#4035—61no—
156C4×D20—21no—
157C4×D20C2×D311yescharacteristic
158C42×D5—21no—
159C42×D5C2×D311yescharacteristic
160#4016—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#3950—31no—
171#3949—31no—
172#3946—31no—
173#3946—31no—
174#3941—31no—
175#3941—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3080—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—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5C2×D411yescharacteristic
197C2×C3×Dic5C2×D411yescharacteristic
198C2×C3×Dic5C2×D411yescharacteristic
199C3×D20—24no—
200C3×D20—21no—
201C3×D20C2×Q812yes—
202C3×C4×D5—24no—
203C3×C4×D5—41no—
204C3×C4×D5—41no—
205C3×C4×D5—42no—
206C3×C4×D5—42no—
207C3×C4×D5C2×Q812yes—
208C3×C4×D5#4112yes—
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×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×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#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#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×Q8C22×D311yescharacteristic
259#713—22no—
260#713Dic614yes—
261C2×D20—21no—
262C2×D20C22×D311yescharacteristic
263C2×C4×D5—21no—
264C2×C4×D5—21no—
265C2×C4×D5—21no—
266C2×C4×D5—61no—
267C2×C4×D5—61no—
268C2×C4×D5#6711yescharacteristic
269C2×C4×D5#6711yescharacteristic
270C2×C4×D5C22×D311yescharacteristic
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—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—61no—
288C4⋊Dic5—61no—
289C4⋊Dic5C22×D311yescharacteristic
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294#683—61no—
295#683—61no—
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—31no—
308#479—151no—
309#479—151no—
310#479—151no—
311#478—151no—
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×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—51no—
348C22×C3×C4—51no—
349C22×C3×C4—101no—
350C22×C3×C4—101no—
351C22×C3×C4—101no—
352C22×Dic3—101no—
353C22×Dic3—101no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—51no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C22⋊C4—101no—
359C3×C22⋊C4—101no—
360C3×C22⋊C4—101no—
361C3×C42—21no—
362C3×C42—51no—
363C3×C42—51no—
364C3×C42—51no—
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
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—41no—
410C4×D5—41no—
411C4×D5—42no—
412C4×D5—42no—
413C4×D5—122no—
414C4×D5—122no—
415C4×D5C2×Dic612yes—
416C4×D5#23512yes—
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×Q8D3×D511yescharacteristic
432C4×D4—51no—
433C4×D4—51no—
434C4×D4—101no—
435C4×D4—101no—
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—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#57511yescharacteristic
466C2×C3×C5#57511yescharacteristic
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—201no—
486C2×C3×C4—201no—
487C2×C3×C4—202no—
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×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×Q8C2×D3×D511yescharacteristic
526C2×D4—51no—
527C2×D4—101no—
528C22×C4—51no—
529C22×C4—51no—
530C22×C4—51no—
531C22×C4—101no—
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—21no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—51no—
546C4⋊C4—61no—
547C4⋊C4—61no—
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—101no—
561C22⋊C4—101no—
562C22⋊C4—101no—
563C42—21no—
564C42—51no—
565C42—51no—
566C42—51no—
567C42—101no—
568C42—101no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308011yescharacteristic, 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#582211yescharacteristic
594C2×C5#582211yescharacteristic
595D5—22no—
596D5—42no—
597C23—51no—
598C23—101no—
599Q8—21no—
600Q8D5×Dic612yes—
601D4—52no—
602D4—104no—
603D4—101no—
604C2×C4—21no—
605C2×C4—21no—
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—201no—
616C2×C4—201no—
617C2×C4—202no—
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—102no—
631C2×C3—202no—
632C2×C3D5×C22⋊Q811yescharacteristic
633C2×C3#6610211yescharacteristic
634C2×C3#6611111yescharacteristic
635C5#8250911yescharacteristic, complemented, Sylow
636C22—52no—
637C22—101no—
638C22—101no—
639C22—102no—
640C22—201no—
641C22—201no—
642C22C2×D5×#6711yescharacteristic
643C4—21no—
644C4—22no—
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#1061296211yescharacteristic, complemented, Sylow
658C2—102no—
659C2—202no—
660C2D5×#92411yescharacteristic
661C2#1175508411yescharacteristic
662C2#1175531511yescharacteristic
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#3080
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. D5×#870C2semidirect
3. #11751123C2semidirect
4. C5×#5022C2semidirect
5. #11749332C2semidirect
6. #11749329C2semidirect
9. #11747392C2semidirect
10. #11747389C2semidirect
11. #11747189C2semidirect
12. #11747188C2semidirect
13. #11747007C2semidirect
14. #11746888C2semidirect
15. #11746887C2semidirect
130. #5022D5semidirect
570. C3×C5#3080semidirect
635. C5#82509semidirect
657. C3#10612962semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7132
D5×#8702
#117511232
C5×#50222
#117493322
#117493292
#117491982
#117473922
#117473892
#117471892
#117471882
#117470072
#117468882
#117468872
#106129623
#825095