Finite Group Databasebeta

← #14431371

Subgroups — #14431371

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
1#11753671C211yesmaximal, characteristic
2#11753369C211yesmaximal, characteristic, complemented
3#11750955C211yesmaximal, characteristic, complemented
4C5×#4871C211yesmaximal, characteristic, complemented
5C3×D5×#106C211yesmaximal, characteristic, complemented
6#11748135C211yesmaximal, characteristic
7#11747867C211yesmaximal, characteristic, complemented
8#11747814C211yesmaximal, characteristic, complemented
9#11747647C211yesmaximal, characteristic, complemented
10#11747498C211yesmaximal, characteristic
11#11747452C211yesmaximal, characteristic, complemented
12#11747419C211yesmaximal, characteristic, complemented
13#11747291C211yesmaximal, characteristic, complemented
14#11747256C211yesmaximal, characteristic, complemented
15#11747187C211yesmaximal, characteristic, complemented
16#10612902—31nomaximal, Hall
17C2×#6772C2211yescharacteristic
18#91777C2211yescharacteristic
19#91776C2211yescharacteristic
20C5×#893C2211yescharacteristic
21C5×#890C2211yescharacteristic
22C2×C3×C8×D5C2211yescharacteristic
23C3×D5×C4⋊C4C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25#91469C2211yescharacteristic
26#91440—21no—
27C4×#1201—21no—
28#91435C2211yescharacteristic
29#91400—21no—
30D3×#683—21no—
31#91384C2211yescharacteristic
32#91360—21no—
33#91358C2211yescharacteristic
34#91357C2211yescharacteristic
35#91349—21no—
36#91340C2211yescharacteristic
37#91335—21no—
38#91328—21no—
39C2×#6649C2211yescharacteristic
40C3×C5×#106C2211yescharacteristic
41#91100C2211yescharacteristic
42#91098C2211yescharacteristic
43#91094C2211yescharacteristic
44#91092C2211yescharacteristic
45C5×#821C2211yescharacteristic
46C5×Dic3⋊C8C2211yescharacteristic
47C5×#809C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C3×#3949C2211yescharacteristic
50C3×#3940C2211yescharacteristic
51C3×#3940C2211yescharacteristic
52#90989C2211yescharacteristic
53#90987C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55#90983C2211yescharacteristic
56#90975C2211yescharacteristic
57#90974C2211yescharacteristic
58#90967C2211yescharacteristic
59#90966C2211yescharacteristic
60#79130—51nomaximal, Hall
61#66023—31no—
62#65880—31no—
63C5×#478—31no—
64#65352—31no—
65#65297—31no—
66#65170—31no—
67#65166—31no—
68D5×#106D311yescharacteristic, complemented
69#65143—31no—
70#65140—31no—
71#65128—31no—
72#65061—31no—
73#65060—31no—
74#65052—31no—
75#65050—31no—
76C2×Dic30—21no—
77C2×Dic30C2311yescharacteristic
78C2×C5×D12C2311yescharacteristic
79C2×C4×C5×D3—21no—
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5C2311yescharacteristic
83C2×#1204—21no—
84C2×#1201—21no—
85C2×D3×Dic5—21no—
86C2×D3×Dic5—21no—
87#6772—22no—
88#6772Q814yescomplemented
89C2×C3×C5×C8C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94#6712—21no—
95C4×Dic15—21no—
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×(C2×D3)⋊C4—21no—
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C4×C5×Dic3C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C3×C4⋊Dic5C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×#683—21no—
107C3×#683—21no—
108C2×C3×#168C2311yescharacteristic
109C3×C8×D5—22no—
110Dic3⋊Dic5—21no—
111Dic3⋊Dic5—21no—
112#6669—21no—
113#6668—21no—
114#6668D411yescharacteristic
115#6668D411yescharacteristic
116(C2×D3)⋊Dic5—21no—
117#6665—21no—
118#6665D411yescharacteristic
119#6665D411yescharacteristic
120Dic3×Dic5—21no—
121Dic3×Dic5—21no—
122#6649—22no—
123#5504—51no—
124#5500—51no—
125C2×C3×#106—51no—
126#5113—51no—
127#5102—51no—
128#4966—51no—
129#4964—51no—
130#4871—51no—
131#4871D511yescharacteristic, complemented
132#4870—51no—
133#4870—51no—
134#4857—51no—
135#4857—51no—
136#4854—51no—
137#4854—51no—
138C2×#711—31no—
139C5×#125—31no—
140C4×C5×D4—31no—
141D4×Dic5—31no—
142C4×C22⋊D5—61no—
143C2×#683—61no—
144C2×#676—31no—
145C2×C8×D5C2×D311yescharacteristic
146#4043—61no—
147#4042—61no—
148#4038—31no—
149D5×C4⋊C4C2×D311yescharacteristic
150D5×C4⋊C4C2×D311yescharacteristic
151#4036—31no—
152#4035—61no—
153#4034—31no—
154#4034—61no—
155#4033—31no—
156#4027—61no—
157#4023—61no—
158#4018—31no—
159#4015—31no—
160C4×Dic10—31no—
161C5×#107—31no—
162C5×#106C2×D311yescharacteristic
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102—31no—
166#3964—31no—
167#3964—31no—
168#3949—31no—
169#3949C2×D311yescharacteristic
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940C2×D311yescharacteristic
178#3940C2×D311yescharacteristic
179#3939—31no—
180C4⋊#168—31no—
181#3084—151noSylow
182C22×C5×D3—21no—
183C22×C3×D5C2×D411yescharacteristic
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15C2×D411yescharacteristic
190C2×Dic15C2×D411yescharacteristic
191Dic30—21no—
192Dic30—81no—
193Dic30C2×Q812yes—
194C2×C5×Dic3—21no—
195C2×C5×Dic3C2×D411yescharacteristic
196C2×C5×Dic3C2×D411yescharacteristic
197C5×D12—21no—
198C5×D12C2×Q812yes—
199C4×C5×D3—81no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5C2×D411yescharacteristic
203C3×C4×D5—81no—
204C3×C4×D5—81no—
205C3×C4×D5C2×Q812yes—
206C3×C4×D5#4112yes—
207#1204—81no—
208#1201—24no—
209D3×Dic5—24no—
210D3×Dic5—81no—
211C3×C5×C8—21no—
212C3⋊#168—21no—
213C3×#168—21no—
214C5×C3⋊C8—21no—
215C2×#235—51no—
216C22×C3×C8—51no—
217C2×C3×C4⋊C4—51no—
218C2×C3×C4⋊C4—51no—
219C4×#67—101no—
220C4×#67—101no—
221#926—51no—
222#926—51no—
223#924—101no—
224#924—101no—
225C2×#208—51no—
226#893—51no—
227#893C2×D511yescharacteristic
228#892—101no—
229D3×C4⋊C4—101no—
230#890—51no—
231#890—101no—
232#890C2×D511yescharacteristic
233#888—51no—
234#888—51no—
235#888—101no—
236#887—51no—
237#887—51no—
238C3×#106—51no—
239C3×#106—51no—
240C3×#106—51no—
241C3×#106C2×D511yescharacteristic
242#821—51no—
243#821C2×D511yescharacteristic
244#816—51no—
245#816—51no—
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8C2×D511yescharacteristic
250#810—51no—
251#810—51no—
252#809—51no—
253#809C2×D511yescharacteristic
254#808—51no—
255#808—51no—
256#807—51no—
257#807C2×D511yescharacteristic
258C2×C5×D4—31no—
259C22×C4×C5—61no—
260C2×C22⋊D5—61no—
261C22×Dic5—61no—
262C22×Dic5—61no—
263#711—34no—
264#711—62no—
265C2×C4×D5—21no—
266C2×C4×D5—21no—
267C2×C4×D5C22×D311yescharacteristic
268C2×Dic10—31no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×C5×C8—31no—
272C2×C5×C8C22×D311yescharacteristic
273C5×C4⋊C4—31no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—61no—
279C42×C5—31no—
280C22⋊Dic5—61no—
281#685—31no—
282#685—31no—
283#685—61no—
284C4⋊Dic5—31no—
285C4⋊Dic5—61no—
286C4⋊Dic5—61no—
287C4⋊Dic5C22×D311yescharacteristic
288C4⋊Dic5C22×D311yescharacteristic
289#683—21no—
290#683—21no—
291#683—31no—
292#683—31no—
293#683—61no—
294#683—61no—
295#683—61no—
296#683—61no—
297C4×Dic5—31no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C4×Dic5—61no—
301C2×#168—31no—
302C2×#168C22×D311yescharacteristic
303#676—62no—
304C8×D5—22no—
305#544—151no—
306#520—151no—
307#479—151no—
308#479—151no—
309#478—31no—
310#478—151no—
311#476—151no—
312#476—151no—
313#475—151no—
314#475—151no—
315#428—151no—
316C2×#106—51no—
317#424—151no—
318#417—151no—
319#416—151no—
320C22×C3×C5C22×D411yescharacteristic
321C2×C5×D3—22no—
322C2×C5×D3—41no—
323C2×C5×D3—41no—
324C2×C3×D5—21no—
325C2×C3×D5—21no—
326C2×C3×D5C22⋊Q812yes—
327C3×C4×C5—41no—
328C3×C4×C5—41no—
329C3×C4×C5C22×Q811yescharacteristic
330C3×C4×C5C2×#4111yescharacteristic
331Dic15—22no—
332Dic15—21no—
333Dic15—21no—
334Dic15—41no—
335C3×Dic5—41no—
336C3×Dic5—41no—
337C3×Dic5C22⋊Q812yes—
338C5×Dic3—21no—
339C5×Dic3—21no—
340C5×Dic3—41no—
341C22×C3×C4—51no—
342C22×C3×C4—101no—
343C22×C3×C4—101no—
344C2×#67—101no—
345#235—54no—
346#235—102no—
347C2×D12C22×D511yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—101no—
350C2×C4×D3—101no—
351C2×Dic6—51no—
352C2×Dic6—101no—
353C2×Dic6—101no—
354C2×C3×C8—51no—
355C2×C3×C8—102no—
356C2×C3×C8C22×D511yescharacteristic
357C3×C4⋊C4—51no—
358C3×C4⋊C4—51no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4C22×D511yescharacteristic
362C3×C4⋊C4C22×D511yescharacteristic
363#217—51no—
364#217—51no—
365#217—101no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—101no—
368C4⋊Dic3—21no—
369C4⋊Dic3—51no—
370C4⋊Dic3—51no—
371C4⋊Dic3—51no—
372C4⋊Dic3—101no—
373C4⋊Dic3C22×D511yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380C4×Dic3—51no—
381C4×Dic3—101no—
382C4×Dic3—101no—
383C4×Dic3—101no—
384C4×Dic3C22×D511yescharacteristic
385#208—102no—
386C2×C3⋊C8—51no—
387C2×C3⋊C8C22×D511yescharacteristic
388C23×C5—61no—
389C22×D5D3×D411yescharacteristic
390C5×D4—32no—
391C5×D4—61no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—31no—
395C2×C4×C5—31no—
396C2×C4×C5—61no—
397C2×C4×C5—241no—
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—64no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—31no—
403C2×Dic5—31no—
404C2×Dic5—61no—
405C2×Dic5—64no—
406C2×Dic5—61no—
407C2×Dic5—241no—
408C2×Dic5D3×D411yescharacteristic
409C4×D5—81no—
410C4×D5—81no—
411C4×D5#23512yes—
412C4×D5D3×Q812yes—
413Dic10—32no—
414Dic10—61no—
415Dic10—241no—
416Dic10—241no—
417C5×C8—21no—
418C5×C8—61no—
419#168—21no—
420#168—61no—
421C2×#41—151no—
422C2×M16—151no—
423C22×C8—51no—
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—151no—
433C4×Q8—151no—
434C4×D4—31no—
435C4×D4—151no—
436C4×D4—301no—
437C4×D4—301no—
438#117—151no—
439#117—151no—
440#117—301no—
441C2×C4⋊C4—51no—
442C2×C4⋊C4—51no—
443C2×C4⋊C4—301no—
444#107—31no—
445#107—151no—
446#106—51no—
447#106—51no—
448#106—51no—
449#106—151no—
450#106—151no—
451#106D3×D511yescharacteristic
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×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57711yescharacteristic
466C2×C3×C5#57711yescharacteristic
467C3×D5—22no—
468C5×D3—42no—
469C23×C3—51no—
470C22×D3—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—51no—
474C2×C3×C4—52no—
475C2×C3×C4—52no—
476C2×C3×C4—101no—
477C2×C3×C4—101no—
478C2×C3×C4—401no—
479C2×C3×C4—401no—
480C2×C3×C4C23×D511yescharacteristic
481#67—104no—
482C2×Dic3—21no—
483C2×Dic3—51no—
484C2×Dic3—51no—
485C2×Dic3—101no—
486C2×Dic3—101no—
487C2×Dic3D4×D511yescharacteristic
488C2×Dic3D4×D511yescharacteristic
489D12—21no—
490D12Q8×D512yes—
491C4×D3—81no—
492C4×D3—104no—
493C4×D3—401no—
494Dic6—52no—
495Dic6—101no—
496Dic6—401no—
497Dic6—401no—
498C3×C8—21no—
499C3×C8—101no—
500C3⋊C8—21no—
501C3⋊C8—101no—
502C22×C5—62no—
503C22×C5—121no—
504C22×C5—121no—
505C22×C5C2×D3×D411yescharacteristic
506C2×D5—21no—
507C2×D5—21no—
508C2×D5#89612yes—
509C4×C5—41no—
510C4×C5—41no—
511C4×C5—61no—
512C4×C5—61no—
513C4×C5—121no—
514C4×C5C2×#23511yescharacteristic
515C4×C5C2×D3×Q811yescharacteristic
516Dic5—41no—
517Dic5—41no—
518Dic5—61no—
519Dic5—61no—
520Dic5—62no—
521Dic5—121no—
522Dic5#89612yes—
523#41—154no—
524#41—302no—
525C2×Q8—151no—
526C2×Q8—301no—
527C2×Q8—301no—
528C2×D4—31no—
529C2×D4—301no—
530C22×C4—51no—
531C22×C4—61no—
532C22×C4—101no—
533C22×C4—101no—
534C22×C4—301no—
535C22×C4—301no—
536M16—302no—
537C2×C8—31no—
538C2×C8—51no—
539C2×C8—102no—
540C2×C8—151no—
541C2×C8C2×D3×D511yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—51no—
544C4⋊C4—51no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—151no—
550C4⋊C4—151no—
551C4⋊C4—151no—
552C4⋊C4—301no—
553C4⋊C4—301no—
554C4⋊C4—301no—
555C4⋊C4—301no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4C2×D3×D511yescharacteristic
559C4⋊C4C2×D3×D511yescharacteristic
560C22⋊C4—61no—
561C22⋊C4—151no—
562C22⋊C4—151no—
563C22⋊C4—301no—
564C22⋊C4—301no—
565C42—31no—
566C42—151no—
567C42—301no—
568C42—301no—
569C42—301no—
570C3×C5#308411yescharacteristic, complemented, Hall
571C22×C3—52no—
572C22×C3—101no—
573C22×C3—101no—
574C22×C3C2×D4×D511yescharacteristic
575C2×D3—22no—
576C2×D3—41no—
577C2×D3—41no—
578C3×C4—41no—
579C3×C4—41no—
580C3×C4—52no—
581C3×C4—201no—
582C3×C4—201no—
583C3×C4C2×Q8×D511yescharacteristic
584C3×C4D5×#4111yescharacteristic
585Dic3—21no—
586Dic3—21no—
587Dic3—41no—
588Dic3—101no—
589Dic3—101no—
590Dic3—102no—
591Dic3—201no—
592C2×C5—122no—
593C2×C5C2×#89611yescharacteristic
594C2×C5#576211yescharacteristic
595C2×C5#576211yescharacteristic
596D5—22no—
597C23—51no—
598C23—61no—
599Q8—152no—
600Q8—301no—
601Q8—1201no—
602Q8—1201no—
603D4—32no—
604D4—61no—
605D4—304no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—51no—
611C2×C4—52no—
612C2×C4—52no—
613C2×C4—61no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—151no—
617C2×C4—151no—
618C2×C4—241no—
619C2×C4—304no—
620C2×C4—301no—
621C2×C4—301no—
622C2×C4—401no—
623C2×C4—401no—
624C2×C4—1201no—
625C2×C4C22×D3×D511yescharacteristic
626C8—21no—
627C8—61no—
628C8—101no—
629C8—301no—
630C2×C3—102no—
631C2×C3D5×C22⋊Q811yescharacteristic
632C2×C3#6610411yescharacteristic
633C2×C3#6610911yescharacteristic
634D3—42no—
635C5#7913011yescharacteristic, complemented, Sylow
636C22—52no—
637C22—62no—
638C22—101no—
639C22—101no—
640C22—121no—
641C22—121no—
642C22D3×D4×D511yescharacteristic
643C4—41no—
644C4—41no—
645C4—52no—
646C4—61no—
647C4—61no—
648C4—121no—
649C4—201no—
650C4—201no—
651C4—301no—
652C4—301no—
653C4—302no—
654C4—601no—
655C4D5×#23511yescharacteristic
656C4D3×Q8×D511yescharacteristic
657C3#1061290211yescharacteristic, complemented, Sylow
658C2—102no—
659C2—122no—
660C2D5×#89611yescharacteristic
661C2#1175408111yescharacteristic
662C2#1175408711yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#6772C22
hypercenter#106D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11753369C2semidirect
3. #11750955C2semidirect
4. C5×#4871C2semidirect
5. C3×D5×#106C2semidirect
7. #11747867C2semidirect
8. #11747814C2semidirect
9. #11747647C2semidirect
11. #11747452C2semidirect
12. #11747419C2semidirect
13. #11747291C2semidirect
14. #11747256C2semidirect
15. #11747187C2semidirect
68. D5×#106D3semidirect
88. #6772Q8semidirect
131. #4871D5semidirect
570. C3×C5#3084semidirect
635. C5#79130semidirect
657. C3#10612902semidirect

Maximal subgroups

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

subgroupindex
#117536712
#117533692
#117509552
C5×#48712
C3×D5×#1062
#117481352
#117478672
#117478142
#117476472
#117474982
#117474522
#117474192
#117472912
#117472562
#117471872
#106129023
#791305