Finite Group Databasebeta

← #14430710

Subgroups — #14430710

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
1Dic3×#711C211yesmaximal, characteristic
2D5×#890C211yesmaximal, characteristic, complemented
3#11750867C211yesmaximal, characteristic, complemented
4C5×#4763C211yesmaximal, characteristic, complemented
5C3×#65060C211yesmaximal, characteristic
6#11749089C211yesmaximal, characteristic, complemented
7#11749088C211yesmaximal, characteristic, complemented
8#11748951C211yesmaximal, characteristic
9#11747877C211yesmaximal, characteristic, complemented
10#11747863C211yesmaximal, characteristic, complemented
11#11747618C211yesmaximal, characteristic, complemented
12#11747596C211yesmaximal, characteristic, complemented
13#11747452C211yesmaximal, characteristic, complemented
14#11747301C211yesmaximal, characteristic, complemented
15#11747295C211yesmaximal, characteristic, complemented
16#10612898—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18D4×Dic15C2211yescharacteristic
19#91779C2211yescharacteristic
20C5×D4×Dic3C2211yescharacteristic
21C5×#890C2211yescharacteristic
22C2×C3×#676C2211yescharacteristic
23C3×D5×C4⋊C4C2211yescharacteristic
24#91559—21no—
25Dic3×C22⋊D5—21no—
26#91528—21no—
27C2×Dic3×Dic5—21no—
28D5×C4⋊Dic3—21no—
29D5×C4⋊Dic3C2211yescharacteristic
30D5×Dic3⋊C4—21no—
31C4×D5×Dic3C2211yescharacteristic
32#91384C2211yescharacteristic
33#91381C2211yescharacteristic
34#91358C2211yescharacteristic
35#91335—21no—
36#91334—21no—
37#91331C2211yescharacteristic
38Dic3×Dic10C2211yescharacteristic
39C2×#6649C2211yescharacteristic
40C3×C5×#102C2211yescharacteristic
41#91116C2211yescharacteristic
42#91102C2211yescharacteristic
43#91098C2211yescharacteristic
44#91092C2211yescharacteristic
45C5×#832C2211yescharacteristic
46C5×#817C2211yescharacteristic
47C5×Dic3⋊C8C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C3×#3964C2211yescharacteristic
50C3×#3948C2211yescharacteristic
51C3×#3942C2211yescharacteristic
52#90989C2211yescharacteristic
53#90988C2211yescharacteristic
54#90987C2211yescharacteristic
55#90985C2211yescharacteristic
56Dic3⋊#168C2211yescharacteristic
57#90983C2211yescharacteristic
58#90971C2211yescharacteristic
59#90970C2211yescharacteristic
60#78871—51nomaximal, Hall
61D5×#125—31no—
62C4×#711—31no—
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#65060D311yescharacteristic
74#65055—31no—
75#65052—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×Dic15—21no—
78C22×C5×Dic3—21no—
79C2×C3×C22⋊D5—21no—
80C22×C3×Dic5—21no—
81C3×#711—22no—
82C3×#711Q814yes—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5C2311yescharacteristic
85C2×C3×Dic10C2311yescharacteristic
86C2×D5×Dic3—21no—
87C2×D5×Dic3D411yescharacteristic
88C2×D5×Dic3D411yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91#6719—21no—
92C4⋊Dic15—21no—
93C4⋊Dic15C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C5×C4⋊Dic3C2311yescharacteristic
102C5×Dic3⋊C4—21no—
103C4×C5×Dic3C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×#683—21no—
107C2×C3×#168C2311yescharacteristic
108C3×#676—22no—
109Dic3⋊Dic5—21no—
110#6669—21no—
111#6668—21no—
112#6668—21no—
113#6668—21no—
114#6668—21no—
115#6668—21no—
116#6665—21no—
117Dic3×Dic5—21no—
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5D411yescharacteristic
121Dic3×Dic5D411yescharacteristic
122#6649—22no—
123Dic3×#41—51no—
124C2×#890—51no—
125C3×#417—51no—
126#5232—51no—
127#5121—51no—
128#5118—51no—
129#4964—51no—
130#4799—51no—
131#4799—51no—
132#4796—51no—
133#4796—51no—
134#4766—51no—
135#4766—51no—
136#4763—51no—
137#4763D511yescharacteristic, complemented
138C2×#711C2×D311yescharacteristic
139C5×#125—31no—
140C4×C5×D4—31no—
141D4×Dic5—31no—
142C4×C22⋊D5—61no—
143C2×C4×Dic5—61no—
144C2×#676—31no—
145C2×#676C2×D311yescharacteristic
146#4038—31no—
147D5×C4⋊C4—31no—
148D5×C4⋊C4—61no—
149D5×C4⋊C4—61no—
150D5×C4⋊C4C2×D311yescharacteristic
151#4036—31no—
152#4036—31no—
153#4035—61no—
154#4035—61no—
155#4033—31no—
156#4027—61no—
157#4023—61no—
158C42×D5—31no—
159#4016—31no—
160C4×Dic10—31no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102C2×D311yescharacteristic
166#3964—31no—
167#3964C2×D311yescharacteristic
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948C2×D311yescharacteristic
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942C2×D311yescharacteristic
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×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—42no—
191C2×Dic15C2×D411yescharacteristic
192C2×Dic15C2×D411yescharacteristic
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—42no—
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C3×C22⋊D5—24no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—24no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5C2×D411yescharacteristic
203C3×C4×D5—42no—
204C3×C4×D5C2×Q812yes—
205C3×C4×D5#4112yes—
206C3×Dic10—21no—
207C3×Dic10C2×Q812yes—
208D5×Dic3—41no—
209D5×Dic3—41no—
210D5×Dic3—42no—
211C3×C5×C8—21no—
212C3⋊#168—21no—
213C3×#168—21no—
214C5×C3⋊C8—21no—
215C2×C3×#41—51no—
216C2×C3×M16—51no—
217C2×C3×C4⋊C4—51no—
218Q8×Dic3—51no—
219Q8×Dic3—51no—
220D4×Dic3—51no—
221D4×Dic3—101no—
222D4×Dic3—101no—
223D4×Dic3C2×D511yescharacteristic
224#926—51no—
225#926—101no—
226C2×C4⋊Dic3—51no—
227C2×C4⋊Dic3—101no—
228C2×Dic3⋊C4—101no—
229C2×C4×Dic3—51no—
230C2×C4×Dic3—101no—
231C2×#208—51no—
232#890—51no—
233#890—51no—
234#890—51no—
235#890—101no—
236#890—101no—
237#890C2×D511yescharacteristic
238C3×#103—51no—
239C3×#103—51no—
240C3×#102—51no—
241C3×#102C2×D511yescharacteristic
242#835—51no—
243#835—51no—
244#832—51no—
245#832C2×D511yescharacteristic
246#818—51no—
247#818—51no—
248#817—51no—
249#817C2×D511yescharacteristic
250Dic3⋊C8—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8C2×D511yescharacteristic
254#808—51no—
255#808—51no—
256#807—51no—
257#807C2×D511yescharacteristic
258C2×C5×D4C22×D311yescharacteristic
259C22×C4×C5—61no—
260C2×C22⋊D5—21no—
261C22×Dic5—21no—
262C22×Dic5—61no—
263#711—22no—
264#711Dic614yes—
265C2×C4×D5—21no—
266C2×C4×D5—31no—
267C2×C4×D5—31no—
268C2×C4×D5—61no—
269C2×C4×D5C22×D311yescharacteristic
270C2×Dic10C22×D311yescharacteristic
271C2×C5×C8—31no—
272C2×C5×C8C22×D311yescharacteristic
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—61no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—61no—
279C42×C5—31no—
280C22⋊Dic5—61no—
281#685—61no—
282C4⋊Dic5—31no—
283C4⋊Dic5—31no—
284C4⋊Dic5—61no—
285C4⋊Dic5—61no—
286C4⋊Dic5C22×D311yescharacteristic
287#683—21no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294#683—61no—
295C4×Dic5—31no—
296C4×Dic5—31no—
297C4×Dic5—31no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C4×Dic5—61no—
301C2×#168—31no—
302C2×#168C22×D311yescharacteristic
303#676—22no—
304#676—62no—
305C2×#125—151no—
306C4×#41—151no—
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—51no—
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—41no—
328C3×C4×C5C22×Q811yescharacteristic
329C3×C4×C5C2×#4111yescharacteristic
330Dic15—21no—
331Dic15—21no—
332Dic15—41no—
333Dic15—41no—
334C3×Dic5—22no—
335C3×Dic5—41no—
336C3×Dic5C22⋊Q812yes—
337C5×Dic3—21no—
338C5×Dic3—21no—
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—51no—
347C22×C3×C4—101no—
348C22×C3×C4—101no—
349C22×Dic3—21no—
350C22×Dic3—51no—
351C22×Dic3—51no—
352C22×Dic3—101no—
353C22×Dic3—101no—
354C3×M16—102no—
355C2×C3×C8—51no—
356C2×C3×C8C22×D511yescharacteristic
357C3×C4⋊C4—51no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4C22×D511yescharacteristic
360#217—21no—
361#217—101no—
362#217—101no—
363C4⋊Dic3—21no—
364C4⋊Dic3—51no—
365C4⋊Dic3—51no—
366C4⋊Dic3—101no—
367C4⋊Dic3—101no—
368C4⋊Dic3—101no—
369C4⋊Dic3—101no—
370C4⋊Dic3—101no—
371C4⋊Dic3—101no—
372C4⋊Dic3C22×D511yescharacteristic
373C4⋊Dic3C22×D511yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378C4×Dic3—51no—
379C4×Dic3—51no—
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—21no—
389C22×D5D3×D411yescharacteristic
390C5×D4—21no—
391C5×D4C2×Dic612yes—
392C2×C4×C5—21no—
393C2×C4×C5—31no—
394C2×C4×C5—31no—
395C2×C4×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5—122no—
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—24no—
400C2×Dic5—21no—
401C2×Dic5—24no—
402C2×Dic5—21no—
403C2×Dic5—31no—
404C2×Dic5—31no—
405C2×Dic5—61no—
406C2×Dic5—61no—
407C2×Dic5—122no—
408C2×Dic5D3×D411yescharacteristic
409C4×D5—42no—
410C4×D5—121no—
411C4×D5—121no—
412C4×D5—122no—
413C4×D5C2×Dic612yes—
414C4×D5#23712yes—
415Dic10—21no—
416Dic10C2×Dic612yes—
417C5×C8—21no—
418C5×C8—61no—
419#168—21no—
420#168—61no—
421C2×#41—51no—
422C2×M16—51no—
423C2×M16—151no—
424#125—31no—
425#125—151no—
426#125—151no—
427#125—151no—
428#125—301no—
429#125—301no—
430C4×Q8—151no—
431C4×Q8—151no—
432C4×D4—31no—
433C4×D4—151no—
434C4×D4—301no—
435C4×D4—301no—
436#117—151no—
437#117—301no—
438C2×C4⋊C4—51no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—301no—
441C2×C4⋊C4—301no—
442C2×C42—151no—
443C2×C42—301no—
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—51no—
457#103—51no—
458#103—151no—
459#103—151no—
460#102—31no—
461#102—51no—
462#102—151no—
463#102D3×D511yescharacteristic
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—51no—
478C2×C3×C4—52no—
479C2×C3×C4—52no—
480C2×C3×C4—104no—
481C2×C3×C4—101no—
482C2×C3×C4—101no—
483C2×C3×C4—202no—
484C2×C3×C4C23×D511yescharacteristic
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—42no—
488C2×Dic3—51no—
489C2×Dic3—51no—
490C2×Dic3—101no—
491C2×Dic3—101no—
492C2×Dic3—201no—
493C2×Dic3—201no—
494C2×Dic3—202no—
495C2×Dic3—202no—
496C2×Dic3D4×D511yescharacteristic
497C2×Dic3D4×D511yescharacteristic
498C3×C8—21no—
499C3×C8—101no—
500C3⋊C8—21no—
501C3⋊C8—101no—
502C22×C5—22no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5C2×D3×D411yescharacteristic
506C2×D5—21no—
507C2×D5—21no—
508C2×D5#87812yes—
509C4×C5—41no—
510C4×C5—61no—
511C4×C5—61no—
512C4×C5—121no—
513C4×C5—121no—
514C4×C5C22×Dic611yescharacteristic
515C4×C5C2×#23711yescharacteristic
516Dic5—22no—
517Dic5—41no—
518Dic5—61no—
519Dic5—61no—
520Dic5—121no—
521Dic5—121no—
522Dic5#87812yes—
523#41—54no—
524#41—102no—
525C2×Q8—51no—
526C2×D4—101no—
527C2×D4C2×D3×D511yescharacteristic
528C22×C4—51no—
529C22×C4—61no—
530C22×C4—101no—
531C22×C4—101no—
532C22×C4—151no—
533C22×C4—151no—
534C22×C4—301no—
535C22×C4—301no—
536M16—102no—
537M16—302no—
538C2×C8—31no—
539C2×C8—51no—
540C2×C8—151no—
541C2×C8C2×D3×D511yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—51no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—101no—
548C4⋊C4—151no—
549C4⋊C4—151no—
550C4⋊C4—301no—
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—61no—
561C22⋊C4—301no—
562C22⋊C4—301no—
563C42—31no—
564C42—151no—
565C42—151no—
566C42—151no—
567C42—301no—
568C42—301no—
569C42—301no—
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—41no—
579C3×C4—52no—
580C3×C4—102no—
581C3×C4—201no—
582C3×C4C2×Q8×D511yescharacteristic
583C3×C4D5×#4111yescharacteristic
584Dic3—21no—
585Dic3—21no—
586Dic3—41no—
587Dic3—41no—
588Dic3—101no—
589Dic3—101no—
590Dic3—201no—
591Dic3—201no—
592C2×C5—42no—
593C2×C5C2×#87811yescharacteristic
594C2×C5#577311yescharacteristic
595C2×C5#577711yescharacteristic
596D5—22no—
597C23—21no—
598C23—51no—
599Q8—52no—
600Q8—101no—
601D4—21no—
602D4—104no—
603D4D5×Dic612yes—
604C2×C4—21no—
605C2×C4—31no—
606C2×C4—31no—
607C2×C4—51no—
608C2×C4—52no—
609C2×C4—52no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—104no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—122no—
616C2×C4—151no—
617C2×C4—151no—
618C2×C4—202no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—601no—
622C2×C4—601no—
623C2×C4—602no—
624C2×C4—602no—
625C2×C4C22×D3×D511yescharacteristic
626C8—21no—
627C8—61no—
628C8—101no—
629C8—301no—
630C2×C3—42no—
631C2×C3—102no—
632C2×C3D5×C22⋊Q811yescharacteristic
633C2×C3#6610211yescharacteristic
634C2×C3#6610711yescharacteristic
635C5#7887111yescharacteristic, complemented, Sylow
636C22—22no—
637C22—41no—
638C22—41no—
639C22—52no—
640C22—101no—
641C22—101no—
642C22D3×D4×D511yescharacteristic
643C4—41no—
644C4—52no—
645C4—61no—
646C4—61no—
647C4—102no—
648C4—121no—
649C4—121no—
650C4—201no—
651C4—301no—
652C4—301no—
653C4—601no—
654C4—601no—
655C4C2×D5×Dic611yescharacteristic
656C4D5×#23711yescharacteristic
657C3#1061289811yescharacteristic, complemented, Sylow
658C2—42no—
659C2—102no—
660C2D5×#87811yescharacteristic
661C2#1175404911yescharacteristic
662C2#1175407511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#711C22
hypercenter#102D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D5×#890C2semidirect
3. #11750867C2semidirect
4. C5×#4763C2semidirect
6. #11749089C2semidirect
7. #11749088C2semidirect
9. #11747877C2semidirect
10. #11747863C2semidirect
11. #11747618C2semidirect
12. #11747596C2semidirect
13. #11747452C2semidirect
14. #11747301C2semidirect
15. #11747295C2semidirect
137. #4763D5semidirect
570. C3×C5#3080semidirect
635. C5#78871semidirect
657. C3#10612898semidirect

Maximal subgroups

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

subgroupindex
Dic3×#7112
D5×#8902
#117508672
C5×#47632
C3×#650602
#117490892
#117490882
#117489512
#117478772
#117478632
#117476182
#117475962
#117474522
#117473012
#117472952
#106128983
#788715