Finite Group Databasebeta

← #14458439

Subgroups — #14458439

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756394C211yesmaximal, characteristic, complemented
2#11756368C211yesmaximal, characteristic
3C3×C5×#465C211yesmaximal, characteristic, complemented
4#11751270C211yesmaximal, characteristic, complemented
5#11751264C211yesmaximal, characteristic, complemented
6C2×#91105C211yesmaximal, characteristic, complemented
7C8×#1220C211yesmaximal, characteristic, complemented
8#11751147C211yesmaximal, characteristic, complemented
9#11751135C211yesmaximal, characteristic, complemented
10#11750971C211yesmaximal, characteristic, complemented
11#11750964C211yesmaximal, characteristic, complemented
12#11750908C211yesmaximal, characteristic, complemented
13#11750889C211yesmaximal, characteristic, complemented
14D15×#102C211yesmaximal, characteristic, complemented
15#11750861C211yesmaximal, characteristic, complemented
16#10612411—31nomaximal, Hall
17C2×D4×D15—21no—
18C2×D4×D15C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C2×C3×C5×SD16C2211yescharacteristic, complemented
21C22×C3×C5×C8C2211yescharacteristic, complemented
22C3×C5×C22⋊Q8C2211yescharacteristic, complemented
23C3×C5×#121C2211yescharacteristic
24#91835C2211yescharacteristic, complemented
25Q8×Dic15C2211yescharacteristic, complemented
26C2×#6717C2211yescharacteristic
27C2×#6717C2211yescharacteristic, complemented
28#91829C2211yescharacteristic
29#91826—21no—
30C4×#1220C2211yescharacteristic
31C2×C4⋊Dic15C2211yescharacteristic, complemented
32C2×C8×D15C2211yescharacteristic, complemented
33#91786—21no—
34#91784C2211yescharacteristic
35#91782C2211yescharacteristic
36C4⋊C4×D15C2211yescharacteristic, complemented
37#91778—21no—
38#91777C2211yescharacteristic, complemented
39#91773—21no—
40#91771—21no—
41#91770—21no—
42#91767—21no—
43C3×C5×#106C2211yescharacteristic, complemented
44C3×C5×#103C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic, complemented
46#91116C2211yescharacteristic, complemented
47#91116C2211yescharacteristic, complemented
48#91114C2211yescharacteristic, complemented
49#91105C2211yescharacteristic
50#91105C2211yescharacteristic
51#91105C2211yescharacteristic, complemented
52#91105C2211yescharacteristic, complemented
53#91104C2211yescharacteristic, complemented
54#91098C2211yescharacteristic, complemented
55C8×Dic15C2211yescharacteristic, complemented
56#91093C2211yescharacteristic
57#91093C2211yescharacteristic, complemented
58#91092C2211yescharacteristic, complemented
59#91092C2211yescharacteristic, complemented
60#80680—51nomaximal, Hall
61#65969—31no—
62#65943—31no—
63C5×#465D311yescharacteristic, complemented
64#65458—31no—
65#65452—31no—
66C2×#3953—31no—
67C8×C22⋊D5—31no—
68#65335—31no—
69#65323—31no—
70#65159—31no—
71#65152—31no—
72#65096—31no—
73#65077—31no—
74D5×#102—31no—
75#65049—31no—
76C23×D15—21no—
77C23×D15—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84C2×#1220—21no—
85C2×#1220D411yescharacteristic
86C22×Dic15—21no—
87D4×D15—22no—
88D4×D15—41no—
89D4×D15—44no—
90C2×D60—22no—
91C2×D60—21no—
92C2×D60—21no—
93C2×D60—41no—
94C2×D60C2311yescharacteristic
95C2×D60C2311yescharacteristic
96C2×C4×D15—21no—
97C2×C4×D15—21no—
98C2×C4×D15C2311yescharacteristic
99C2×Dic30—21no—
100C3×C5×SD16—41no—
101C2×C3×C5×C8—41no—
102C2×C3×C5×C8C2311yescharacteristic
103C2×C3×C5×C8C2311yescharacteristic
104C3×C5×C4⋊C4—21no—
105C3×C5×C4⋊C4C2311yescharacteristic
106C3×C5×C4⋊C4C2311yescharacteristic
107C3×C5×C22⋊C4—21no—
108C3×C5×C22⋊C4—21no—
109#6719D411yescharacteristic
110#6717—22no—
111#6717—41no—
112#6714—21no—
113#6714—21no—
114#6714—21no—
115#6714D411yescharacteristic
116C4⋊Dic15—21no—
117C4⋊Dic15—21no—
118C4⋊Dic15C2311yescharacteristic
119C4⋊Dic15C2311yescharacteristic
120#6712—21no—
121#6712—21no—
122#6712—21no—
123#6712D411yescharacteristic
124C4×Dic15—21no—
125C4×Dic15C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128C8×D15—41no—
129#5635—51no—
130#5609—51no—
131C3×#465D511yescharacteristic, complemented
132#5169—51no—
133#5163—51no—
134C2×#821—51no—
135C8×#67—51no—
136#5046—51no—
137#5034—51no—
138#4870—51no—
139#4863—51no—
140#4807—51no—
141#4788—51no—
142D3×#102—51no—
143#4760—51no—
144C2×D4×D5—31no—
145C2×D4×D5—61no—
146C22×D20—31no—
147C2×C5×SD16C2×D311yescharacteristic, complemented
148C22×C5×C8C2×D311yescharacteristic, complemented
149C5×C22⋊Q8C2×D311yescharacteristic, complemented
150C5×#121C2×D311yescharacteristic
151#4092—31no—
152Q8×Dic5—31no—
153C2×#688—31no—
154C2×#688—31no—
155#4086—31no—
156#4083—61no—
157C4×C22⋊D5—31no—
158C2×C4⋊Dic5—31no—
159C2×C8×D5—31no—
160#4043—61no—
161#4041—31no—
162#4039—31no—
163D5×C4⋊C4—31no—
164#4035—61no—
165#4034—31no—
166#4030—61no—
167#4028—61no—
168#4027—61no—
169#4024—61no—
170C5×#106C2×D311yescharacteristic, complemented
171C5×#103C2×D311yescharacteristic, complemented
172C5×#102C2×D311yescharacteristic, complemented
173#3964—31no—
174#3964—31no—
175C22⋊#168—31no—
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3952—31no—
181#3946—31no—
182C8×Dic5—31no—
183#3941—31no—
184#3941—31no—
185#3940—31no—
186#3940—31no—
187#3295—151noSylow
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—42no—
193C22×D15—42no—
194C22×D15—42no—
195C22×D15—42no—
196C22×D15—81no—
197C22×D15—81no—
198C22×D15C2×D411yescharacteristic
199C3×C5×Q8—21no—
200C3×C5×Q8—21no—
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—42no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2411yescharacteristic
211#1220—42no—
212#1220—42no—
213#1220—81no—
214#1220SD1614yescomplemented
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—81no—
218C2×Dic15C2×D411yescharacteristic
219C2×Dic15C2×D411yescharacteristic
220C2×Dic15C2×D411yescharacteristic
221D60—21no—
222D60—21no—
223D60—21no—
224D60—42no—
225D60—42no—
226D60#4112yes—
227C4×D15—21no—
228C4×D15—21no—
229C4×D15—42no—
230C4×D15—81no—
231Dic30—81no—
232C3×C5×C8—21no—
233C3×C5×C8—21no—
234C3⋊#168—21no—
235C3⋊#168—21no—
236C2×D3×D4—51no—
237C2×D3×D4—101no—
238C22×D12—51no—
239C2×C3×SD16C2×D511yescharacteristic, complemented
240C22×C3×C8C2×D511yescharacteristic, complemented
241C3×C22⋊Q8C2×D511yescharacteristic, complemented
242C3×#121C2×D511yescharacteristic
243#946—51no—
244Q8×Dic3—51no—
245C2×#215—51no—
246C2×#215—51no—
247#940—51no—
248#937—101no—
249C4×#67—51no—
250C2×C4⋊Dic3—51no—
251C2×D3×C8—51no—
252#897—101no—
253#895—51no—
254#893—51no—
255D3×C4⋊C4—51no—
256#889—101no—
257#888—51no—
258#884—101no—
259#882—101no—
260#67⋊C4—101no—
261#878—101no—
262C3×#106C2×D511yescharacteristic, complemented
263C3×#103C2×D511yescharacteristic, complemented
264C3×#102C2×D511yescharacteristic, complemented
265#832—51no—
266#832—51no—
267#830—51no—
268#821—51no—
269#821—51no—
270#821—51no—
271#821—51no—
272(C2×D3)⋊C8—51no—
273Dic3⋊C8—51no—
274C8×Dic3—51no—
275#809—51no—
276#809—51no—
277#808—51no—
278#808—51no—
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×Q8C22×D311yescharacteristic
282C2×C5×D4—21no—
283C2×C5×D4C22×D311yescharacteristic
284C22×C4×C5C22×D311yescharacteristic
285C2×C22⋊D5—31no—
286C2×C22⋊D5—61no—
287C2×C22⋊D5—61no—
288C2×C22⋊D5—61no—
289C22×Dic5—61no—
290D4×D5—62no—
291D4×D5—121no—
292D4×D5—124no—
293C2×D20—31no—
294C2×D20—31no—
295C2×D20—62no—
296C2×D20—61no—
297C2×D20—61no—
298C2×D20—121no—
299C2×C4×D5—31no—
300C2×C4×D5—61no—
301C2×C4×D5—61no—
302C2×Dic10—61no—
303C5×SD16—41no—
304C2×C5×C8—41no—
305C2×C5×C8C22×D311yescharacteristic
306C2×C5×C8C22×D311yescharacteristic
307C5×C4⋊C4—21no—
308C5×C4⋊C4C22×D311yescharacteristic
309C5×C4⋊C4C22×D311yescharacteristic
310C5×C22⋊C4—21no—
311C5×C22⋊C4—21no—
312C22⋊Dic5—31no—
313#688—62no—
314#688—121no—
315#685—31no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322C4⋊Dic5—61no—
323#683—31no—
324#683—61no—
325#683—61no—
326#683—61no—
327C4×Dic5—31no—
328C4×Dic5—61no—
329C2×#168—31no—
330C2×#168—31no—
331C8×D5—121no—
332#554—151no—
333D42—151no—
334#486—151no—
335#481—151no—
336#481—151no—
337#476—151no—
338#465—151no—
339#465D1511yescharacteristic, complemented
340#460—151no—
341#450—151no—
342#450—151no—
343C4×SD16—151no—
344C8×D4—151no—
345C2×#102—151no—
346C2×#102—151no—
347C22×C3×C5—21no—
348C22×C3×C5—21no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5C2×SD1612yes—
353C22×C3×C5C22×D411yescharacteristic
354C2×D15—21no—
355C2×D15—21no—
356C2×D15—22no—
357C2×D15—41no—
358C2×D15—41no—
359C2×D15—41no—
360C2×D15—41no—
361C2×D15—41no—
362C2×D15—84no—
363C2×D15—84no—
364C2×D15C2×SD1612yes—
365C3×C4×C5—21no—
366C3×C4×C5—41no—
367C3×C4×C5—41no—
368C3×C4×C5—41no—
369C3×C4×C5C2×#4111yescharacteristic
370C3×C4×C5H(5,𝔽2)11yescharacteristic
371Dic15—21no—
372Dic15—21no—
373Dic15—41no—
374Dic15—41no—
375Dic15C2×SD1612yes—
376C23×D3—101no—
377C23×D3—101no—
378C2×C3×Q8C22×D511yescharacteristic
379C2×C3×D4—21no—
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—51no—
383C2×#67—101no—
384C2×#67—101no—
385C2×#67—101no—
386C22×Dic3—101no—
387D3×D4—102no—
388D3×D4—201no—
389D3×D4—204no—
390C2×D12—51no—
391C2×D12—51no—
392C2×D12—102no—
393C2×D12—101no—
394C2×D12—101no—
395C2×D12—201no—
396C2×C4×D3—51no—
397C2×C4×D3—101no—
398C2×C4×D3—101no—
399C2×Dic6—101no—
400C3×SD16—41no—
401C2×C3×C8—41no—
402C2×C3×C8C22×D511yescharacteristic
403C2×C3×C8C22×D511yescharacteristic
404C3×C4⋊C4—21no—
405C3×C4⋊C4C22×D511yescharacteristic
406C3×C4⋊C4C22×D511yescharacteristic
407C3×C22⋊C4—21no—
408C3×C22⋊C4—21no—
409#217—51no—
410#215—102no—
411#215—201no—
412(C2×D3)⋊C4—51no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415(C2×D3)⋊C4—101no—
416C4⋊Dic3—51no—
417C4⋊Dic3—51no—
418C4⋊Dic3—101no—
419C4⋊Dic3—101no—
420Dic3⋊C4—51no—
421Dic3⋊C4—101no—
422Dic3⋊C4—101no—
423Dic3⋊C4—101no—
424C4×Dic3—51no—
425C4×Dic3—101no—
426C2×C3⋊C8—51no—
427C2×C3⋊C8—51no—
428D3×C8—201no—
429C23×C5—21no—
430C23×C5D3×D411yescharacteristic
431C22×D5—31no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—122no—
435C22×D5—122no—
436C22×D5—122no—
437C22×D5—122no—
438C22×D5—241no—
439C22×D5—241no—
440C5×Q8—21no—
441C5×Q8—21no—
442C5×D4—21no—
443C5×D4—21no—
444C5×D4—42no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5D3×D411yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—34no—
453C22⋊D5—122no—
454C22⋊D5—122no—
455C22⋊D5—241no—
456C2×Dic5—31no—
457C2×Dic5—31no—
458C2×Dic5—31no—
459C2×Dic5—61no—
460C2×Dic5—61no—
461C2×Dic5—241no—
462D20—32no—
463D20—61no—
464D20—61no—
465D20—61no—
466D20—122no—
467D20—122no—
468C4×D5—61no—
469C4×D5—61no—
470C4×D5—122no—
471C4×D5—241no—
472Dic10—241no—
473C5×C8—21no—
474C5×C8—21no—
475#168—61no—
476#168—61no—
477C22×D4—151no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—151no—
481C2×SD16—151no—
482C2×SD16C2×D1511yescharacteristic, complemented
483C22×C8—151no—
484C22×C8C2×D1511yescharacteristic, complemented
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—151no—
489C22⋊Q8—301no—
490C22⋊Q8—301no—
491C22⋊Q8C2×D1511yescharacteristic, complemented
492#121—151no—
493#121—301no—
494#121C2×D1511yescharacteristic
495#120—301no—
496#120—301no—
497C4×Q8—151no—
498C4×D4—151no—
499C4×D4—151no—
500C4×D4—301no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503#106—151no—
504#106—151no—
505#106C2×D1511yescharacteristic, complemented
506C4⋊C8—151no—
507#103C2×D1511yescharacteristic, complemented
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#102—151no—
515#102—151no—
516#102C2×D1511yescharacteristic, complemented
517C22⋊C8—151no—
518C22⋊C8—151no—
519C4×C8—151no—
520C2×C3×C5—22no—
521C2×C3×C5—81no—
522C2×C3×C5#54611yescharacteristic
523C2×C3×C5C22×SD1611yescharacteristic
524C2×C3×C5#57611yescharacteristic
525D15—22no—
526D15—42no—
527D15—81no—
528C23×C3—21no—
529C23×C3D4×D511yescharacteristic
530C22×D3—51no—
531C22×D3—101no—
532C22×D3—101no—
533C22×D3—202no—
534C22×D3—202no—
535C22×D3—202no—
536C22×D3—202no—
537C22×D3—401no—
538C22×D3—401no—
539C3×Q8—21no—
540C3×Q8—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—42no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4D4×D511yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551#67—54no—
552#67—202no—
553#67—202no—
554#67—401no—
555C2×Dic3—51no—
556C2×Dic3—51no—
557C2×Dic3—51no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—401no—
561D12—52no—
562D12—101no—
563D12—101no—
564D12—101no—
565D12—202no—
566D12—202no—
567C4×D3—101no—
568C4×D3—101no—
569C4×D3—202no—
570C4×D3—401no—
571Dic6—401no—
572C3×C8—21no—
573C3×C8—21no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5—41no—
581C22×C5D3×SD1612yes—
582C22×C5C2×D3×D411yescharacteristic
583C2×D5—32no—
584C2×D5—61no—
585C2×D5—61no—
586C2×D5—62no—
587C2×D5—121no—
588C2×D5—121no—
589C2×D5—121no—
590C2×D5—121no—
591C2×D5—121no—
592C2×D5—244no—
593C2×D5—244no—
594C4×C5—21no—
595C4×C5—41no—
596C4×C5—41no—
597C4×C5—41no—
598C4×C5#100411yescharacteristic
599C4×C5D3×#4111yescharacteristic
600Dic5—32no—
601Dic5—61no—
602Dic5—61no—
603Dic5—121no—
604Dic5—121no—
605C24—301no—
606C24—301no—
607C2×Q8—301no—
608C2×Q8C22×D1511yescharacteristic
609C2×D4—21no—
610C2×D4—151no—
611C2×D4—151no—
612C2×D4—151no—
613C2×D4—302no—
614C2×D4—301no—
615C2×D4—301no—
616C2×D4—301no—
617C2×D4—301no—
618C2×D4—302no—
619C2×D4—301no—
620C2×D4—601no—
621C2×D4—601no—
622C2×D4—604no—
623C2×D4C22×D1511yescharacteristic
624C22×C4—151no—
625C22×C4—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C22×D1511yescharacteristic
629SD16—41no—
630SD16—302no—
631SD16—601no—
632C2×C8—41no—
633C2×C8—151no—
634C2×C8—151no—
635C2×C8—601no—
636C2×C8C22×D1511yescharacteristic
637C2×C8C22×D1511yescharacteristic
638C4⋊C4—21no—
639C4⋊C4—151no—
640C4⋊C4—151no—
641C4⋊C4—151no—
642C4⋊C4—301no—
643C4⋊C4—301no—
644C4⋊C4—301no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4C22×D1511yescharacteristic
648C4⋊C4C22×D1511yescharacteristic
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—151no—
652C22⋊C4—151no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—151no—
657C42—301no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3D5×SD1612yes—
665C22×C3C2×D4×D511yescharacteristic
666C2×D3—52no—
667C2×D3—101no—
668C2×D3—101no—
669C2×D3—102no—
670C2×D3—201no—
671C2×D3—201no—
672C2×D3—201no—
673C2×D3—201no—
674C2×D3—201no—
675C2×D3—404no—
676C2×D3—404no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4#414411yescharacteristic
682C3×C4D5×#4111yescharacteristic
683Dic3—52no—
684Dic3—101no—
685Dic3—101no—
686Dic3—201no—
687Dic3—201no—
688C2×C5—22no—
689C2×C5—81no—
690C2×C5#561011yescharacteristic
691C2×C5C2×D3×SD1611yescharacteristic
692C2×C5#576911yescharacteristic
693D5—62no—
694D5—122no—
695D5—241no—
696C23—21no—
697C23—151no—
698C23—301no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23—602no—
703C23—602no—
704C23—1201no—
705C23—1201no—
706C23D4×D1511yescharacteristic
707Q8—21no—
708Q8—21no—
709Q8—1201no—
710D4—21no—
711D4—21no—
712D4—42no—
713D4—154no—
714D4—152no—
715D4—301no—
716D4—301no—
717D4—301no—
718D4—602no—
719D4—602no—
720D4—602no—
721D4—602no—
722D4—1201no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—151no—
729C2×C4—151no—
730C2×C4—151no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—602no—
736C2×C4—1201no—
737C2×C4—1201no—
738C2×C4D4×D1511yescharacteristic
739C2×C4C23×D1511yescharacteristic
740C8—21no—
741C8—21no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—81no—
746C2×C3#6594411yescharacteristic
747C2×C3C2×D5×SD1611yescharacteristic
748C2×C3#6610311yescharacteristic
749D3—102no—
750D3—202no—
751D3—401no—
752C5#8068011yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—152no—
759C22—301no—
760C22—301no—
761C22—302no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22—601no—
766C22—601no—
767C22—1204no—
768C22—1204no—
769C22SD16×D1512yes—
770C22C2×D4×D1511yescharacteristic
771C4—21no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—152no—
776C4—301no—
777C4—301no—
778C4—601no—
779C4—601no—
780C4#9209511yescharacteristic
781C4#41×D1511yescharacteristic
782C3#1061241111yescharacteristic, complemented, Sylow
783C2—22no—
784C2—81no—
785C2—302no—
786C2—602no—
787C2—1201no—
788C2#1175636911yescharacteristic
789C2C2×SD16×D1511yescharacteristic
790C2#1175652811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#465C2
socleC22×C3×C5C22×D4
prime radical#11756368C2
hypercenter#465D15
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11756394C2semidirect
3. C3×C5×#465C2semidirect
4. #11751270C2semidirect
5. #11751264C2semidirect
6. C2×#91105C2semidirect
7. C8×#1220C2semidirect
8. #11751147C2semidirect
9. #11751135C2semidirect
10. #11750971C2semidirect
11. #11750964C2semidirect
12. #11750908C2semidirect
13. #11750889C2semidirect
14. D15×#102C2semidirect
15. #11750861C2semidirect
20. C2×C3×C5×SD16C22semidirect
21. C22×C3×C5×C8C22semidirect
22. C3×C5×C22⋊Q8C22semidirect
24. #91835C22semidirect
25. Q8×Dic15C22semidirect
27. C2×#6717C22semidirect
31. C2×C4⋊Dic15C22semidirect
32. C2×C8×D15C22semidirect
36. C4⋊C4×D15C22semidirect
38. #91777C22semidirect
43. C3×C5×#106C22semidirect
44. C3×C5×#103C22semidirect
45. C3×C5×#102C22semidirect
46. #91116C22semidirect
47. #91116C22semidirect
48. #91114C22semidirect
51. #91105C22semidirect
52. #91105C22semidirect
53. #91104C22semidirect
54. #91098C22semidirect
55. C8×Dic15C22semidirect
57. #91093C22semidirect
58. #91092C22semidirect
59. #91092C22semidirect
63. C5×#465D3semidirect
131. C3×#465D5semidirect
147. C2×C5×SD16C2×D3semidirect
148. C22×C5×C8C2×D3semidirect
149. C5×C22⋊Q8C2×D3semidirect
170. C5×#106C2×D3semidirect
171. C5×#103C2×D3semidirect
172. C5×#102C2×D3semidirect
214. #1220SD16semidirect
239. C2×C3×SD16C2×D5semidirect
240. C22×C3×C8C2×D5semidirect
241. C3×C22⋊Q8C2×D5semidirect
262. C3×#106C2×D5semidirect
263. C3×#103C2×D5semidirect
264. C3×#102C2×D5semidirect
339. #465D15semidirect
482. C2×SD16C2×D15semidirect
484. C22×C8C2×D15semidirect
491. C22⋊Q8C2×D15semidirect
505. #106C2×D15semidirect
507. #103C2×D15semidirect
516. #102C2×D15semidirect
658. C3×C5#3295semidirect
752. C5#80680semidirect
782. C3#10612411semidirect

Maximal subgroups

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

subgroupindex
#117563942
#117563682
C3×C5×#4652
#117512702
#117512642
C2×#911052
C8×#12202
#117511472
#117511352
#117509712
#117509642
#117509082
#117508892
D15×#1022
#117508612
#106124113
#806805