Finite Group Databasebeta

← #14458469

Subgroups — #14458469

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
1C3×#65969C211yesmaximal, characteristic, complemented
2#11754647C211yesmaximal, characteristic
3#11751147C211yesmaximal, characteristic, complemented
4C5×#5048C211yesmaximal, characteristic, complemented
5#11749397C211yesmaximal, characteristic, complemented
6#11749338C211yesmaximal, characteristic, complemented
7#11749269C211yesmaximal, characteristic, complemented
8#11749221C211yesmaximal, characteristic, complemented
9C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
10C2×#90968C211yesmaximal, characteristic, complemented
11#11748385C211yesmaximal, characteristic, complemented
12D5×#809C211yesmaximal, characteristic, complemented
13#11747240C211yesmaximal, characteristic, complemented
14#11747165C211yesmaximal, characteristic, complemented
15#11747138C211yesmaximal, characteristic, complemented
16#10612411—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×#6790—21no—
19C2×D5×D12C2211yescharacteristic
20C3×C5×C22⋊Q8C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22C2×#6717C2211yescharacteristic, complemented
23C2×C5×#215C2211yescharacteristic, complemented
24C5×#930C2211yescharacteristic
25C22×C5×C3⋊C8C2211yescharacteristic, complemented
26C3×#4092C2211yescharacteristic, complemented
27C3×Q8×Dic5C2211yescharacteristic, complemented
28C3×C4×C22⋊D5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
30C3×#4043—21no—
31C3×D5×C4⋊C4C2211yescharacteristic, complemented
32C3×#4035—21no—
33C3×#4034C2211yescharacteristic, complemented
34C3×#4027—21no—
35C3×#4024—21no—
36#91573—21no—
37#91476—21no—
38#91451C2211yescharacteristic
39#91450C2211yescharacteristic
40#91420—21no—
41#91418C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91114C2211yescharacteristic, complemented
44#91093C2211yescharacteristic
45#91093C2211yescharacteristic, complemented
46C5×#835C2211yescharacteristic, complemented
47C5×#809C2211yescharacteristic, complemented
48C5×#808C2211yescharacteristic, complemented
49#90986C2211yescharacteristic, complemented
50#90986C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90968C2211yescharacteristic
53#90968C2211yescharacteristic
54#90968C2211yescharacteristic, complemented
55#90968C2211yescharacteristic, complemented
56#90966C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83634—51nomaximal, Hall
61#65969D311yescharacteristic, complemented
62#65943—31no—
63C5×#465—31no—
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—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×D60—22no—
81C2×D60—21no—
82C2×D60—41no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×C5×#67—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C3×C22⋊D5D411yescharacteristic
88C22×C3×Dic5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×Dic10—21no—
92#6790—44no—
93C2×#1203—21no—
94C2×#1203—21no—
95C2×#1203—21no—
96C2×#1202—21no—
97C2×#1200—21no—
98D5×D12—22no—
99D5×D12—41no—
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103#6717—22no—
104#6717—41no—
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#215—41no—
108C5×(C2×D3)⋊C4—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C2×C5×C3⋊C8—41no—
111C2×C5×C3⋊C8C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C3×C22⋊Dic5D411yescharacteristic
114C3×#685—21no—
115C3×#685D411yescharacteristic
116C3×C4⋊Dic5—21no—
117C3×C4⋊Dic5—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C3×#683—21no—
121C3×#683—21no—
122C3×#683—21no—
123C3×#683D411yescharacteristic
124C3×C4×Dic5—21no—
125C3×C4×Dic5C2311yescharacteristic
126#6667—21no—
127#6667—21no—
128D5×C3⋊C8—41no—
129C3×#554—51no—
130D4×D12—51no—
131#5088—51no—
132#5084—51no—
133#5048—51no—
134#5048D511yescharacteristic, complemented
135#5046—51no—
136#5046—51no—
137#5027—51no—
138C4×#215—51no—
139D4×C3⋊C8—51no—
140#4968—51no—
141#4968—51no—
142C2×#809—51no—
143C2×#809—51no—
144C2×D4×D5—31no—
145C2×D4×D5—61no—
146C22×D20—31no—
147C2×C5×SD16—31no—
148C22×C5×C8—31no—
149C5×C22⋊Q8C2×D311yescharacteristic, complemented
150C5×#121—31no—
151#4092C2×D311yescharacteristic, complemented
152Q8×Dic5C2×D311yescharacteristic, complemented
153C2×#688—31no—
154C2×#688—31no—
155#4086—31no—
156#4083—61no—
157C4×C22⋊D5C2×D311yescharacteristic
158C2×C4⋊Dic5C2×D311yescharacteristic, complemented
159C2×C8×D5—31no—
160#4043—21no—
161#4041—31no—
162#4039—31no—
163D5×C4⋊C4C2×D311yescharacteristic, complemented
164#4035—21no—
165#4034C2×D311yescharacteristic, complemented
166#4030—61no—
167#4028—61no—
168#4027—21no—
169#4024—21no—
170C5×#106—31no—
171C5×#103—31no—
172C5×#102—31no—
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×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C22×C5×D3—21no—
195C22×C3×D5C2×D411yescharacteristic
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C2×D3×D5—81no—
199C3×C5×Q8—21no—
200C3×C5×Q8—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2411yescharacteristic
207D60—21no—
208D60—21no—
209D60—21no—
210D60—42no—
211D60#4112yes—
212C5×#67—42no—
213C2×C5×Dic3—21no—
214C5×D12—21no—
215C5×D12—21no—
216C3×C22⋊D5SD1614yescomplemented
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—81no—
220C2×C3×Dic5C2×D411yescharacteristic
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225C3×C4×D5—81no—
226C3×Dic10—81no—
227#1203—42no—
228#1203—42no—
229#1203—81no—
230#1202—42no—
231#1200—42no—
232C3⋊#168—21no—
233C3⋊#168—21no—
234C5×C3⋊C8—21no—
235C5×C3⋊C8—21no—
236C2×D3×D4—101no—
237C22×D12—51no—
238C22×D12—51no—
239C3×C4⋊Q8—51no—
240C3×#125—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8—101no—
243C3×C22⋊Q8—101no—
244C3×C22⋊Q8C2×D511yescharacteristic, complemented
245C3×C4×Q8—51no—
246C3×C4×D4—51no—
247C3×C4×D4—101no—
248C2×C3×C4⋊C4—51no—
249C2×C3×C4⋊C4—51no—
250C2×#215—51no—
251C2×#215—51no—
252C2×#215C2×D511yescharacteristic, complemented
253#930—51no—
254#930C2×D511yescharacteristic
255C22×C3⋊C8—51no—
256C22×C3⋊C8C2×D511yescharacteristic, complemented
257#895—101no—
258#882—101no—
259#882—101no—
260#874—51no—
261C4×D12—51no—
262#835C2×D511yescharacteristic, complemented
263#830—51no—
264#830—51no—
265#809—51no—
266#809—51no—
267#809—51no—
268#809—51no—
269#809—51no—
270#809—51no—
271#809—51no—
272#809—51no—
273#809C2×D511yescharacteristic, complemented
274#808—51no—
275#808—51no—
276#808C2×D511yescharacteristic, complemented
277C4⋊(C3⋊C8)—51no—
278C4×C3⋊C8—51no—
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×Q8C22×D311yescharacteristic
282C2×C5×D4—31no—
283C2×C5×D4—61no—
284C22×C4×C5C22×D311yescharacteristic
285C2×C22⋊D5—61no—
286C2×C22⋊D5—61no—
287C2×C22⋊D5—61no—
288C2×C22⋊D5#6711yescharacteristic
289C22×Dic5—21no—
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—21no—
300C2×C4×D5—61no—
301C2×C4×D5C22×D311yescharacteristic
302C2×Dic10—21no—
303C5×SD16—121no—
304C2×C5×C8—31no—
305C2×C5×C8—31no—
306C2×C5×C8—121no—
307C5×C4⋊C4—21no—
308C5×C4⋊C4—31no—
309C5×C4⋊C4C22×D311yescharacteristic
310C5×C22⋊C4—21no—
311C5×C22⋊C4—61no—
312C22⋊Dic5#6711yescharacteristic
313#688—62no—
314#688—121no—
315#685—21no—
316#685—61no—
317#685—61no—
318#685#6711yescharacteristic
319C4⋊Dic5—21no—
320C4⋊Dic5—21no—
321C4⋊Dic5C22×D311yescharacteristic
322C4⋊Dic5C22×D311yescharacteristic
323#683—21no—
324#683—21no—
325#683—21no—
326#683#6711yescharacteristic
327C4×Dic5—21no—
328C4×Dic5C22×D311yescharacteristic
329C2×#168—31no—
330C2×#168—31no—
331C8×D5—121no—
332#554—51no—
333D42—151no—
334#486—151no—
335#481—151no—
336#481—151no—
337#476—151no—
338#465—31no—
339#465—151no—
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×C5C2×SD1612yes—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—84no—
358C2×C5×D3—41no—
359C2×C5×D3—41no—
360C2×C5×D3—41no—
361C2×C3×D5—21no—
362C2×C3×D5—21no—
363C2×C3×D5C2×SD1612yes—
364D3×D5—84no—
365C3×C4×C5—21no—
366C3×C4×C5—41no—
367C3×C4×C5—41no—
368C3×C4×C5C2×#4111yescharacteristic
369C3×C4×C5H(5,𝔽2)11yescharacteristic
370C3×Dic5—21no—
371C3×Dic5—21no—
372C3×Dic5—41no—
373C3×Dic5—41no—
374C3×Dic5C2×SD1612yes—
375C5×Dic3—41no—
376C23×D3—101no—
377C23×D3—101no—
378C2×C3×Q8—101no—
379C2×C3×Q8C22×D511yescharacteristic
380C2×C3×D4—51no—
381C22×C3×C4—51no—
382C22×C3×C4—101no—
383C22×C3×C4—101no—
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—21no—
386C2×#67—101no—
387D3×D4—204no—
388C2×D12—51no—
389C2×D12—51no—
390C2×D12—102no—
391C2×D12—102no—
392C2×D12—101no—
393C2×D12—101no—
394C2×D12—101no—
395C2×D12—101no—
396C2×D12—201no—
397C2×D12—201no—
398C2×D12C22×D511yescharacteristic
399C2×C4×D3—101no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—51no—
403C3×C4⋊C4—51no—
404C3×C4⋊C4—101no—
405C3×C4⋊C4—101no—
406C3×C4⋊C4—101no—
407C3×C4⋊C4—101no—
408C3×C4⋊C4—101no—
409C3×C4⋊C4C22×D511yescharacteristic
410C3×C22⋊C4—21no—
411C3×C22⋊C4—51no—
412C3×C22⋊C4—51no—
413C3×C22⋊C4—101no—
414C3×C42—51no—
415C3×C42—101no—
416#215—41no—
417#215—102no—
418#215—201no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—101no—
421(C2×D3)⋊C4—101no—
422C4⋊Dic3C22×D511yescharacteristic
423C2×C3⋊C8—41no—
424C2×C3⋊C8—51no—
425C2×C3⋊C8—51no—
426C2×C3⋊C8—201no—
427C2×C3⋊C8C22×D511yescharacteristic
428C2×C3⋊C8C22×D511yescharacteristic
429C23×C5—61no—
430C23×C5C2×#6711yescharacteristic
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C22×D5—122no—
436C22×D5—122no—
437C22×D5—241no—
438C22×D5—241no—
439C22×D5C2×#6711yescharacteristic
440C5×Q8—21no—
441C5×Q8—21no—
442C5×D4—61no—
443C5×D4—61no—
444C5×D4—122no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—61no—
450C2×C4×C5C2×#6711yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—122no—
453C22⋊D5—122no—
454C22⋊D5—241no—
455C22⋊D5#21514yescomplemented
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—81no—
459C2×Dic5C2×#6711yescharacteristic
460C2×Dic5C2×#6711yescharacteristic
461C2×Dic5C2×#6711yescharacteristic
462D20—32no—
463D20—61no—
464D20—61no—
465D20—61no—
466D20—122no—
467D20—122no—
468C4×D5—21no—
469C4×D5—21no—
470C4×D5—81no—
471C4×D5—122no—
472Dic10—81no—
473C5×C8—61no—
474C5×C8—61no—
475#168—61no—
476#168—61no—
477C22×D4—151no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—31no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—31no—
484C22×C8—151no—
485C4⋊Q8—51no—
486#127—151no—
487#125—101no—
488C22⋊Q8—51no—
489C22⋊Q8—101no—
490C22⋊Q8—101no—
491C22⋊Q8D3×D511yescharacteristic, complemented
492#121—31no—
493#121—151no—
494#121—301no—
495#120—301no—
496#120—301no—
497C4×Q8—51no—
498C4×D4—51no—
499C4×D4—101no—
500C4×D4—151no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—51no—
503#106—31no—
504#106—151no—
505#106—151no—
506C4⋊C8—151no—
507#103—31no—
508#102—31no—
509#102—151no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#102—151no—
515#102—151no—
516#102—151no—
517C22⋊C8—151no—
518C22⋊C8—151no—
519C4×C8—151no—
520C2×C3×C5—22no—
521C2×C3×C5#54611yescharacteristic
522C2×C3×C5C22×SD1611yescharacteristic
523C2×C3×C5#57611yescharacteristic
524D15—42no—
525D15—81no—
526C3×D5—22no—
527C5×D3—81no—
528C23×C3—51no—
529C23×C3D4×D511yescharacteristic
530C22×D3—21no—
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×Q8—401no—
542C3×D4—54no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—51no—
548C2×C3×C4—51no—
549C2×C3×C4—51no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—401no—
555C2×C3×C4—401no—
556C2×C3×C4D4×D511yescharacteristic
557C2×C3×C4C23×D511yescharacteristic
558#67—42no—
559#67—202no—
560C2×Dic3—21no—
561D12—21no—
562D12—21no—
563D12—52no—
564D12—101no—
565D12—101no—
566D12—101no—
567D12—202no—
568D12—202no—
569D12—202no—
570D12—401no—
571C4×D3—202no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—101no—
575C3⋊C8—101no—
576C22×C5—21no—
577C22×C5—21no—
578C22×C5—121no—
579C22×C5—121no—
580C22×C5—121no—
581C22×C5C2×#21512yes—
582C22×C5C22×#6711yescharacteristic
583C2×D5—21no—
584C2×D5—21no—
585C2×D5—62no—
586C2×D5—121no—
587C2×D5—121no—
588C2×D5—121no—
589C2×D5—121no—
590C2×D5—121no—
591C2×D5—244no—
592C2×D5—244no—
593C2×D5C2×#21512yes—
594C4×C5—21no—
595C4×C5—41no—
596C4×C5—41no—
597C4×C5—121no—
598C4×C5D3×#4111yescharacteristic
599C4×C5#100911yescharacteristic
600Dic5—21no—
601Dic5—21no—
602Dic5—41no—
603Dic5—41no—
604Dic5C2×#21512yes—
605C24—301no—
606C24—301no—
607C2×Q8—101no—
608C2×Q8C2×D3×D511yescharacteristic
609C2×D4—31no—
610C2×D4—51no—
611C2×D4—61no—
612C2×D4—151no—
613C2×D4—151no—
614C2×D4—302no—
615C2×D4—301no—
616C2×D4—301no—
617C2×D4—301no—
618C2×D4—301no—
619C2×D4—302no—
620C2×D4—301no—
621C2×D4—601no—
622C2×D4—601no—
623C2×D4—604no—
624C22×C4—51no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—121no—
630SD16—302no—
631SD16—601no—
632C2×C8—31no—
633C2×C8—31no—
634C2×C8—121no—
635C2×C8—151no—
636C2×C8—151no—
637C2×C8—601no—
638C4⋊C4—21no—
639C4⋊C4—31no—
640C4⋊C4—51no—
641C4⋊C4—51no—
642C4⋊C4—51no—
643C4⋊C4—101no—
644C4⋊C4—101no—
645C4⋊C4—101no—
646C4⋊C4—101no—
647C4⋊C4—101no—
648C4⋊C4C2×D3×D511yescharacteristic
649C22⋊C4—21no—
650C22⋊C4—51no—
651C22⋊C4—51no—
652C22⋊C4—61no—
653C22⋊C4—101no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—51no—
657C42—101no—
658C3×C5#329511yescharacteristic, complemented, Hall
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—52no—
662C22×C3—101no—
663C22×C3—101no—
664C22×C3D5×SD1612yes—
665C22×C3C2×D4×D511yescharacteristic
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
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—52no—
681C3×C4—101no—
682C3×C4—101no—
683C3×C4—201no—
684C3×C4—201no—
685C3×C4#414411yescharacteristic
686C3×C4D5×#4111yescharacteristic
687Dic3—41no—
688C2×C5—22no—
689C2×C5—241no—
690C2×C5C22×#21511yescharacteristic
691C2×C5#582911yescharacteristic
692C2×C5#583511yescharacteristic
693D5—22no—
694D5—122no—
695D5—241no—
696C23—51no—
697C23—61no—
698C23—301no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23—602no—
703C23—602no—
704C23—1201no—
705C23—1201no—
706C23D5×#6711yescharacteristic
707Q8—21no—
708Q8—21no—
709Q8—401no—
710D4—54no—
711D4—61no—
712D4—61no—
713D4—122no—
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—51no—
728C2×C4—51no—
729C2×C4—51no—
730C2×C4—61no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—401no—
736C2×C4—401no—
737C2×C4—602no—
738C2×C4D5×#6711yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—61no—
741C8—61no—
742C8—301no—
743C8—301no—
744C2×C3—22no—
745C2×C3—102no—
746C2×C3#6594411yescharacteristic
747C2×C3C2×D5×SD1611yescharacteristic
748C2×C3#6610311yescharacteristic
749D3—81no—
750D3—202no—
751D3—401no—
752C5#8363411yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—52no—
756C22—101no—
757C22—101no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—302no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22—601no—
766C22—601no—
767C22—1204no—
768C22—1204no—
769C22D5×#21512yes—
770C22C2×D5×#6711yescharacteristic
771C4—21no—
772C4—41no—
773C4—41no—
774C4—52no—
775C4—101no—
776C4—101no—
777C4—121no—
778C4—201no—
779C4—201no—
780C4#9202411yescharacteristic
781C4#9202711yescharacteristic
782C3#1061241111yescharacteristic, complemented, Sylow
783C2—22no—
784C2—102no—
785C2—241no—
786C2—602no—
787C2—1201no—
788C2#1175506411yescharacteristic
789C2C2×D5×#21511yescharacteristic
790C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754647C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65969C2semidirect
3. #11751147C2semidirect
4. C5×#5048C2semidirect
5. #11749397C2semidirect
6. #11749338C2semidirect
7. #11749269C2semidirect
8. #11749221C2semidirect
9. C3⋊C8×C22⋊D5C2semidirect
10. C2×#90968C2semidirect
11. #11748385C2semidirect
12. D5×#809C2semidirect
13. #11747240C2semidirect
14. #11747165C2semidirect
15. #11747138C2semidirect
20. C3×C5×C22⋊Q8C22semidirect
22. C2×#6717C22semidirect
23. C2×C5×#215C22semidirect
25. C22×C5×C3⋊C8C22semidirect
26. C3×#4092C22semidirect
27. C3×Q8×Dic5C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
31. C3×D5×C4⋊C4C22semidirect
33. C3×#4034C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91114C22semidirect
45. #91093C22semidirect
46. C5×#835C22semidirect
47. C5×#809C22semidirect
48. C5×#808C22semidirect
49. #90986C22semidirect
50. #90986C22semidirect
51. #90982C22semidirect
54. #90968C22semidirect
55. #90968C22semidirect
56. #90966C22semidirect
57. #90966C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
61. #65969D3semidirect
134. #5048D5semidirect
149. C5×C22⋊Q8C2×D3semidirect
151. #4092C2×D3semidirect
152. Q8×Dic5C2×D3semidirect
158. C2×C4⋊Dic5C2×D3semidirect
163. D5×C4⋊C4C2×D3semidirect
165. #4034C2×D3semidirect
216. C3×C22⋊D5SD16semidirect
244. C3×C22⋊Q8C2×D5semidirect
252. C2×#215C2×D5semidirect
256. C22×C3⋊C8C2×D5semidirect
262. #835C2×D5semidirect
273. #809C2×D5semidirect
276. #808C2×D5semidirect
455. C22⋊D5#215semidirect
491. C22⋊Q8D3×D5semidirect
658. C3×C5#3295semidirect
752. C5#83634semidirect
782. C3#10612411semidirect

Maximal subgroups

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

subgroupindex
C3×#659692
#117546472
#117511472
C5×#50482
#117493972
#117493382
#117492692
#117492212
C3⋊C8×C22⋊D52
C2×#909682
#117483852
D5×#8092
#117472402
#117471652
#117471382
#106124113
#836345