Finite Group Databasebeta

← #14458475

Subgroups — #14458475

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#11754647C211yesmaximal, characteristic
2#11754500C211yesmaximal, characteristic, complemented
3#11750832C211yesmaximal, characteristic, complemented
4C5×#4735C211yesmaximal, characteristic, complemented
5C3×#65014C211yesmaximal, characteristic, complemented
6#11748533C211yesmaximal, characteristic, complemented
7C2×#90969C211yesmaximal, characteristic, complemented
8#11748115C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747995C211yesmaximal, characteristic, complemented
11#11747897C211yesmaximal, characteristic, complemented
12#11747843C211yesmaximal, characteristic, complemented
13#11747762C211yesmaximal, characteristic, complemented
14#11747760C211yesmaximal, characteristic, complemented
15#11747614C211yesmaximal, characteristic, complemented
16#10613073—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×#6790—21no—
19C2×D5×D12C2211yescharacteristic
20#91813C2211yescharacteristic, complemented
21C2×#6706C2211yescharacteristic
22C2×#6706C2211yescharacteristic, complemented
23C5×#930C2211yescharacteristic
24C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
25C3×C4×C22⋊D5C2211yescharacteristic
26C22×C3×#168C2211yescharacteristic, complemented
27C2×C3×C8×D5C2211yescharacteristic, complemented
28#91575—21no—
29#91573—21no—
30Dic3×C22⋊D5—21no—
31#91476—21no—
32#91468C2211yescharacteristic, complemented
33#91451C2211yescharacteristic
34#91450C2211yescharacteristic
35#91430—21no—
36#91420—21no—
37#91418C2211yescharacteristic
38D5×C4⋊Dic3C2211yescharacteristic, complemented
39#91360C2211yescharacteristic, complemented
40#91335—21no—
41#91333C2211yescharacteristic, complemented
42C2×#6659C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic, complemented
44#91105C2211yescharacteristic
45#91105C2211yescharacteristic, complemented
46C5×#821C2211yescharacteristic, complemented
47C5×#821C2211yescharacteristic, complemented
48C5×#817C2211yescharacteristic, complemented
49C5×#817C2211yescharacteristic, complemented
50C3×#3952C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90969C2211yescharacteristic
56#90969C2211yescharacteristic
57#90969C2211yescharacteristic, complemented
58#90969C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#79439—51nomaximal, Hall
61#65943—31no—
62#65845—31no—
63C5×#481—31no—
64#65330—31no—
65C2×#3941—31no—
66#65159—31no—
67#65153—31no—
68#65152—31no—
69#65141—31no—
70#65065—31no—
71D5×#102—31no—
72#65051—31no—
73#65049—31no—
74#65020—31no—
75#65014D311yescharacteristic, complemented
76C23×D15—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×D60—22no—
80C2×D60—21no—
81C2×D60—41no—
82C2×D60C2311yescharacteristic
83C2×D60C2311yescharacteristic
84C2×Dic30C2311yescharacteristic
85C2×C5×#67—21no—
86C22×C5×Dic3—21no—
87C2×C5×D12C2311yescharacteristic
88C2×C3×C22⋊D5D411yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90#6790—44no—
91C2×#1204—21no—
92C2×#1203—21no—
93C2×#1203—21no—
94C2×#1203—21no—
95C2×#1202—21no—
96C2×#1200—21no—
97C2×D5×Dic3—21no—
98D5×D12—22no—
99D5×D12—41no—
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102#6719—21no—
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105#6706—22no—
106#6706—41no—
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C5×C4⋊Dic3C2311yescharacteristic
111C5×C4⋊Dic3C2311yescharacteristic
112C3×C22⋊Dic5D411yescharacteristic
113C3×#685D411yescharacteristic
114C3×#683D411yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116C2×C3×#168—41no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C3×C8×D5—41no—
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123#6668—21no—
124#6667—21no—
125#6667—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128#6659—41no—
129D4×D12—51no—
130#5543—51no—
131C3×C8×D4—51no—
132#5114—51no—
133#5114—51no—
134C2×#821—51no—
135C2×#821—51no—
136#4848—51no—
137#4842—51no—
138#4735—51no—
139#4735D511yescharacteristic, complemented
140#4731—51no—
141#4731—51no—
142#4694—51no—
143C4×#204—51no—
144C2×D4×D5—31no—
145C2×D4×D5—61no—
146C22×D20—31no—
147C5×#121—31no—
148C2×C5×C4⋊C4—31no—
149#4086—31no—
150#4083—61no—
151C2×#687—31no—
152C4×C22⋊D5—61no—
153C4×C22⋊D5C2×D311yescharacteristic
154#4070—31no—
155#4070—61no—
156C22×#168C2×D311yescharacteristic, complemented
157C2×#677—31no—
158C2×#677—31no—
159C2×C8×D5C2×D311yescharacteristic, complemented
160#4043—31no—
161#4042—61no—
162#4041—31no—
163#4039—31no—
164D5×C4⋊C4—31no—
165#4035—61no—
166#4034—31no—
167#4033—31no—
168#4030—61no—
169#4028—61no—
170C5×#106—31no—
171C5×#106—31no—
172C5×#102—31no—
173C5×#102—31no—
174C5×C22⋊C8C2×D311yescharacteristic, complemented
175#3964—31no—
176#3953—31no—
177#3953—31no—
178#3952C2×D311yescharacteristic, complemented
179#3946C2×D311yescharacteristic, complemented
180C8×Dic5C2×D311yescharacteristic, complemented
181#3942—31no—
182#3941—31no—
183#3941—31no—
184#3941—31no—
185#3941—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—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205D60—21no—
206D60—21no—
207D60—21no—
208D60—42no—
209D60#4112yes—
210Dic30—21no—
211Dic30—21no—
212C5×#67—42no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—81no—
217C5×D12—21no—
218C5×D12—21no—
219C3×C22⋊D5SD1614yescomplemented
220C2×C3×Dic5C2×D411yescharacteristic
221C2×C3×Dic5C2×D411yescharacteristic
222C2×C3×Dic5C2×D411yescharacteristic
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225#1204—81no—
226#1203—42no—
227#1203—42no—
228#1203—81no—
229#1202—42no—
230#1200—42no—
231D5×Dic3—81no—
232C3×C5×C8—21no—
233C3×C5×C8—21no—
234C3×#168—21no—
235C3×#168—21no—
236C2×D3×D4—101no—
237C22×D12—51no—
238C22×D12—51no—
239C22×C3×C8—51no—
240C22×C3×C8—51no—
241C3×C4×D4—51no—
242D4×Dic3—101no—
243#930—51no—
244#930C2×D511yescharacteristic
245C2×C4⋊Dic3—51no—
246C2×C4⋊Dic3C2×D511yescharacteristic, complemented
247#924—51no—
248#924—51no—
249C2×#204—51no—
250C2×#204—51no—
251C2×#204—51no—
252#895—101no—
253#890—101no—
254#882—101no—
255#882—101no—
256#878—101no—
257#878—101no—
258#874—51no—
259C4×D12—51no—
260#869—51no—
261C4×Dic6—51no—
262C3×C4⋊C8—51no—
263C3×C22⋊C8—51no—
264C3×C22⋊C8C2×D511yescharacteristic, complemented
265C3×C4×C8—51no—
266#821—51no—
267#821—51no—
268#821—51no—
269#821—51no—
270#821—51no—
271#821—51no—
272#821—51no—
273#821C2×D511yescharacteristic, complemented
274#821C2×D511yescharacteristic, complemented
275#817—51no—
276#817C2×D511yescharacteristic, complemented
277#817C2×D511yescharacteristic, complemented
278#816—51no—
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C2×C5×D4—61no—
283C22×C4×C5—61no—
284C22×C4×C5C22×D311yescharacteristic
285C2×C22⋊D5—61no—
286C2×C22⋊D5—61no—
287C2×C22⋊D5—61no—
288C2×C22⋊D5D1211yescharacteristic
289D4×D5—62no—
290D4×D5—121no—
291D4×D5—124no—
292C2×D20—31no—
293C2×D20—31no—
294C2×D20—62no—
295C2×D20—61no—
296C2×D20—61no—
297C2×D20—121no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5C22×D311yescharacteristic
301C2×Dic10—31no—
302C2×Dic10—61no—
303C2×C5×C8C22×D311yescharacteristic
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4—31no—
308C5×C4⋊C4—61no—
309C5×C22⋊C4—61no—
310C22⋊Dic5—61no—
311C22⋊Dic5D1211yescharacteristic
312#687—121no—
313#685—61no—
314#685—61no—
315#685—61no—
316#685D1211yescharacteristic
317C4⋊Dic5—31no—
318C4⋊Dic5—61no—
319#683—61no—
320#683—61no—
321#683—61no—
322#683—61no—
323#683D1211yescharacteristic
324C4×Dic5—61no—
325C4×Dic5C22×D311yescharacteristic
326C2×#168—41no—
327C2×#168C22×D311yescharacteristic
328C2×#168C22×D311yescharacteristic
329#677—62no—
330#677—121no—
331C8×D5—41no—
332#554—151no—
333D42—151no—
334#486—151no—
335#481—31no—
336#481—151no—
337#476—151no—
338#465—151no—
339#465—151no—
340#460—151no—
341#450—151no—
342#450—151no—
343C4×SD16—151no—
344C8×D4—51no—
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×C5C2×#4111yescharacteristic
367C3×C4×C5H(5,𝔽2)11yescharacteristic
368Dic15—41no—
369Dic15—41no—
370C3×Dic5—21no—
371C3×Dic5—21no—
372C3×Dic5C2×SD1612yes—
373C5×Dic3—41no—
374C5×Dic3—41no—
375C5×Dic3—41no—
376C23×D3—101no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C22×C3×C4—51no—
380C22×C3×C4C22×D511yescharacteristic
381C2×#67—21no—
382C2×#67—101no—
383C22×Dic3—21no—
384C22×Dic3—101no—
385D3×D4—204no—
386C2×D12—51no—
387C2×D12—51no—
388C2×D12—102no—
389C2×D12—102no—
390C2×D12—101no—
391C2×D12—101no—
392C2×D12—101no—
393C2×D12—101no—
394C2×D12—201no—
395C2×D12—201no—
396C2×D12C22×D511yescharacteristic
397C2×C4×D3—101no—
398C2×Dic6—51no—
399C2×Dic6—101no—
400C2×C3×C8—51no—
401C2×C3×C8—51no—
402C2×C3×C8—201no—
403C2×C3×C8—201no—
404C2×C3×C8C22×D511yescharacteristic
405C2×C3×C8C22×D511yescharacteristic
406C3×C4⋊C4—51no—
407C3×C22⋊C4—51no—
408C3×C22⋊C4—51no—
409C3×C42—51no—
410#217—101no—
411#217—101no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415C4⋊Dic3—21no—
416C4⋊Dic3—51no—
417C4⋊Dic3—101no—
418C4⋊Dic3—101no—
419C4⋊Dic3C22×D511yescharacteristic
420C4⋊Dic3C22×D511yescharacteristic
421C4⋊Dic3C22×D511yescharacteristic
422Dic3⋊C4—101no—
423Dic3⋊C4—101no—
424Dic3⋊C4—101no—
425C4×Dic3—101no—
426#204—102no—
427#204—201no—
428#204—201no—
429C23×C5—61no—
430C23×C5C2×D1211yescharacteristic
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×D1211yescharacteristic
440C5×D4—61no—
441C5×D4—61no—
442C5×D4—122no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—241no—
449C2×C4×C5C2×D1211yescharacteristic
450C2×C4×C5C23×D311yescharacteristic
451C22⋊D5—122no—
452C22⋊D5—122no—
453C22⋊D5—241no—
454C22⋊D5#20414yescomplemented
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5C2×D1211yescharacteristic
458C2×Dic5C2×D1211yescharacteristic
459C2×Dic5C2×D1211yescharacteristic
460D20—32no—
461D20—61no—
462D20—61no—
463D20—61no—
464D20—122no—
465D20—122no—
466C4×D5—21no—
467C4×D5—21no—
468C4×D5—122no—
469C4×D5—241no—
470Dic10—61no—
471Dic10—61no—
472Dic10—241no—
473C5×C8—21no—
474C5×C8—21no—
475#168—21no—
476#168—21no—
477C22×D4—151no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—151no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—51no—
484C22×C8—51no—
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—151no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—31no—
493#121—151no—
494#121—301no—
495#120—301no—
496#120—301no—
497C4×Q8—151no—
498C4×D4—51no—
499C4×D4—151no—
500C4×D4—301no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—151no—
503#106—31no—
504#106—31no—
505#106—151no—
506C4⋊C8—51no—
507#103—151no—
508#102—31no—
509#102—31no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#102—151no—
515#102—151no—
516#102—151no—
517C22⋊C8—51no—
518C22⋊C8D3×D511yescharacteristic, complemented
519C4×C8—51no—
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×D4—54no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—51no—
543C2×C3×C4—51no—
544C2×C3×C4—51no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4D4×D511yescharacteristic
548C2×C3×C4C23×D511yescharacteristic
549#67—42no—
550#67—202no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—81no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—401no—
558D12—21no—
559D12—21no—
560D12—52no—
561D12—101no—
562D12—101no—
563D12—101no—
564D12—202no—
565D12—202no—
566D12—202no—
567D12—401no—
568C4×D3—202no—
569Dic6—101no—
570Dic6—101no—
571Dic6—401no—
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×#20412yes—
582C22×C5C22×D1211yescharacteristic
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×#20412yes—
594C4×C5—21no—
595C4×C5—121no—
596C4×C5—121no—
597C4×C5—121no—
598C4×C5#100411yescharacteristic
599C4×C5D3×#4111yescharacteristic
600Dic5—21no—
601Dic5—21no—
602Dic5—121no—
603Dic5—121no—
604Dic5C2×#20412yes—
605C24—301no—
606C24—301no—
607C2×Q8—151no—
608C2×Q8—301no—
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—61no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—302no—
630SD16—601no—
631SD16—601no—
632C2×C8—51no—
633C2×C8—51no—
634C2×C8—201no—
635C2×C8—201no—
636C2×C8C2×D3×D511yescharacteristic
637C2×C8C2×D3×D511yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—51no—
642C4⋊C4—61no—
643C4⋊C4—151no—
644C4⋊C4—301no—
645C4⋊C4—301no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C22⋊C4—51no—
650C22⋊C4—51no—
651C22⋊C4—61no—
652C22⋊C4—301no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C42—51no—
657C42—301no—
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—52no—
679C3×C4—101no—
680C3×C4—101no—
681C3×C4D5×#4111yescharacteristic
682C3×C4#414911yescharacteristic
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—201no—
687Dic3—201no—
688C2×C5—22no—
689C2×C5—241no—
690C2×C5#555411yescharacteristic
691C2×C5C22×#20411yescharacteristic
692C2×C5#575211yescharacteristic
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×D1211yescharacteristic
707Q8—301no—
708Q8—301no—
709Q8—1201no—
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—51no—
726C2×C4—51no—
727C2×C4—51no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—241no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—602no—
737C2×C4—1201no—
738C2×C4D5×D1211yescharacteristic
739C2×C4C22×D3×D511yescharacteristic
740C8—21no—
741C8—21no—
742C8—101no—
743C8—101no—
744C2×C3—22no—
745C2×C3—102no—
746C2×C3#6598811yescharacteristic
747C2×C3C2×D5×SD1611yescharacteristic
748C2×C3#6610811yescharacteristic
749D3—81no—
750D3—202no—
751D3—401no—
752C5#7943911yescharacteristic, 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×#20412yes—
770C22C2×D5×D1211yescharacteristic
771C4—21no—
772C4—52no—
773C4—101no—
774C4—101no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—601no—
779C4—601no—
780C4#9202411yescharacteristic
781C4#9202611yescharacteristic
782C3#1061307311yescharacteristic, complemented, Sylow
783C2—22no—
784C2—102no—
785C2—241no—
786C2—602no—
787C2—1201no—
788C2#1175326611yescharacteristic
789C2C2×D5×#20411yescharacteristic
790C2#1175402411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11754647C2
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11754500C2semidirect
3. #11750832C2semidirect
4. C5×#4735C2semidirect
5. C3×#65014C2semidirect
6. #11748533C2semidirect
7. C2×#90969C2semidirect
8. #11748115C2semidirect
9. D5×#821C2semidirect
10. #11747995C2semidirect
11. #11747897C2semidirect
12. #11747843C2semidirect
13. #11747762C2semidirect
14. #11747760C2semidirect
15. #11747614C2semidirect
20. #91813C22semidirect
22. C2×#6706C22semidirect
24. C2×C5×C4⋊Dic3C22semidirect
26. C22×C3×#168C22semidirect
27. C2×C3×C8×D5C22semidirect
32. #91468C22semidirect
38. D5×C4⋊Dic3C22semidirect
39. #91360C22semidirect
41. #91333C22semidirect
42. C2×#6659C22semidirect
43. C3×C5×C22⋊C8C22semidirect
45. #91105C22semidirect
46. C5×#821C22semidirect
47. C5×#821C22semidirect
48. C5×#817C22semidirect
49. C5×#817C22semidirect
50. C3×#3952C22semidirect
51. C3×#3946C22semidirect
52. C3×C8×Dic5C22semidirect
53. #90985C22semidirect
54. #90975C22semidirect
57. #90969C22semidirect
58. #90969C22semidirect
59. #90967C22semidirect
75. #65014D3semidirect
139. #4735D5semidirect
156. C22×#168C2×D3semidirect
159. C2×C8×D5C2×D3semidirect
174. C5×C22⋊C8C2×D3semidirect
178. #3952C2×D3semidirect
179. #3946C2×D3semidirect
180. C8×Dic5C2×D3semidirect
219. C3×C22⋊D5SD16semidirect
246. C2×C4⋊Dic3C2×D5semidirect
264. C3×C22⋊C8C2×D5semidirect
273. #821C2×D5semidirect
274. #821C2×D5semidirect
276. #817C2×D5semidirect
277. #817C2×D5semidirect
454. C22⋊D5#204semidirect
518. C22⋊C8D3×D5semidirect
658. C3×C5#3295semidirect
752. C5#79439semidirect
782. C3#10613073semidirect

Maximal subgroups

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

subgroupindex
#117546472
#117545002
#117508322
C5×#47352
C3×#650142
#117485332
C2×#909692
#117481152
D5×#8212
#117479952
#117478972
#117478432
#117477622
#117477602
#117476142
#106130733
#794395