Finite Group Databasebeta

← #14458487

Subgroups — #14458487

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#11754510C211yesmaximal, characteristic, complemented
3C2×#91105C211yesmaximal, characteristic, complemented
4C5×#5114C211yesmaximal, characteristic, complemented
5C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
6#11748554C211yesmaximal, characteristic, complemented
7#11748379C211yesmaximal, characteristic, complemented
8#11748114C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747995C211yesmaximal, characteristic, complemented
11#11747938C211yesmaximal, characteristic, complemented
12#11747842C211yesmaximal, characteristic, complemented
13#11747833C211yesmaximal, characteristic, complemented
14#11747762C211yesmaximal, characteristic, complemented
15#11747614C211yesmaximal, characteristic, complemented
16#10612411—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×#6790—21no—
19C2×D5×D12C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C5×#930C2211yescharacteristic
23C5×#924C2211yescharacteristic, complemented
24C2×C5×#204C2211yescharacteristic, complemented
25C3×C4×C22⋊D5C2211yescharacteristic
26C2×C3×C8×D5C2211yescharacteristic, complemented
27#91576—21no—
28#91573—21no—
29#91559—21no—
30#91476—21no—
31#91468C2211yescharacteristic, complemented
32#91451C2211yescharacteristic
33#91450C2211yescharacteristic
34#91422—21no—
35#91420—21no—
36#91418C2211yescharacteristic
37D5×C4⋊Dic3C2211yescharacteristic, complemented
38#91359C2211yescharacteristic, complemented
39#91334—21no—
40Dic5×Dic6C2211yescharacteristic, complemented
41C2×#6660C2211yescharacteristic
42C2×#6660C2211yescharacteristic, complemented
43#91105C2211yescharacteristic
44#91105C2211yescharacteristic
45#91105C2211yescharacteristic, complemented
46#91105C2211yescharacteristic, complemented
47C5×#821C2211yescharacteristic, complemented
48C5×#817C2211yescharacteristic, complemented
49C5×#816C2211yescharacteristic, complemented
50C3×C22⋊#168C2211yescharacteristic, complemented
51C3×#3952C2211yescharacteristic, complemented
52C3×#3946C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54#90985C2211yescharacteristic, complemented
55#90985C2211yescharacteristic, complemented
56#90969C2211yescharacteristic
57#90969C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#79439—51nomaximal, Hall
61#65969—31no—
62#65943—31no—
63C5×#465—31no—
64#65458—31no—
65#65452—31no—
66C2×#3953—31no—
67C8×C22⋊D5D311yescharacteristic, complemented
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—
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15—21no—
80C2×D60—22no—
81C2×D60—21no—
82C2×D60—41no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C2×C5×#67—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C5×Dic6C2311yescharacteristic
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×C8—41no—
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C5×#217—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C5×#204—41no—
112C3×C22⋊Dic5D411yescharacteristic
113C3×#685D411yescharacteristic
114C3×#683D411yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118C3×C8×D5—41no—
119Dic3⋊Dic5—21no—
120#6669—21no—
121#6668—21no—
122#6668—21no—
123#6667—21no—
124#6667—21no—
125#6665—21no—
126Dic3×Dic5—21no—
127#6660—22no—
128#6660—41no—
129D4×D12—51no—
130#5543—51no—
131C3×C8×D4—51no—
132#5114—51no—
133#5114D511yescharacteristic, complemented
134C2×#821—51no—
135C2×#821—51no—
136#4848—51no—
137#4842—51no—
138#4735—51no—
139#4735—51no—
140#4731—51no—
141#4731—51no—
142#4694—51no—
143C4×#204—51no—
144C2×D4×D5—31no—
145C2×D4×D5—61no—
146C22×D20—31no—
147C2×C5×SD16—31no—
148C22×C5×C8C2×D311yescharacteristic, complemented
149C5×C22⋊Q8—31no—
150C5×#121—31no—
151#4092—31no—
152Q8×Dic5—31no—
153C2×#688—31no—
154C2×#688—31no—
155#4086—31no—
156#4083—61no—
157C4×C22⋊D5C2×D311yescharacteristic
158C2×C4⋊Dic5—31no—
159C2×C8×D5C2×D311yescharacteristic, complemented
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×#106—31no—
171C5×#103—31no—
172C5×#102—31no—
173#3964—31no—
174#3964—31no—
175C22⋊#168C2×D311yescharacteristic, complemented
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3952C2×D311yescharacteristic, complemented
181#3946C2×D311yescharacteristic, complemented
182C8×Dic5C2×D311yescharacteristic, complemented
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—
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—
205C2×Dic15—81no—
206D60—21no—
207D60—21no—
208D60—21no—
209D60—42no—
210D60#4112yes—
211C5×#67—42no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C5×D12—21no—
216C5×D12—21no—
217C5×Dic6—21no—
218C5×Dic6—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×C8C2×D511yescharacteristic, complemented
241C3×C4×D4—51no—
242D4×Dic3—101no—
243#930—51no—
244#930C2×D511yescharacteristic
245C2×C4⋊Dic3—51no—
246C2×C4⋊Dic3—51no—
247#924—51no—
248#924C2×D511yescharacteristic, complemented
249C2×#204—51no—
250C2×#204—51no—
251C2×#204C2×D511yescharacteristic, complemented
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⋊C8—51no—
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#821—51no—
274#821C2×D511yescharacteristic, complemented
275#817—51no—
276#817—51no—
277#817C2×D511yescharacteristic, complemented
278#816C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×Q8—31no—
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⋊D5D1211yescharacteristic
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—61no—
300C2×C4×D5—61no—
301C2×C4×D5C22×D311yescharacteristic
302C2×Dic10—61no—
303C5×SD16—121no—
304C2×C5×C8—41no—
305C2×C5×C8C22×D311yescharacteristic
306C2×C5×C8C22×D311yescharacteristic
307C5×C4⋊C4—31no—
308C5×C4⋊C4—31no—
309C5×C4⋊C4—61no—
310C5×C22⋊C4—61no—
311C5×C22⋊C4—61no—
312C22⋊Dic5D1211yescharacteristic
313#688—62no—
314#688—121no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685D1211yescharacteristic
319C4⋊Dic5—31no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322C4⋊Dic5—61no—
323#683—61no—
324#683—61no—
325#683—61no—
326#683D1211yescharacteristic
327C4×Dic5—61no—
328C4×Dic5C22×D311yescharacteristic
329C2×#168C22×D311yescharacteristic
330C2×#168C22×D311yescharacteristic
331C8×D5—41no—
332#554—151no—
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—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—101no—
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—101no—
399C2×Dic6C22×D511yescharacteristic
400C2×C3×C8—41no—
401C2×C3×C8—51no—
402C2×C3×C8—51no—
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—21no—
411#217—101no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415C4⋊Dic3—51no—
416C4⋊Dic3—51no—
417C4⋊Dic3—101no—
418C4⋊Dic3—101no—
419C4⋊Dic3—101no—
420C4⋊Dic3C22×D511yescharacteristic
421C4⋊Dic3C22×D511yescharacteristic
422Dic3⋊C4—21no—
423Dic3⋊C4—101no—
424Dic3⋊C4—101no—
425C4×Dic3—101no—
426#204—41no—
427#204—102no—
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×Q8—61no—
441C5×Q8—61no—
442C5×D4—61no—
443C5×D4—61no—
444C5×D4—122no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5C2×D1211yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—122no—
453C22⋊D5—122no—
454C22⋊D5—241no—
455C22⋊D5#20414yescomplemented
456C2×Dic5—61no—
457C2×Dic5—61no—
458C2×Dic5—241no—
459C2×Dic5C2×D1211yescharacteristic
460C2×Dic5C2×D1211yescharacteristic
461C2×Dic5C2×D1211yescharacteristic
462D20—32no—
463D20—61no—
464D20—61no—
465D20—61no—
466D20—122no—
467D20—122no—
468C4×D5—21no—
469C4×D5—21no—
470C4×D5—122no—
471C4×D5—241no—
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—31no—
481C2×SD16—151no—
482C2×SD16—151no—
483C22×C8—51no—
484C22×C8D3×D511yescharacteristic, complemented
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—31no—
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—151no—
502C2×C4⋊C4—151no—
503#106—31no—
504#106—151no—
505#106—151no—
506C4⋊C8—51no—
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—51no—
518C22⋊C8—51no—
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—101no—
555C2×Dic3—101no—
556C2×Dic3—401no—
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—21no—
570Dic6—21no—
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—31no—
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—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—121no—
630SD16—302no—
631SD16—601no—
632C2×C8—41no—
633C2×C8—51no—
634C2×C8—51no—
635C2×C8—201no—
636C2×C8C2×D3×D511yescharacteristic
637C2×C8C2×D3×D511yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—51no—
641C4⋊C4—61no—
642C4⋊C4—151no—
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—61no—
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×C4#414411yescharacteristic
682C3×C4D5×#4111yescharacteristic
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—61no—
708Q8—61no—
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—301no—
734C2×C4—301no—
735C2×C4—602no—
736C2×C4—1201no—
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#6594411yescharacteristic
747C2×C3C2×D5×SD1611yescharacteristic
748C2×C3#6610311yescharacteristic
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#9201611yescharacteristic
781C4#9204911yescharacteristic
782C3#1061241111yescharacteristic, complemented, Sylow
783C2—22no—
784C2—102no—
785C2—241no—
786C2—602no—
787C2—1201no—
788C2C2×D5×#20411yescharacteristic
789C2#1175396311yescharacteristic
790C2#1175464811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×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. #11754510C2semidirect
3. C2×#91105C2semidirect
4. C5×#5114C2semidirect
5. C3×C8×C22⋊D5C2semidirect
6. #11748554C2semidirect
7. #11748379C2semidirect
8. #11748114C2semidirect
9. D5×#821C2semidirect
10. #11747995C2semidirect
11. #11747938C2semidirect
12. #11747842C2semidirect
13. #11747833C2semidirect
14. #11747762C2semidirect
15. #11747614C2semidirect
20. C22×C3×C5×C8C22semidirect
21. C2×C4⋊Dic15C22semidirect
23. C5×#924C22semidirect
24. C2×C5×#204C22semidirect
26. C2×C3×C8×D5C22semidirect
31. #91468C22semidirect
37. D5×C4⋊Dic3C22semidirect
38. #91359C22semidirect
40. Dic5×Dic6C22semidirect
42. C2×#6660C22semidirect
45. #91105C22semidirect
46. #91105C22semidirect
47. C5×#821C22semidirect
48. C5×#817C22semidirect
49. C5×#816C22semidirect
50. C3×C22⋊#168C22semidirect
51. C3×#3952C22semidirect
52. C3×#3946C22semidirect
53. C3×C8×Dic5C22semidirect
54. #90985C22semidirect
55. #90985C22semidirect
57. #90969C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
67. C8×C22⋊D5D3semidirect
133. #5114D5semidirect
148. C22×C5×C8C2×D3semidirect
159. C2×C8×D5C2×D3semidirect
175. C22⋊#168C2×D3semidirect
180. #3952C2×D3semidirect
181. #3946C2×D3semidirect
182. C8×Dic5C2×D3semidirect
219. C3×C22⋊D5SD16semidirect
240. C22×C3×C8C2×D5semidirect
248. #924C2×D5semidirect
251. C2×#204C2×D5semidirect
274. #821C2×D5semidirect
277. #817C2×D5semidirect
278. #816C2×D5semidirect
455. C22⋊D5#204semidirect
484. C22×C8D3×D5semidirect
658. C3×C5#3295semidirect
752. C5#79439semidirect
782. C3#10612411semidirect

Maximal subgroups

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

subgroupindex
#117546472
#117545102
C2×#911052
C5×#51142
C3×C8×C22⋊D52
#117485542
#117483792
#117481142
D5×#8212
#117479952
#117479382
#117478422
#117478332
#117477622
#117476142
#106124113
#794395