Finite Group Databasebeta

← #14458470

Subgroups — #14458470

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
1D12×C22⋊D5C211yesmaximal, characteristic
2#11754510C211yesmaximal, characteristic, complemented
3#11750836C211yesmaximal, characteristic, complemented
4C5×#4731C211yesmaximal, characteristic, complemented
5C3×#65014C211yesmaximal, characteristic, complemented
6#11748535C211yesmaximal, characteristic, complemented
7C2×#90967C211yesmaximal, characteristic, complemented
8#11748114C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747995C211yesmaximal, characteristic, complemented
11#11747896C211yesmaximal, characteristic, complemented
12#11747842C211yesmaximal, characteristic, complemented
13#11747758C211yesmaximal, characteristic, complemented
14Dic5×#204C211yesmaximal, characteristic, complemented
15#11747613C211yesmaximal, characteristic, complemented
16#10611889—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×D3×C22⋊D5—21no—
19C2×D5×D12C2211yescharacteristic
20#91819C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C5×#924C2211yescharacteristic, complemented
23C2×C5×#204C2211yescharacteristic
24C2×C5×#204C2211yescharacteristic, complemented
25C3×C4×C22⋊D5C2211yescharacteristic
26C22×C3×#168C2211yescharacteristic, complemented
27C2×C3×C8×D5C2211yescharacteristic, complemented
28#91576—21no—
29#91570—21no—
30#91559—21no—
31#91475—21no—
32#91468C2211yescharacteristic, complemented
33#91451C2211yescharacteristic
34#91449C2211yescharacteristic
35#91422—21no—
36#91416—21no—
37Dic5×D12C2211yescharacteristic
38D5×C4⋊Dic3C2211yescharacteristic, complemented
39#91359C2211yescharacteristic, complemented
40#91334—21no—
41Dic5×Dic6C2211yescharacteristic, complemented
42C2×#6660C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic, complemented
44#91105C2211yescharacteristic, complemented
45#91105C2211yescharacteristic, complemented
46#91101C2211yescharacteristic, complemented
47#91101C2211yescharacteristic, complemented
48C5×#821C2211yescharacteristic
49C5×#821C2211yescharacteristic, complemented
50C3×#3952C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90973C2211yescharacteristic, complemented
55#90969C2211yescharacteristic, complemented
56#90967C2211yescharacteristic
57#90967C2211yescharacteristic
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#79439—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65969—31no—
63C5×#450—31no—
64C2×#3964—31no—
65#65460—31no—
66#65458—31no—
67#65452—31no—
68SD16×Dic5—31no—
69#65337—31no—
70#65066—31no—
71D5×#102—31no—
72#65050—31no—
73#65049—31no—
74#65024—31no—
75#65014D311yescharacteristic, complemented
76C23×C5×D3—21no—
77C22×D3×D5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80C22×Dic15—21no—
81C2×D60C2311yescharacteristic
82C2×C5×D12—22no—
83C2×C5×D12—21no—
84C2×C5×D12—41no—
85C2×C5×D12C2311yescharacteristic
86C2×C5×D12C2311yescharacteristic
87C2×C5×Dic6C2311yescharacteristic
88C2×C3×C22⋊D5D411yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90D3×C22⋊D5—44no—
91C2×#1204—21no—
92C2×#1203—21no—
93C2×#1203—21no—
94C2×#1203—21no—
95C2×#1201—21no—
96C2×D3×Dic5—21no—
97C2×D5×Dic3—21no—
98D5×D12—22no—
99D5×D12—41no—
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102#6714—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C4⋊Dic15C2311yescharacteristic
107C5×#217—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C5×Dic3⋊C4—21no—
110C5×#204—22no—
111C5×#204—41no—
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(C2×D3)⋊Dic5—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128#6660—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#4735—51no—
140#4731—51no—
141#4731D511yescharacteristic, complemented
142#4694—51no—
143C4×#204—51no—
144C22×C5×D4—31no—
145C22×C22⋊D5—61no—
146C2×D4×D5—31no—
147C2×C5×SD16—31no—
148C2×C5×SD16—31no—
149C5×C22⋊Q8—31no—
150#4099—61no—
151#4092—31no—
152Q8×Dic5—31no—
153C2×#688—31no—
154#4086—31no—
155#4085—61no—
156#4084—31no—
157#4083—61no—
158D4×Dic5—31no—
159#4076—31no—
160C4×C22⋊D5C2×D311yescharacteristic
161C2×C4⋊Dic5—31no—
162C22×#168C2×D311yescharacteristic, complemented
163C2×C8×D5C2×D311yescharacteristic, complemented
164#4043—61no—
165D5×C4⋊C4—31no—
166#4035—61no—
167#4034—31no—
168#4027—61no—
169#4024—61no—
170C5×#102—31no—
171C5×#102—31no—
172C5×C22⋊C8C2×D311yescharacteristic, complemented
173#3967—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178#3953—31no—
179#3953—31no—
180#3952C2×D311yescharacteristic, complemented
181#3949—31no—
182#3949—31no—
183#3946C2×D311yescharacteristic, complemented
184C8×Dic5C2×D311yescharacteristic, complemented
185#3941—31no—
186#3940—31no—
187#3295—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—42no—
193C22×C5×D3—42no—
194C22×C5×D3—81no—
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
203#1220—42no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—81no—
208D60—21no—
209D60—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—21no—
215C5×D12—42no—
216C5×D12#4112yes—
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#1201—42no—
230D3×Dic5—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×D12C2×D511yescharacteristic
239C22×C3×C8—51no—
240C22×C3×C8—51no—
241C3×C4×D4—51no—
242D4×Dic3—101no—
243#930—51no—
244#930—51no—
245C2×C4⋊Dic3—51no—
246C2×C4⋊Dic3—51no—
247#924—51no—
248#924C2×D511yescharacteristic, complemented
249C2×#204—51no—
250C2×#204C2×D511yescharacteristic
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⋊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
274#821C2×D511yescharacteristic, complemented
275#817—51no—
276#817—51no—
277#817—51no—
278#816—51no—
279C24×C5—61no—
280C23×D5—61no—
281C2×C5×Q8—31no—
282C2×C5×D4—31no—
283C2×C5×D4—31no—
284C2×C5×D4—62no—
285C2×C5×D4—61no—
286C2×C5×D4—121no—
287C22×C4×C5C22×D311yescharacteristic
288C2×C22⋊D5—61no—
289C2×C22⋊D5—61no—
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C2×C22⋊D5—61no—
293C2×C22⋊D5—124no—
294C2×C22⋊D5D1211yescharacteristic
295C22×Dic5—61no—
296C22×Dic5—61no—
297D4×D5—62no—
298D4×D5—121no—
299C2×D20—31no—
300C2×C4×D5—61no—
301C2×C4×D5C22×D311yescharacteristic
302C2×Dic10—61no—
303C5×SD16—62no—
304C5×SD16—121no—
305C2×C5×C8C22×D311yescharacteristic
306C2×C5×C8C22×D311yescharacteristic
307C5×C4⋊C4—31no—
308C5×C4⋊C4—61no—
309C5×C22⋊C4—61no—
310C22⋊Dic5—61no—
311C22⋊Dic5—61no—
312C22⋊Dic5D1211yescharacteristic
313#688—121no—
314#685—61no—
315#685—61no—
316#685D1211yescharacteristic
317C4⋊Dic5—31no—
318C4⋊Dic5—31no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5—61no—
322#683—61no—
323#683—61no—
324#683—61no—
325#683D1211yescharacteristic
326C4×Dic5—61no—
327C4×Dic5C22×D311yescharacteristic
328C2×#168—41no—
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—151no—
339#465—151no—
340#460—151no—
341#450—31no—
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—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×C5×D3—22no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C5×D3—41no—
359C2×C5×D3—41no—
360C2×C5×D3—84no—
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—
370Dic15—41no—
371C3×Dic5—21no—
372C3×Dic5—21no—
373C3×Dic5C2×SD1612yes—
374C5×Dic3—41no—
375C5×Dic3—41no—
376C23×D3—21no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C22×C3×C4—51no—
380C22×C3×C4C22×D511yescharacteristic
381C2×#67—101no—
382C2×#67—101no—
383C22×Dic3—101no—
384C22×Dic3—101no—
385D3×D4—204no—
386C2×D12—22no—
387C2×D12—21no—
388C2×D12—41no—
389C2×D12—51no—
390C2×D12—102no—
391C2×D12—101no—
392C2×D12—101no—
393C2×D12—101no—
394C2×D12—201no—
395C2×D12C22×D511yescharacteristic
396C2×D12C22×D511yescharacteristic
397C2×C4×D3—101no—
398C2×Dic6—101no—
399C2×Dic6C22×D511yescharacteristic
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—21no—
411#217—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415C4⋊Dic3—51no—
416C4⋊Dic3—51no—
417C4⋊Dic3—51no—
418C4⋊Dic3—101no—
419C4⋊Dic3—101no—
420C4⋊Dic3—101no—
421C4⋊Dic3C22×D511yescharacteristic
422Dic3⋊C4—21no—
423Dic3⋊C4—101no—
424Dic3⋊C4—101no—
425C4×Dic3—101no—
426#204—22no—
427#204—41no—
428#204—201no—
429C23×C5—61no—
430C23×C5—61no—
431C23×C5—122no—
432C23×C5—122no—
433C23×C5—241no—
434C23×C5C2×D1211yescharacteristic
435C22×D5—61no—
436C22×D5—122no—
437C22×D5—122no—
438C22×D5—241no—
439C22×D5C2×D1211yescharacteristic
440C5×Q8—61no—
441C5×Q8—61no—
442C5×D4—32no—
443C5×D4—61no—
444C5×D4—61no—
445C5×D4—61no—
446C5×D4—122no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5C2×D1211yescharacteristic
452C2×C4×C5C23×D311yescharacteristic
453C22⋊D5—122no—
454C22⋊D5—122no—
455C22⋊D5—122no—
456C22⋊D5—122no—
457C22⋊D5—241no—
458C22⋊D5#20414yescomplemented
459C2×Dic5—61no—
460C2×Dic5—61no—
461C2×Dic5—61no—
462C2×Dic5—122no—
463C2×Dic5—241no—
464C2×Dic5C2×D1211yescharacteristic
465C2×Dic5C2×D1211yescharacteristic
466C2×Dic5C2×D1211yescharacteristic
467D20—61no—
468D20—61no—
469C4×D5—21no—
470C4×D5—21no—
471C4×D5—241no—
472Dic10—241no—
473C5×C8—21no—
474C5×C8—21no—
475#168—21no—
476#168—21no—
477C22×D4—31no—
478C22×D4—151no—
479C22×D4—301no—
480C2×SD16—31no—
481C2×SD16—31no—
482C2×SD16—151no—
483C22×C8—51no—
484C22×C8—51no—
485C4⋊Q8—151no—
486#127—151no—
487#125—301no—
488C22⋊Q8—31no—
489C22⋊Q8—151no—
490C22⋊Q8—301no—
491C22⋊Q8—301no—
492#121—151no—
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—151no—
504#106—151no—
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—81no—
525C3×D5—22no—
526C5×D3—42no—
527C5×D3—81no—
528C23×C3—51no—
529C23×C3D4×D511yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—81no—
535C22×D3—101no—
536C22×D3—202no—
537C22×D3—202no—
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—202no—
550#67—202no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—401no—
557C2×Dic3—401no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—42no—
562D12—101no—
563D12—101no—
564D12—202no—
565D12—202no—
566D12—401no—
567D12#71112yes—
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—62no—
579C22×C5—121no—
580C22×C5—121no—
581C22×C5—121no—
582C22×C5—121no—
583C22×C5—121no—
584C22×C5—244no—
585C22×C5C2×#20412yes—
586C22×C5C22×D1211yescharacteristic
587C2×D5—21no—
588C2×D5—21no—
589C2×D5—121no—
590C2×D5—121no—
591C2×D5—121no—
592C2×D5—244no—
593C2×D5C2×#20412yes—
594C4×C5—21no—
595C4×C5—121no—
596C4×C5—121no—
597C4×C5#100411yescharacteristic
598C4×C5D3×#4111yescharacteristic
599Dic5—21no—
600Dic5—21no—
601Dic5—121no—
602Dic5—121no—
603Dic5—121no—
604Dic5C2×#20412yes—
605C24—61no—
606C24—301no—
607C2×Q8—31no—
608C2×Q8—301no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—51no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—121no—
615C2×D4—151no—
616C2×D4—301no—
617C2×D4—301no—
618C2×D4—301no—
619C2×D4—302no—
620C2×D4—301no—
621C2×D4—301no—
622C2×D4—601no—
623C2×D4—604no—
624C22×C4—51no—
625C22×C4—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4C2×D3×D511yescharacteristic
629SD16—62no—
630SD16—121no—
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—51no—
640C4⋊C4—61no—
641C4⋊C4—151no—
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—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—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C2×D3—201no—
674C2×D3—201no—
675C2×D3—201no—
676C2×D3—404no—
677C3×C4—21no—
678C3×C4—52no—
679C3×C4—101no—
680C3×C4—101no—
681C3×C4C2×#71111yescharacteristic
682C3×C4#414411yescharacteristic
683Dic3—41no—
684Dic3—41no—
685Dic3—201no—
686Dic3—201no—
687Dic3—201no—
688C2×C5—22no—
689C2×C5—122no—
690C2×C5—241no—
691C2×C5#555411yescharacteristic
692C2×C5C22×#20411yescharacteristic
693C2×C5#575211yescharacteristic
694D5—22no—
695D5—241no—
696C23—51no—
697C23—61no—
698C23—61no—
699C23—122no—
700C23—122no—
701C23—241no—
702C23—301no—
703C23—602no—
704C23—602no—
705C23—1201no—
706C23D5×D1211yescharacteristic
707Q8—61no—
708Q8—61no—
709Q8—1201no—
710D4—32no—
711D4—54no—
712D4—61no—
713D4—61no—
714D4—61no—
715D4—122no—
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—101no—
731C2×C4—101no—
732C2×C4—301no—
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#6592511yescharacteristic
747C2×C3C2×D5×SD1611yescharacteristic
748C2×C3#6610811yescharacteristic
749D3—42no—
750D3—81no—
751D3—401no—
752C5#7943911yescharacteristic, complemented, Sylow
753C22—21no—
754C22—21no—
755C22—52no—
756C22—62no—
757C22—101no—
758C22—101no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—244no—
765C22—601no—
766C22—601no—
767C22—601no—
768C22—1204no—
769C22D5×#20412yes—
770C22C2×D5×D1211yescharacteristic
771C4—21no—
772C4—52no—
773C4—101no—
774C4—101no—
775C4—121no—
776C4—121no—
777C4—601no—
778C4—601no—
779C4—601no—
780C4D3×#71111yescharacteristic
781C4#9202511yescharacteristic
782C3#1061188911yescharacteristic, complemented, Sylow
783C2—22no—
784C2—102no—
785C2—122no—
786C2—241no—
787C2—1201no—
788C2#1175326511yescharacteristic
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 radicalD12×C22⋊D5C2
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. #11750836C2semidirect
4. C5×#4731C2semidirect
5. C3×#65014C2semidirect
6. #11748535C2semidirect
7. C2×#90967C2semidirect
8. #11748114C2semidirect
9. D5×#821C2semidirect
10. #11747995C2semidirect
11. #11747896C2semidirect
12. #11747842C2semidirect
13. #11747758C2semidirect
14. Dic5×#204C2semidirect
15. #11747613C2semidirect
21. C2×C4⋊Dic15C22semidirect
22. C5×#924C22semidirect
24. C2×C5×#204C22semidirect
26. C22×C3×#168C22semidirect
27. C2×C3×C8×D5C22semidirect
32. #91468C22semidirect
38. D5×C4⋊Dic3C22semidirect
39. #91359C22semidirect
41. Dic5×Dic6C22semidirect
42. C2×#6660C22semidirect
43. C3×C5×C22⋊C8C22semidirect
44. #91105C22semidirect
45. #91105C22semidirect
46. #91101C22semidirect
47. #91101C22semidirect
49. C5×#821C22semidirect
50. C3×#3952C22semidirect
51. C3×#3946C22semidirect
52. C3×C8×Dic5C22semidirect
53. #90985C22semidirect
54. #90973C22semidirect
55. #90969C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
75. #65014D3semidirect
141. #4731D5semidirect
162. C22×#168C2×D3semidirect
163. C2×C8×D5C2×D3semidirect
172. C5×C22⋊C8C2×D3semidirect
180. #3952C2×D3semidirect
183. #3946C2×D3semidirect
184. C8×Dic5C2×D3semidirect
219. C3×C22⋊D5SD16semidirect
248. #924C2×D5semidirect
251. C2×#204C2×D5semidirect
264. C3×C22⋊C8C2×D5semidirect
274. #821C2×D5semidirect
458. C22⋊D5#204semidirect
518. C22⋊C8D3×D5semidirect
658. C3×C5#3295semidirect
752. C5#79439semidirect
782. C3#10611889semidirect

Maximal subgroups

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

subgroupindex
D12×C22⋊D52
#117545102
#117508362
C5×#47312
C3×#650142
#117485352
C2×#909672
#117481142
D5×#8212
#117479952
#117478962
#117478422
#117477582
Dic5×#2042
#117476132
#106118893
#794395