Finite Group Databasebeta

← #12068153

Subgroups — #12068153

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10617749C211yesmaximal, characteristic
2C5×#2990C211yesmaximal, characteristic, complemented
3#10614253C211yesmaximal, characteristic, complemented
4#10601613C211yesmaximal, characteristic, complemented
5#10601612C211yesmaximal, characteristic, complemented
6#10601611C211yesmaximal, characteristic, complemented
7#10601610C211yesmaximal, characteristic, complemented
8#10601568C211yesmaximal, characteristic, complemented
9#10601565C211yesmaximal, characteristic, complemented
10#10601297C211yesmaximal, characteristic, complemented
11#10601296C211yesmaximal, characteristic, complemented
12#10601232C211yesmaximal, characteristic, complemented
13#10601225C211yesmaximal, characteristic, complemented
14#10601224C211yesmaximal, characteristic, complemented
15C2×#64705C211yesmaximal, characteristic, complemented
16C4×C5×#41C2211yescharacteristic
17#66164C412yes—
18#65919—21no—
19#65919—21no—
20#65887—21no—
21#65887—21no—
22#65884—21no—
23#65884—21no—
24#65884—21no—
25#65884—21no—
26#65869C412yes—
27#65869C412yes—
28#65855C412yes—
29#65811C2211yescharacteristic
30#65811C2211yescharacteristic
31#65811C2211yescharacteristic
32#65811C2211yescharacteristic
33C2×#4020C2211yescharacteristic
34#65804C2211yescharacteristic
35C5×#446—21no—
36C5×#435—21no—
37C5×#435—21no—
38C5×C8×D4—21no—
39C5×#432C2211yescharacteristic
40C5×#432C2211yescharacteristic, complemented
41C5×#431C2211yescharacteristic, complemented
42C5×#423C2211yescharacteristic, complemented
43C2×C5×C4⋊C8C2211yescharacteristic
44C2×C5×C4⋊C8C2211yescharacteristic, complemented
45#65313—21no—
46#65300—21no—
47#65300—21no—
48D4×#168—21no—
49#65215C2211yescharacteristic
50#65215C2211yescharacteristic, complemented
51#65214C2211yescharacteristic, complemented
52#65213C2211yescharacteristic, complemented
53C2×C4⋊#168C2211yescharacteristic
54C2×C4⋊#168C2211yescharacteristic, complemented
55#64706C2211yescharacteristic, complemented
56#64706C2211yescharacteristic, complemented
57#64706C2211yescharacteristic, complemented
58#64706C2211yescharacteristic, complemented
59#64705C2211yescharacteristic
60#64705C2211yescharacteristic
61#64705C2211yescharacteristic
62#64705C2211yescharacteristic
63#64705C2211yescharacteristic
64#64705C2211yescharacteristic
65#64705C2211yescharacteristic
66#64705C2211yescharacteristic
67#64702C2211yescharacteristic, complemented
68#64702C2211yescharacteristic, complemented
69#64702C2211yescharacteristic, complemented
70#64702C2211yescharacteristic, complemented
71#17771—51nomaximal, Sylow
72C2×C5×#41C2×C411yescharacteristic
73C2×#709—21no—
74C2×#709—21no—
75C2×#709—21no—
76C2×#709—21no—
77C22×D20—21no—
78C22×D20—21no—
79C22×D20C2×C412yes—
80C2×C5×M16—21no—
81C22×C5×C8—21no—
82C22×C5×C8—21no—
83C4×C5×Q8D411yescharacteristic
84C4×C5×Q8D411yescharacteristic
85C4×C5×D4D411yescharacteristic
86C4×C5×D4D411yescharacteristic
87C4×C5×D4D411yescharacteristic
88C4×C5×D4D411yescharacteristic
89C4×C5×D4D411yescharacteristic
90C4×C5×D4D411yescharacteristic
91C5×#117C2×C411yescharacteristic
92C5×#117C2×C411yescharacteristic
93C5×#117C2×C411yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C2×C42×C5C2311yescharacteristic
97#4093—22no—
98#4086—22no—
99#4083—22no—
100#4083—22no—
101#4076—21no—
102#4076—21no—
103#4076—21no—
104#4076—21no—
105#4076C2×C412yes—
106#4076C2×C412yes—
107#4076C2×C412yes—
108#4076C2×C412yes—
109#4072C2×C412yes—
110#4070—21no—
111#4070—21no—
112C2×#681—21no—
113C22×#168—21no—
114C22×#168—21no—
115#4040—22no—
116#4040—22no—
117#4040—22no—
118#4040—22no—
119#4039—22no—
120#4039—22no—
121#4030—22no—
122#4030—22no—
123#4030—22no—
124#4030—22no—
125D5×C22⋊C4—22no—
126D5×C22⋊C4—22no—
127#4021—21no—
128#4021—21no—
129#4021—21no—
130#4021—21no—
131#4020—21no—
132#4020—21no—
133#4020C2×C412yes—
134#4020C2311yescharacteristic
135#4020C2311yescharacteristic
136C4×D20—21no—
137C4×D20—21no—
138C4×D20—21no—
139C4×D20—21no—
140C4×D20C2×C412yes—
141C4×D20C2×C412yes—
142C4×D20C2×C412yes—
143C4×D20C2×C412yes—
144#4016C2×C412yes—
145#4015C2311yescharacteristic
146#4015C2311yescharacteristic
147C4×Dic10—21no—
148C4×Dic10—21no—
149C5×C4⋊C8—21no—
150C5×C4⋊C8—21no—
151C5×C4⋊C8—21no—
152C5×C4⋊C8C2311yescharacteristic
153C5×C4⋊C8C2311yescharacteristic
154C5×C4⋊C8C2311yescharacteristic
155C5×C4⋊C8C2311yescharacteristic
156C5×C22⋊C8—21no—
157C5×C22⋊C8—21no—
158C5×C22⋊C8—21no—
159C5×#97—21no—
160C5×#97—21no—
161C4×C5×C8—21no—
162C22⋊#168—21no—
163C22⋊#168—21no—
164C22⋊#168—21no—
165C4⋊#168—21no—
166C4⋊#168—21no—
167C4⋊#168—21no—
168C4⋊#168C2311yescharacteristic
169C4⋊#168C2311yescharacteristic
170C4⋊#168C2311yescharacteristic
171C4⋊#168C2311yescharacteristic
172#3935—21no—
173#3935—21no—
174C4×#168—21no—
175#3508—51no—
176#2990—51no—
177#2990D511yescharacteristic, complemented
178#1557—51no—
179#1557—51no—
180#1555—51no—
181#1553—51no—
182#1553—51no—
183#1552—51no—
184#1552—51no—
185#1547—51no—
186#1547—51no—
187#1540—51no—
188#1540—51no—
189C2×#331—51no—
190C23×D5—22no—
191C5×#41—42no—
192C2×C5×Q8C22⋊C411yescharacteristic
193C2×C5×D4C22⋊C411yescharacteristic
194C2×C5×D4C22⋊C411yescharacteristic
195C2×C5×D4C22⋊C411yescharacteristic
196C22×C4×C5C22×C411yescharacteristic
197C22×C4×C5C22×C411yescharacteristic
198C22×C4×C5C22×C411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2×D411yescharacteristic
203C22×C4×C5C2×D411yescharacteristic
204C22×C4×C5C2×D411yescharacteristic
205C2×C22⋊D5—22no—
206C2×C22⋊D5—22no—
207C2×C22⋊D5—22no—
208C2×C22⋊D5—22no—
209#709—81no—
210#709—81no—
211#709—81no—
212#709—81no—
213#709—81no—
214#709—81no—
215#709—81no—
216#709—81no—
217C2×D20—22no—
218C2×D20—21no—
219C2×D20—21no—
220C2×D20—21no—
221C2×D20—21no—
222C2×D20—22no—
223C2×D20—22no—
224C2×D20—44no—
225C2×D20—81no—
226C2×D20—81no—
227C2×D20—81no—
228C2×D20—81no—
229C2×D20C22×C412yes—
230C2×D20C22×C412yes—
231C2×C4×D5—22no—
232C2×C4×D5—22no—
233C2×C4×D5—22no—
234C2×C4×D5—22no—
235C2×Dic10—21no—
236C2×Dic10—21no—
237C5×M16—81no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—81no—
243C2×C5×C8—81no—
244C5×C4⋊C4C22⋊C411yescharacteristic
245C5×C4⋊C4C22⋊C411yescharacteristic
246C5×C4⋊C4C22⋊C411yescharacteristic
247C5×C4⋊C4C22⋊C411yescharacteristic
248C5×C4⋊C4C22⋊C411yescharacteristic
249C5×C4⋊C4C22⋊C411yescharacteristic
250C5×C22⋊C4C22⋊C411yescharacteristic
251C5×C22⋊C4C22⋊C411yescharacteristic
252C5×C22⋊C4C22⋊C411yescharacteristic
253C5×C22⋊C4C22⋊C411yescharacteristic
254C5×C22⋊C4C22⋊C411yescharacteristic
255C5×C22⋊C4C22⋊C411yescharacteristic
256C42×C5C22×C411yescharacteristic
257C42×C5C22×C411yescharacteristic
258C42×C5C22×C411yescharacteristic
259C42×C5C2×D411yescharacteristic
260C42×C5C2×D411yescharacteristic
261C42×C5C2×D411yescharacteristic
262C42×C5C2×D411yescharacteristic
263C42×C5C2×D411yescharacteristic
264C42×C5C2×D411yescharacteristic
265C42×C5C2411yescharacteristic
266C22⋊Dic5—22no—
267#685—22no—
268#685—22no—
269#685—22no—
270#685—22no—
271#685—22no—
272#685—22no—
273#685—22no—
274#685—22no—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5C22×C412yes—
278C4⋊Dic5C22×C412yes—
279#683—22no—
280#683—22no—
281C4×Dic5—22no—
282#681—81no—
283C2×#168—21no—
284C2×#168—21no—
285C2×#168—21no—
286C2×#168—21no—
287C2×#168—81no—
288C2×#168—81no—
289#559—101no—
290#559—101no—
291#550—101no—
292#550—101no—
293#546—101no—
294#546—101no—
295#546—101no—
296#546—101no—
297#540—52no—
298#540—52no—
299#535—52no—
300#533—51no—
301#532—51no—
302#532—51no—
303#532—51no—
304#532—51no—
305C2×#127—51no—
306#518—52no—
307C4×#41C2×D511yescharacteristic
308#446—21no—
309#446—101no—
310#435—21no—
311#435—21no—
312#435—101no—
313#435—101no—
314C8×D4—21no—
315C8×D4—101no—
316#432—51no—
317#432—51no—
318#432C2×D511yescharacteristic
319#432C2×D511yescharacteristic, complemented
320#431—51no—
321#431C2×D511yescharacteristic, complemented
322#423—51no—
323#423C2×D511yescharacteristic, complemented
324C2×C4⋊C8—51no—
325C2×C4⋊C8—51no—
326C2×C4⋊C8C2×D511yescharacteristic
327C2×C4⋊C8C2×D511yescharacteristic, complemented
328#332—51no—
329#332—51no—
330#332—51no—
331#332—51no—
332#332—51no—
333#332—51no—
334#332—51no—
335#332—51no—
336#331—51no—
337#331—51no—
338#331—51no—
339#331—51no—
340#331—51no—
341#331—51no—
342#331—51no—
343#331—51no—
344C23×C5C2×C22⋊C411yescharacteristic
345C23×C5C2×C22⋊C411yescharacteristic
346C23×C5C2×C22⋊C411yescharacteristic
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—44no—
350C22×D5—82no—
351C22×D5—82no—
352C5×Q8—41no—
353C5×D4—22no—
354C5×D4—22no—
355C5×D4—41no—
356C2×C4×C5—22no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5C2×C22⋊C411yescharacteristic
372C2×C4×C5C2×C22⋊C411yescharacteristic
373C2×C4×C5C2×C22⋊C411yescharacteristic
374C2×C4×C5C2×C22⋊C411yescharacteristic
375C2×C4×C5C2×C22⋊C411yescharacteristic
376C2×C4×C5C2×C22⋊C411yescharacteristic
377C2×C4×C5C2×C22⋊C411yescharacteristic
378C2×C4×C5C2×C22⋊C411yescharacteristic
379C2×C4×C5C2×C22⋊C411yescharacteristic
380C2×C4×C5C23×C411yescharacteristic
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C22×D411yescharacteristic
383C22⋊D5—82no—
384C22⋊D5—82no—
385C22⋊D5—82no—
386C22⋊D5—82no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389D20—42no—
390D20—42no—
391D20—44no—
392D20—41no—
393D20—41no—
394D20—41no—
395D20—41no—
396D20—41no—
397D20—41no—
398D20—41no—
399D20—41no—
400D20—82no—
401D20—82no—
402C4×D5—82no—
403C4×D5—82no—
404C4×D5—82no—
405C4×D5—82no—
406Dic10—41no—
407Dic10—41no—
408Dic10—41no—
409Dic10—41no—
410C5×C8—41no—
411C5×C8—41no—
412C5×C8—41no—
413C5×C8—41no—
414#168—41no—
415#168—41no—
416#168—41no—
417#168—41no—
418C2×#41—101no—
419C2×#41—101no—
420C2×#41—101no—
421C2×#41—101no—
422C2×#41C4×D511yescharacteristic
423C22×D4—52no—
424C22×D4—101no—
425C22×D4—101no—
426C2×M16—21no—
427C2×M16—101no—
428C22×C8—21no—
429C22×C8—21no—
430C22×C8—101no—
431C22×C8—101no—
432C4⋊Q8—51no—
433C4⋊Q8—51no—
434#127—52no—
435#127—51no—
436#127—51no—
437#127—102no—
438#127—101no—
439#127—101no—
440#125—52no—
441#124—102no—
442#124—101no—
443#124—101no—
444#124—101no—
445#124—101no—
446#123—102no—
447#123—102no—
448#123—102no—
449#123—102no—
450C22⋊Q8—101no—
451C22⋊Q8—101no—
452#121—52no—
453#121—52no—
454#121—52no—
455#121—52no—
456#121—101no—
457#121—101no—
458#121—101no—
459#121—101no—
460#121—102no—
461#121—102no—
462#121—102no—
463#121—102no—
464#120—102no—
465#120—102no—
466C4×Q8—101no—
467C4×Q8—101no—
468C4×Q8D2011yescharacteristic
469C4×Q8C22⋊D511yescharacteristic
470C4×D4—52no—
471C4×D4—52no—
472C4×D4—52no—
473C4×D4—52no—
474C4×D4—102no—
475C4×D4—102no—
476C4×D4—101no—
477C4×D4—101no—
478C4×D4—101no—
479C4×D4—101no—
480C4×D4D2011yescharacteristic
481C4×D4D2011yescharacteristic
482C4×D4D2011yescharacteristic
483C4×D4C22⋊D511yescharacteristic
484C4×D4C22⋊D511yescharacteristic
485C4×D4C22⋊D511yescharacteristic
486#117—52no—
487#117C4×D511yescharacteristic
488#117C4×D511yescharacteristic
489#117C4×D511yescharacteristic
490C2×C22⋊C4—102no—
491C2×C22⋊C4—102no—
492C2×C42C22×D511yescharacteristic
493C2×C42C22×D511yescharacteristic
494C2×C42C22×D511yescharacteristic
495C4⋊C8—21no—
496C4⋊C8—21no—
497C4⋊C8—21no—
498C4⋊C8—51no—
499C4⋊C8—51no—
500C4⋊C8—51no—
501C4⋊C8—51no—
502C4⋊C8—101no—
503C4⋊C8—101no—
504C4⋊C8—101no—
505C4⋊C8C22×D511yescharacteristic
506C4⋊C8C22×D511yescharacteristic
507C4⋊C8C22×D511yescharacteristic
508C4⋊C8C22×D511yescharacteristic
509C22⋊C8—21no—
510C22⋊C8—21no—
511C22⋊C8—21no—
512C22⋊C8—101no—
513C22⋊C8—101no—
514C22⋊C8—101no—
515#97—21no—
516#97—21no—
517#97—101no—
518#97—101no—
519C4×C8—21no—
520C4×C8—101no—
521C22×C5—21no—
522C22×C5—21no—
523C22×C5—21no—
524C22×C5—21no—
525C22×C5—21no—
526C22×C5—21no—
527C22×C5—21no—
528C22×C5—21no—
529C22×C5#41312yes—
530C22×C5C22×C22⋊C411yescharacteristic
531C2×D5—42no—
532C2×D5—42no—
533C2×D5—42no—
534C2×D5—42no—
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—164no—
538C4×C5—21no—
539C4×C5—21no—
540C4×C5—21no—
541C4×C5—21no—
542C4×C5—21no—
543C4×C5—21no—
544C4×C5—21no—
545C4×C5—21no—
546C4×C5—21no—
547C4×C5—21no—
548C4×C5#57611yescharacteristic
549C4×C5#57611yescharacteristic
550C4×C5#57711yescharacteristic
551C4×C5#57711yescharacteristic
552Dic5—42no—
553Dic5—42no—
554C24—102no—
555#41—42no—
556#41—401no—
557#41—401no—
558#41—401no—
559#41—401no—
560#41—401no—
561#41—401no—
562#41—401no—
563#41—401no—
564C2×Q8—101no—
565C2×Q8—101no—
566C2×Q8#68511yescharacteristic
567C2×D4—52no—
568C2×D4—52no—
569C2×D4—102no—
570C2×D4—102no—
571C2×D4—102no—
572C2×D4—102no—
573C2×D4—101no—
574C2×D4—101no—
575C2×D4—101no—
576C2×D4—101no—
577C2×D4—102no—
578C2×D4—102no—
579C2×D4—102no—
580C2×D4—204no—
581C2×D4—401no—
582C2×D4—401no—
583C2×D4—401no—
584C2×D4—401no—
585C2×D4#68511yescharacteristic
586C2×D4#68511yescharacteristic
587C2×D4#68511yescharacteristic
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4C2×C4×D511yescharacteristic
593C22×C4C2×C4×D511yescharacteristic
594C22×C4C2×C4×D511yescharacteristic
595C22×C4C2×D2011yescharacteristic
596C22×C4C2×D2011yescharacteristic
597C22×C4C2×D2011yescharacteristic
598C22×C4C2×C22⋊D511yescharacteristic
599C22×C4C2×C22⋊D511yescharacteristic
600C22×C4C2×C22⋊D511yescharacteristic
601M16—81no—
602M16—401no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—81no—
608C2×C8—81no—
609C2×C8—101no—
610C2×C8—101no—
611C2×C8—101no—
612C2×C8—101no—
613C2×C8—401no—
614C2×C8—401no—
615C4⋊C4—52no—
616C4⋊C4—52no—
617C4⋊C4—101no—
618C4⋊C4—101no—
619C4⋊C4—102no—
620C4⋊C4—102no—
621C4⋊C4#68511yescharacteristic
622C4⋊C4#68511yescharacteristic
623C4⋊C4#68511yescharacteristic
624C4⋊C4#68511yescharacteristic
625C4⋊C4#68511yescharacteristic
626C4⋊C4#68511yescharacteristic
627C22⋊C4—102no—
628C22⋊C4—102no—
629C22⋊C4—102no—
630C22⋊C4—102no—
631C22⋊C4—102no—
632C22⋊C4—102no—
633C22⋊C4—102no—
634C22⋊C4—102no—
635C22⋊C4—102no—
636C22⋊C4#68511yescharacteristic
637C22⋊C4#68511yescharacteristic
638C22⋊C4#68511yescharacteristic
639C22⋊C4#68511yescharacteristic
640C22⋊C4#68511yescharacteristic
641C22⋊C4#68511yescharacteristic
642C42—102no—
643C42C2×C4×D511yescharacteristic
644C42C2×C4×D511yescharacteristic
645C42C2×C4×D511yescharacteristic
646C42C2×D2011yescharacteristic
647C42C2×D2011yescharacteristic
648C42C2×D2011yescharacteristic
649C42C2×C22⋊D511yescharacteristic
650C42C2×C22⋊D511yescharacteristic
651C42C2×C22⋊D511yescharacteristic
652C42C23×D511yescharacteristic
653C2×C5—22no—
654C2×C5—41no—
655C2×C5—41no—
656C2×C5C2×#41311yescharacteristic
657C2×C5#289711yescharacteristic
658C2×C5#289711yescharacteristic
659D5—82no—
660D5—82no—
661C23—102no—
662C23—102no—
663C23—204no—
664C23—402no—
665C23—402no—
666C23C2×#68511yescharacteristic
667C23C2×#68511yescharacteristic
668C23C2×#68511yescharacteristic
669Q8—41no—
670Q8—201no—
671Q8—201no—
672Q8—201no—
673Q8—201no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—202no—
678D4—202no—
679D4—204no—
680D4—201no—
681D4—201no—
682D4—201no—
683D4—201no—
684D4—201no—
685D4—201no—
686D4—201no—
687D4—201no—
688D4—402no—
689D4—402no—
690D4—402no—
691D4—402no—
692D4—402no—
693D4—402no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—402no—
712C2×C4—402no—
713C2×C4—402no—
714C2×C4—402no—
715C2×C4C2×#68511yescharacteristic
716C2×C4C2×#68511yescharacteristic
717C2×C4C2×#68511yescharacteristic
718C2×C4C2×#68511yescharacteristic
719C2×C4C2×#68511yescharacteristic
720C2×C4C2×#68511yescharacteristic
721C2×C4C2×#68511yescharacteristic
722C2×C4C2×#68511yescharacteristic
723C2×C4C2×#68511yescharacteristic
724C2×C4C22×C4×D511yescharacteristic
725C2×C4C22×D2011yescharacteristic
726C2×C4C22×C22⋊D511yescharacteristic
727C8—41no—
728C8—41no—
729C8—41no—
730C8—41no—
731C8—201no—
732C8—201no—
733C8—201no—
734C8—201no—
735C5#1777111yescharacteristic, complemented, Sylow
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—202no—
745C22—202no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—804no—
751C22#6542112yes—
752C22C22×#68511yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—202no—
764C4—202no—
765C4#6608511yescharacteristic
766C4#6608611yescharacteristic
767C4#6616911yescharacteristic
768C4#6617111yescharacteristic
769C2—22no—
770C2—41no—
771C2—41no—
772C2—402no—
773C2—402no—
774C2#1061429411yescharacteristic
775C2C2×#6542111yescharacteristic
776C2#1061552811yescharacteristic
subgroupG/H
centerC22C22×#685
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#2990C2
socleC22×C5C22×C22⋊C4
prime radical#10617749C2
cosocleC42×C5C24
hypercenter#2990D5
hypocenterC5#17771
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. C5×#2990C2semidirect
3. #10614253C2semidirect
4. #10601613C2semidirect
5. #10601612C2semidirect
6. #10601611C2semidirect
7. #10601610C2semidirect
8. #10601568C2semidirect
9. #10601565C2semidirect
10. #10601297C2semidirect
11. #10601296C2semidirect
12. #10601232C2semidirect
13. #10601225C2semidirect
14. #10601224C2semidirect
15. C2×#64705C2semidirect
40. C5×#432C22semidirect
41. C5×#431C22semidirect
42. C5×#423C22semidirect
44. C2×C5×C4⋊C8C22semidirect
50. #65215C22semidirect
51. #65214C22semidirect
52. #65213C22semidirect
54. C2×C4⋊#168C22semidirect
55. #64706C22semidirect
56. #64706C22semidirect
57. #64706C22semidirect
58. #64706C22semidirect
67. #64702C22semidirect
68. #64702C22semidirect
69. #64702C22semidirect
70. #64702C22semidirect
177. #2990D5semidirect
319. #432C2×D5semidirect
321. #431C2×D5semidirect
323. #423C2×D5semidirect
327. C2×C4⋊C8C2×D5semidirect
735. C5#17771semidirect

Maximal subgroups

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

subgroupindex
#106177492
C5×#29902
#106142532
#106016132
#106016122
#106016112
#106016102
#106015682
#106015652
#106012972
#106012962
#106012322
#106012252
#106012242
C2×#647052
#177715