Finite Group Databasebeta

← C53×#24467 #27231979

Subgroups — C53×#24467 #27231979

Order 13568.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3488C211yesmaximal, characteristic
2C53×#3056C211yesmaximal, characteristic, complemented
3C2×C53×#455C211yesmaximal, characteristic, complemented
4C53×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C53C211yesmaximal, characteristic, complemented
6C53×#2850C211yesmaximal, characteristic, complemented
7C53×#2040C211yesmaximal, characteristic, complemented
8C53×#2037C211yesmaximal, characteristic, complemented
9C53×#2007C211yesmaximal, characteristic, complemented
10C53×#2004C211yesmaximal, characteristic, complemented
11C53×#1900C211yesmaximal, characteristic, complemented
12C53×#1896C211yesmaximal, characteristic, complemented
13C53×#1882C211yesmaximal, characteristic, complemented
14C53×#1860C211yesmaximal, characteristic, complemented
15C53×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C53C2211yescharacteristic
17C22×#41×C53C2211yescharacteristic
18C2×#137×C53C2211yescharacteristic
19C2×#137×C53C2211yescharacteristic, complemented
20C2×#137×C53C2211yescharacteristic, complemented
21C22×M16×C53C2211yescharacteristic, complemented
22C53×#550—21no—
23C53×#548—21no—
24C53×#546—21no—
25C53×#546—22no—
26D42×C53—22no—
27D42×C53—21no—
28C53×#537—21no—
29C53×#537C2211yescharacteristic
30C53×#535—21no—
31C53×#535C2211yescharacteristic
32C2×#124×C53C2211yescharacteristic, complemented
33C53×#525—21no—
34C53×#525C2211yescharacteristic
35C2×C22⋊Q8×C53C2211yescharacteristic, complemented
36C2×#121×C53—21no—
37C2×#121×C53C2211yescharacteristic
38C53×#520C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic, complemented
40C53×#470—21no—
41C53×#468—21no—
42C53×#467—21no—
43C53×#465—21no—
44C53×#455—24no—
45C53×#452—21no—
46C53×#452—21no—
47C53×#451—21no—
48C53×#450—21no—
49C53×#428C2211yescharacteristic, complemented
50C2×#104×C53—24no—
51C2×#104×C53C2211yescharacteristic
52C2×#104×C53C2211yescharacteristic
53C2×#104×C53C2211yescharacteristic, complemented
54C2×#104×C53C2211yescharacteristic, complemented
55C2×#104×C53C2211yescharacteristic, complemented
56C2×#104×C53C2211yescharacteristic, complemented
57C53×#419C2211yescharacteristic, complemented
58C53×#417C2211yescharacteristic
59C53×#417C2211yescharacteristic, complemented
60C53×#417C2211yescharacteristic, complemented
61C2×#100×C53C2211yescharacteristic, complemented
62C2×#100×C53C2211yescharacteristic, complemented
63C53×#407C2211yescharacteristic, complemented
64C53×#391C2211yescharacteristic, complemented
65C53×#390C2211yescharacteristic, complemented
66C53×#388—22no—
67C53×#386—22no—
68C53×#382C2211yescharacteristic, complemented
69C53×#343C2211yescharacteristic, complemented
70C53×#343C2211yescharacteristic, complemented
71C53×#339C2211yescharacteristic, complemented
72C53×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C53—22no—
74H(5,𝔽2)×C53—22no—
75H(5,𝔽2)×C53—41no—
76H(5,𝔽2)×C53—41no—
77C2×#41×C53—21no—
78C2×#41×C53—21no—
79C2×#41×C53—21no—
80C2×#41×C53—21no—
81C2×#41×C53—22no—
82C2×#41×C53—22no—
83C2×#41×C53—41no—
84C2×#41×C53—41no—
85C2×#41×C53D411yescharacteristic
86C2×#41×C53D411yescharacteristic
87C2×#41×C53C2311yescharacteristic
88C2×#41×C53C2311yescharacteristic
89C2×#41×C53C2311yescharacteristic
90C22×Q8×C53D411yescharacteristic
91C22×Q8×C53C2311yescharacteristic
92C22×D4×C53—21no—
93C22×D4×C53—22no—
94C22×D4×C53—22no—
95C22×D4×C53—21no—
96C22×D4×C53—21no—
97C22×D4×C53D411yescharacteristic
98C22×D4×C53D412yes—
99C22×D4×C53C2311yescharacteristic
100C23×C4×C53—21no—
101C23×C4×C53—21no—
102C23×C4×C53C2311yescharacteristic
103#137×C53—22no—
104#137×C53—22no—
105#137×C53—22no—
106#137×C53—41no—
107#137×C53—41no—
108#137×C53—41no—
109C2×Q16×C53—21no—
110C2×Q16×C53—21no—
111C2×Q16×C53—21no—
112C2×SD16×C53—21no—
113C2×SD16×C53—21no—
114C2×SD16×C53—21no—
115C2×M16×C53—22no—
116C2×M16×C53—21no—
117C2×M16×C53—41no—
118C2×M16×C53C2311yescharacteristic
119C2×M16×C53C2311yescharacteristic
120C2×M16×C53C2311yescharacteristic
121C2×M16×C53C2311yescharacteristic
122C22×C8×C53—21no—
123#127×C53—22no—
124#127×C53—21no—
125#124×C53—22no—
126#124×C53—22no—
127#124×C53—21no—
128#124×C53—41no—
129#123×C53—22no—
130#123×C53—21no—
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53—21no—
133C22⋊Q8×C53—21no—
134C22⋊Q8×C53—21no—
135C22⋊Q8×C53—21no—
136C22⋊Q8×C53—21no—
137C22⋊Q8×C53—21no—
138C22⋊Q8×C53D411yescharacteristic
139C22⋊Q8×C53D411yescharacteristic
140#121×C53—22no—
141#121×C53—22no—
142#121×C53—22no—
143#121×C53—22no—
144#121×C53—22no—
145#121×C53—21no—
146#121×C53—21no—
147#121×C53—21no—
148#121×C53—21no—
149#121×C53—21no—
150#121×C53—21no—
151#121×C53—21no—
152#121×C53—21no—
153#121×C53—22no—
154#121×C53D411yescharacteristic
155#121×C53D411yescharacteristic
156#120×C53—22no—
157#120×C53—22no—
158#120×C53—22no—
159#120×C53—21no—
160#120×C53—22no—
161C4×Q8×C53—21no—
162C4×D4×C53—22no—
163C4×D4×C53—22no—
164C4×D4×C53—21no—
165C4×D4×C53—22no—
166C4×D4×C53—21no—
167C4×D4×C53—21no—
168#117×C53—21no—
169#117×C53C2311yescharacteristic
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—22no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—22no—
177C2×C22⋊C4×C53—22no—
178C2×C22⋊C4×C53D412yes—
179C2×C42×C53—21no—
180C2×C42×C53—22no—
181C2×C42×C53—41no—
182C2×C42×C53C2311yescharacteristic
183C2×C42×C53C2311yescharacteristic
184#107×C53—21no—
185#106×C53—21no—
186#104×C53—22no—
187#104×C53—22no—
188#104×C53—22no—
189#104×C53—22no—
190#104×C53—41no—
191#104×C53D414yescomplemented
192#103×C53—21no—
193#103×C53—21no—
194#103×C53—21no—
195#103×C53—21no—
196#103×C53—21no—
197#102×C53—21no—
198#102×C53—21no—
199#102×C53—21no—
200#100×C53—22no—
201#100×C53—41no—
202C22⋊C8×C53—21no—
203C22⋊C8×C53—21no—
204#95×C53—22no—
205#95×C53—22no—
206C24×C53—22no—
207C24×C53—21no—
208C24×C53C2×D411yescharacteristic
209C24×C53C2×D412yes—
210#41×C53—21no—
211#41×C53—21no—
212#41×C53—22no—
213#41×C53—22no—
214#41×C53—21no—
215#41×C53—21no—
216#41×C53—21no—
217#41×C53—21no—
218#41×C53—21no—
219#41×C53—21no—
220#41×C53—21no—
221#41×C53—21no—
222#41×C53—42no—
223#41×C53—42no—
224#41×C53—41no—
225#41×C53—41no—
226#41×C53—42no—
227#41×C53—42no—
228#41×C53—42no—
229#41×C53—42no—
230#41×C53—42no—
231#41×C53—42no—
232#41×C53C2×D412yes—
233#41×C53#4112yes—
234C2×Q8×C53—21no—
235C2×Q8×C53—22no—
236C2×Q8×C53—21no—
237C2×Q8×C53—21no—
238C2×Q8×C53—21no—
239C2×Q8×C53—21no—
240C2×Q8×C53—21no—
241C2×Q8×C53—21no—
242C2×Q8×C53—41no—
243C2×Q8×C53C2×D411yescharacteristic
244C2×Q8×C53C2×D411yescharacteristic
245C2×Q8×C53C2×D411yescharacteristic
246C2×D4×C53—21no—
247C2×D4×C53—22no—
248C2×D4×C53—22no—
249C2×D4×C53—22no—
250C2×D4×C53—22no—
251C2×D4×C53—21no—
252C2×D4×C53—21no—
253C2×D4×C53—21no—
254C2×D4×C53—21no—
255C2×D4×C53—21no—
256C2×D4×C53—22no—
257C2×D4×C53—22no—
258C2×D4×C53—22no—
259C2×D4×C53—21no—
260C2×D4×C53—22no—
261C2×D4×C53—21no—
262C2×D4×C53—21no—
263C2×D4×C53—21no—
264C2×D4×C53—21no—
265C2×D4×C53—21no—
266C2×D4×C53—21no—
267C2×D4×C53—21no—
268C2×D4×C53—41no—
269C2×D4×C53—42no—
270C2×D4×C53—42no—
271C2×D4×C53—42no—
272C2×D4×C53—42no—
273C2×D4×C53—44no—
274C2×D4×C53—44no—
275C2×D4×C53—42no—
276C2×D4×C53—42no—
277C2×D4×C53—44no—
278C2×D4×C53—84no—
279C2×D4×C53C2×D411yescharacteristic
280C2×D4×C53C2×D411yescharacteristic
281C2×D4×C53C2×D411yescharacteristic
282C22×C4×C53—21no—
283C22×C4×C53—21no—
284C22×C4×C53—21no—
285C22×C4×C53—21no—
286C22×C4×C53—21no—
287C22×C4×C53—22no—
288C22×C4×C53—21no—
289C22×C4×C53—21no—
290C22×C4×C53—21no—
291C22×C4×C53—22no—
292C22×C4×C53—21no—
293C22×C4×C53—21no—
294C22×C4×C53—21no—
295C22×C4×C53—21no—
296C22×C4×C53—21no—
297C22×C4×C53—21no—
298C22×C4×C53—42no—
299C22×C4×C53—42no—
300C22×C4×C53—42no—
301C22×C4×C53—42no—
302C22×C4×C53—42no—
303C22×C4×C53C2×D411yescharacteristic
304C22×C4×C53C2×D411yescharacteristic
305C22×C4×C53C2×D411yescharacteristic
306C22×C4×C53C2×D411yescharacteristic
307C22×C4×C53C2×D411yescharacteristic
308C22×C4×C53C2×D412yes—
309C22×C4×C53C2411yescharacteristic
310Q16×C53—42no—
311Q16×C53—42no—
312Q16×C53—42no—
313SD16×C53—42no—
314SD16×C53—42no—
315SD16×C53—42no—
316M16×C53—21no—
317M16×C53—21no—
318M16×C53—21no—
319M16×C53—21no—
320M16×C53—21no—
321M16×C53—21no—
322M16×C53—21no—
323M16×C53—42no—
324M16×C53C2×D412yescomplemented
325C2×C8×C53—21no—
326C2×C8×C53—21no—
327C2×C8×C53—21no—
328C2×C8×C53—21no—
329C2×C8×C53—42no—
330C4⋊C4×C53—22no—
331C4⋊C4×C53—22no—
332C4⋊C4×C53—21no—
333C4⋊C4×C53—21no—
334C4⋊C4×C53—21no—
335C4⋊C4×C53—21no—
336C4⋊C4×C53—21no—
337C4⋊C4×C53—21no—
338C4⋊C4×C53—41no—
339C4⋊C4×C53—41no—
340C4⋊C4×C53C2×D411yescharacteristic
341C4⋊C4×C53C2×D411yescharacteristic
342C22⋊C4×C53—22no—
343C22⋊C4×C53—22no—
344C22⋊C4×C53—22no—
345C22⋊C4×C53—22no—
346C22⋊C4×C53—22no—
347C22⋊C4×C53—21no—
348C22⋊C4×C53—21no—
349C22⋊C4×C53—21no—
350C22⋊C4×C53—21no—
351C22⋊C4×C53—22no—
352C22⋊C4×C53—22no—
353C22⋊C4×C53—21no—
354C22⋊C4×C53—44no—
355C22⋊C4×C53—44no—
356C22⋊C4×C53—41no—
357C22⋊C4×C53—41no—
358C42×C53—22no—
359C42×C53—21no—
360C42×C53—21no—
361C42×C53—21no—
362C42×C53—21no—
363C42×C53—42no—
364C42×C53C2×D412yescomplemented
365C23×C53—21no—
366C23×C53—21no—
367C23×C53—21no—
368C23×C53—22no—
369C23×C53—21no—
370C23×C53—22no—
371C23×C53—21no—
372C23×C53—22no—
373C23×C53—22no—
374C23×C53—41no—
375C23×C53—42no—
376C23×C53—44no—
377C23×C53—42no—
378C23×C53—42no—
379C23×C53—42no—
380C23×C53—81no—
381C23×C53—82no—
382C23×C53—82no—
383C23×C53#12011yescharacteristic
384C23×C53#12011yescharacteristic
385C23×C53C22×D411yescharacteristic
386Q8×C53—21no—
387Q8×C53—21no—
388Q8×C53—21no—
389Q8×C53—21no—
390Q8×C53—21no—
391Q8×C53—42no—
392Q8×C53—41no—
393Q8×C53—41no—
394Q8×C53—41no—
395Q8×C53—41no—
396Q8×C53#12112yes—
397D4×C53—22no—
398D4×C53—22no—
399D4×C53—21no—
400D4×C53—21no—
401D4×C53—21no—
402D4×C53—21no—
403D4×C53—21no—
404D4×C53—42no—
405D4×C53—42no—
406D4×C53—44no—
407D4×C53—42no—
408D4×C53—44no—
409D4×C53—41no—
410D4×C53—41no—
411D4×C53—41no—
412D4×C53—41no—
413D4×C53—44no—
414D4×C53—42no—
415D4×C53—41no—
416D4×C53—41no—
417D4×C53—41no—
418D4×C53—41no—
419D4×C53—81no—
420D4×C53—82no—
421D4×C53—82no—
422D4×C53—82no—
423D4×C53—82no—
424D4×C53#12112yes—
425C2×C4×C53—21no—
426C2×C4×C53—21no—
427C2×C4×C53—21no—
428C2×C4×C53—21no—
429C2×C4×C53—21no—
430C2×C4×C53—21no—
431C2×C4×C53—21no—
432C2×C4×C53—21no—
433C2×C4×C53—21no—
434C2×C4×C53—22no—
435C2×C4×C53—21no—
436C2×C4×C53—21no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—21no—
440C2×C4×C53—21no—
441C2×C4×C53—21no—
442C2×C4×C53—22no—
443C2×C4×C53—21no—
444C2×C4×C53—22no—
445C2×C4×C53—42no—
446C2×C4×C53—42no—
447C2×C4×C53—42no—
448C2×C4×C53—44no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—48no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—42no—
459C2×C4×C53—42no—
460C2×C4×C53—41no—
461C2×C4×C53—41no—
462C2×C4×C53—41no—
463C2×C4×C53—41no—
464C2×C4×C53—82no—
465C2×C4×C53#12011yescharacteristic
466C2×C4×C53#12011yescharacteristic
467C2×C4×C53C22×D411yescharacteristic
468C2×C4×C53C22×D411yescharacteristic
469C2×C4×C53C22×D411yescharacteristic
470C2×C4×C53C2×#4111yescharacteristic
471C2×C4×C53H(5,𝔽2)11yescharacteristic
472C2×C4×C53H(5,𝔽2)11yescharacteristic
473C8×C53—22no—
474C8×C53—41no—
475C8×C53—41no—
476C8×C53—41no—
477#24467C5311yesmaximal, characteristic, direct product factor, Sylow
478C22×C53—21no—
479C22×C53—21no—
480C22×C53—21no—
481C22×C53—21no—
482C22×C53—21no—
483C22×C53—22no—
484C22×C53—21no—
485C22×C53—21no—
486C22×C53—42no—
487C22×C53—42no—
488C22×C53—41no—
489C22×C53—41no—
490C22×C53—41no—
491C22×C53—41no—
492C22×C53—42no—
493C22×C53—42no—
494C22×C53—41no—
495C22×C53—41no—
496C22×C53—41no—
497C22×C53—42no—
498C22×C53—41no—
499C22×C53—84no—
500C22×C53—82no—
501C22×C53—82no—
502C22×C53—164no—
503C22×C53#45512yescomplemented
504C22×C53C2×#12011yescharacteristic
505C22×C53D4211yescharacteristic
506C22×C53#54611yescharacteristic
507C4×C53—21no—
508C4×C53—21no—
509C4×C53—22no—
510C4×C53—42no—
511C4×C53—42no—
512C4×C53—41no—
513C4×C53—41no—
514C4×C53—42no—
515C4×C53—41no—
516C4×C53—41no—
517C4×C53—81no—
518C4×C53—81no—
519C4×C53C2×#12111yescharacteristic
520C4×C53#53411yescharacteristic
521C4×C53D4211yescharacteristic
522C4×C53#54611yescharacteristic
523#3488C2×C5311yescharacteristic
524#3056C2×C5311yescharacteristic, complemented
525C2×#455C2×C5311yescharacteristic, complemented
526#3007C2×C5311yescharacteristic, complemented
527C22×#104C2×C5311yescharacteristic, complemented
528#2850C2×C5311yescharacteristic, complemented
529#2040C2×C5311yescharacteristic, complemented
530#2037C2×C5311yescharacteristic, complemented
531#2007C2×C5311yescharacteristic, complemented
532#2004C2×C5311yescharacteristic, complemented
533#1900C2×C5311yescharacteristic, complemented
534#1896C2×C5311yescharacteristic, complemented
535#1882C2×C5311yescharacteristic, complemented
536#1860C2×C5311yescharacteristic, complemented
537#1792C2×C5311yescharacteristic, complemented
538C2×C53—21no—
539C2×C53—21no—
540C2×C53—22no—
541C2×C53—41no—
542C2×C53—42no—
543C2×C53—81no—
544C2×C53—82no—
545C2×C53—81no—
546C2×C53#241011yescharacteristic
547C2×C53C2×#45511yescharacteristic
548C2×C53#301811yescharacteristic
549C2×H(5,𝔽2)C22×C5311yescharacteristic
550C22×#41C22×C5311yescharacteristic
551C2×#137C22×C5311yescharacteristic
552C2×#137C22×C5311yescharacteristic, complemented
553C2×#137C22×C5311yescharacteristic, complemented
554C22×M16C22×C5311yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C5311yescharacteristic
563#535—21no—
564#535C22×C5311yescharacteristic
565C2×#124C22×C5311yescharacteristic, complemented
566#525—21no—
567#525C22×C5311yescharacteristic
568C2×C22⋊Q8C22×C5311yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C5311yescharacteristic
571#520C22×C5311yescharacteristic
572C22×C42C22×C5311yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C5311yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C5311yescharacteristic
585C2×#104C22×C5311yescharacteristic
586C2×#104C22×C5311yescharacteristic, complemented
587C2×#104C22×C5311yescharacteristic, complemented
588C2×#104C22×C5311yescharacteristic, complemented
589C2×#104C22×C5311yescharacteristic, complemented
590#419C22×C5311yescharacteristic, complemented
591#417C22×C5311yescharacteristic
592#417C22×C5311yescharacteristic, complemented
593#417C22×C5311yescharacteristic, complemented
594C2×#100C22×C5311yescharacteristic, complemented
595C2×#100C22×C5311yescharacteristic, complemented
596#407C22×C5311yescharacteristic, complemented
597#391C22×C5311yescharacteristic, complemented
598#390C22×C5311yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C5311yescharacteristic, complemented
602#343C22×C5311yescharacteristic, complemented
603#343C22×C5311yescharacteristic, complemented
604#339C22×C5311yescharacteristic, complemented
605#339C22×C5311yescharacteristic, complemented
606C53#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C5311yescharacteristic
620C2×#41D4×C5311yescharacteristic
621C2×#41C23×C5311yescharacteristic
622C2×#41C23×C5311yescharacteristic
623C2×#41C23×C5311yescharacteristic
624C22×Q8D4×C5311yescharacteristic
625C22×Q8C23×C5311yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C5311yescharacteristic
632C22×D4D4×C5312yes—
633C22×D4C23×C5311yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C5311yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C5311yescharacteristic
653C2×M16C23×C5311yescharacteristic
654C2×M16C23×C5311yescharacteristic
655C2×M16C23×C5311yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C5311yescharacteristic
673C22⋊Q8D4×C5311yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C5311yescharacteristic
689#121D4×C5311yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C5311yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C5311yescharacteristic
707C2×C4⋊C4C23×C5311yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C5312yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C5311yescharacteristic
717C2×C42C23×C5311yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C5314yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C5311yescharacteristic
743C24C2×D4×C5312yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C5312yes—
767#41#41×C5312yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C5311yescharacteristic
778C2×Q8C2×D4×C5311yescharacteristic
779C2×Q8C2×D4×C5311yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C5311yescharacteristic
814C2×D4C2×D4×C5311yescharacteristic
815C2×D4C2×D4×C5311yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C5311yescharacteristic
838C22×C4C2×D4×C5311yescharacteristic
839C22×C4C2×D4×C5311yescharacteristic
840C22×C4C2×D4×C5311yescharacteristic
841C22×C4C2×D4×C5311yescharacteristic
842C22×C4C2×D4×C5312yes—
843C22×C4C24×C5311yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C5312yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C5311yescharacteristic
875C4⋊C4C2×D4×C5311yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C5312yescomplemented
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C5311yescharacteristic
918C23#120×C5311yescharacteristic
919C23C22×D4×C5311yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C5312yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C5312yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C5311yescharacteristic
1000C2×C4#120×C5311yescharacteristic
1001C2×C4C22×D4×C5311yescharacteristic
1002C2×C4C22×D4×C5311yescharacteristic
1003C2×C4C22×D4×C5311yescharacteristic
1004C2×C4C2×#41×C5311yescharacteristic
1005C2×C4H(5,𝔽2)×C5311yescharacteristic
1006C2×C4H(5,𝔽2)×C5311yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C53×#45512yescomplemented
1037C22C2×#120×C5311yescharacteristic
1038C22D42×C5311yescharacteristic
1039C22C53×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C5311yescharacteristic
1053C4C53×#53411yescharacteristic
1054C4D42×C5311yescharacteristic
1055C4C53×#54611yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C53×#241011yescharacteristic
1065C2C2×C53×#45511yescharacteristic
1066C2C53×#301811yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC22×C4C24×C53
prime radicalC53×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#3056C2semidirect
3. C2×C53×#455C2semidirect
4. C53×#3007C2semidirect
5. C22×#104×C53C2semidirect
6. C53×#2850C2semidirect
7. C53×#2040C2semidirect
8. C53×#2037C2semidirect
9. C53×#2007C2semidirect
10. C53×#2004C2semidirect
11. C53×#1900C2semidirect
12. C53×#1896C2semidirect
13. C53×#1882C2semidirect
14. C53×#1860C2semidirect
15. C53×#1792C2semidirect
19. C2×#137×C53C22semidirect
20. C2×#137×C53C22semidirect
21. C22×M16×C53C22semidirect
32. C2×#124×C53C22semidirect
35. C2×C22⋊Q8×C53C22semidirect
39. C22×C42×C53C22semidirect
49. C53×#428C22semidirect
53. C2×#104×C53C22semidirect
54. C2×#104×C53C22semidirect
55. C2×#104×C53C22semidirect
56. C2×#104×C53C22semidirect
57. C53×#419C22semidirect
59. C53×#417C22semidirect
60. C53×#417C22semidirect
61. C2×#100×C53C22semidirect
62. C2×#100×C53C22semidirect
63. C53×#407C22semidirect
64. C53×#391C22semidirect
65. C53×#390C22semidirect
68. C53×#382C22semidirect
69. C53×#343C22semidirect
70. C53×#343C22semidirect
71. C53×#339C22semidirect
72. C53×#339C22semidirect
191. #104×C53D4semidirect
324. M16×C53C2×D4semidirect
364. C42×C53C2×D4semidirect
477. #24467C53direct (N × H)
503. C22×C53#455semidirect
524. #3056C2×C53semidirect
525. C2×#455C2×C53semidirect
526. #3007C2×C53semidirect
527. C22×#104C2×C53semidirect
528. #2850C2×C53semidirect
529. #2040C2×C53semidirect
530. #2037C2×C53semidirect
531. #2007C2×C53semidirect
532. #2004C2×C53semidirect
533. #1900C2×C53semidirect
534. #1896C2×C53semidirect
535. #1882C2×C53semidirect
536. #1860C2×C53semidirect
537. #1792C2×C53semidirect
552. C2×#137C22×C53semidirect
553. C2×#137C22×C53semidirect
554. C22×M16C22×C53semidirect
565. C2×#124C22×C53semidirect
568. C2×C22⋊Q8C22×C53semidirect
572. C22×C42C22×C53semidirect
582. #428C22×C53semidirect
586. C2×#104C22×C53semidirect
587. C2×#104C22×C53semidirect
588. C2×#104C22×C53semidirect
589. C2×#104C22×C53semidirect
590. #419C22×C53semidirect
592. #417C22×C53semidirect
593. #417C22×C53semidirect
594. C2×#100C22×C53semidirect
595. C2×#100C22×C53semidirect
596. #407C22×C53semidirect
597. #391C22×C53semidirect
598. #390C22×C53semidirect
601. #382C22×C53semidirect
602. #343C22×C53semidirect
603. #343C22×C53semidirect
604. #339C22×C53semidirect
605. #339C22×C53semidirect
606. C53#24467direct (N × H)
725. #104D4×C53semidirect
858. M16C2×D4×C53semidirect
898. C42C2×D4×C53semidirect
1036. C22C53×#455semidirect

Maximal subgroups

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

subgroupindex
C53×#34882
C53×#30562
C2×C53×#4552
C53×#30072
C22×#104×C532
C53×#28502
C53×#20402
C53×#20372
C53×#20072
C53×#20042
C53×#19002
C53×#18962
C53×#18822
C53×#18602
C53×#17922
#2446753