Finite Group Databasebeta

← C53×#24471 #27231983

Subgroups — C53×#24471 #27231983

Order 13568.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×C53×#421C211yesmaximal, characteristic, complemented
6C53×#2620C211yesmaximal, characteristic, complemented
7C53×#2039C211yesmaximal, characteristic, complemented
8C53×#2037C211yesmaximal, characteristic, complemented
9C53×#2007C211yesmaximal, characteristic, complemented
10C53×#2004C211yesmaximal, characteristic, complemented
11C53×#1900C211yesmaximal, characteristic, complemented
12C53×#1897C211yesmaximal, characteristic, complemented
13C53×#1882C211yesmaximal, characteristic, complemented
14C53×#1859C211yesmaximal, 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
39C2×#117×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
50C53×#421—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×#396—22no—
65C53×#394—22no—
66C53×#391C2211yescharacteristic, complemented
67C53×#390C2211yescharacteristic, complemented
68C53×#384C2211yescharacteristic, 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×C53C2311yescharacteristic
102#137×C53—22no—
103#137×C53—22no—
104#137×C53—22no—
105#137×C53—41no—
106#137×C53—41no—
107#137×C53—41no—
108C2×Q16×C53—21no—
109C2×Q16×C53—21no—
110C2×Q16×C53—21no—
111C2×SD16×C53—21no—
112C2×SD16×C53—21no—
113C2×SD16×C53—21no—
114C2×M16×C53—22no—
115C2×M16×C53—21no—
116C2×M16×C53—41no—
117C2×M16×C53C2311yescharacteristic
118C2×M16×C53C2311yescharacteristic
119C2×M16×C53C2311yescharacteristic
120C2×M16×C53C2311yescharacteristic
121C22×C8×C53—21no—
122#127×C53—22no—
123#127×C53—21no—
124#124×C53—22no—
125#124×C53—22no—
126#124×C53—21no—
127#124×C53—41no—
128#123×C53—22no—
129#123×C53—21no—
130C22⋊Q8×C53—22no—
131C22⋊Q8×C53—21no—
132C22⋊Q8×C53—21no—
133C22⋊Q8×C53—21no—
134C22⋊Q8×C53—21no—
135C22⋊Q8×C53—21no—
136C22⋊Q8×C53—21no—
137C22⋊Q8×C53D411yescharacteristic
138C22⋊Q8×C53D411yescharacteristic
139#121×C53—22no—
140#121×C53—22no—
141#121×C53—22no—
142#121×C53—22no—
143#121×C53—22no—
144#121×C53—21no—
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—22no—
153#121×C53D411yescharacteristic
154#121×C53D411yescharacteristic
155#120×C53—22no—
156#120×C53—22no—
157#120×C53—22no—
158#120×C53—21no—
159#120×C53—22no—
160C4×Q8×C53—21no—
161C4×D4×C53—22no—
162C4×D4×C53—22no—
163C4×D4×C53—21no—
164C4×D4×C53—22no—
165C4×D4×C53—21no—
166C4×D4×C53—21no—
167#117×C53—21no—
168#117×C53—22no—
169#117×C53—41no—
170#117×C53C2311yescharacteristic
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—22no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—22no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—22no—
181C2×C22⋊C4×C53—22no—
182C2×C22⋊C4×C53D412yes—
183C2×C42×C53C2311yescharacteristic
184C2×C42×C53C2311yescharacteristic
185#107×C53—21no—
186#106×C53—21no—
187#104×C53—22no—
188#104×C53—22no—
189#104×C53—22no—
190#104×C53—22no—
191#104×C53—41no—
192#104×C53D414yescomplemented
193#103×C53—21no—
194#103×C53—21no—
195#103×C53—21no—
196#103×C53—21no—
197#103×C53—21no—
198#102×C53—21no—
199#102×C53—21no—
200#102×C53—21no—
201#100×C53—22no—
202#100×C53—41no—
203C22⋊C8×C53—21no—
204C22⋊C8×C53—21no—
205#95×C53—22no—
206C24×C53—22no—
207C24×C53—21no—
208C24×C53C2×D412yes—
209C24×C53C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C53—21no—
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×C53C2×D411yescharacteristic
301C22×C4×C53C2×D411yescharacteristic
302C22×C4×C53C2×D411yescharacteristic
303C22×C4×C53C2×D411yescharacteristic
304C22×C4×C53C2×D411yescharacteristic
305C22×C4×C53C2×D412yes—
306C22×C4×C53C2411yescharacteristic
307Q16×C53—42no—
308Q16×C53—42no—
309Q16×C53—42no—
310SD16×C53—42no—
311SD16×C53—42no—
312SD16×C53—42no—
313M16×C53—21no—
314M16×C53—21no—
315M16×C53—21no—
316M16×C53—21no—
317M16×C53—21no—
318M16×C53—21no—
319M16×C53—21no—
320M16×C53—42no—
321M16×C53C2×D412yescomplemented
322C2×C8×C53—21no—
323C2×C8×C53—21no—
324C2×C8×C53—21no—
325C2×C8×C53—21no—
326C2×C8×C53—42no—
327C4⋊C4×C53—22no—
328C4⋊C4×C53—22no—
329C4⋊C4×C53—21no—
330C4⋊C4×C53—21no—
331C4⋊C4×C53—21no—
332C4⋊C4×C53—21no—
333C4⋊C4×C53—21no—
334C4⋊C4×C53—21no—
335C4⋊C4×C53—42no—
336C4⋊C4×C53—41no—
337C4⋊C4×C53—41no—
338C4⋊C4×C53—82no—
339C4⋊C4×C53C2×D411yescharacteristic
340C4⋊C4×C53C2×D411yescharacteristic
341C22⋊C4×C53—22no—
342C22⋊C4×C53—22no—
343C22⋊C4×C53—22no—
344C22⋊C4×C53—22no—
345C22⋊C4×C53—22no—
346C22⋊C4×C53—21no—
347C22⋊C4×C53—21no—
348C22⋊C4×C53—21no—
349C22⋊C4×C53—21no—
350C22⋊C4×C53—22no—
351C22⋊C4×C53—22no—
352C22⋊C4×C53—21no—
353C22⋊C4×C53—42no—
354C22⋊C4×C53—44no—
355C22⋊C4×C53—41no—
356C22⋊C4×C53—41no—
357C22⋊C4×C53—82no—
358C42×C53—22no—
359C42×C53—21no—
360C42×C53—21no—
361C42×C53—21no—
362C42×C53—21no—
363C42×C53C2×D412yescomplemented
364C23×C53—21no—
365C23×C53—21no—
366C23×C53—21no—
367C23×C53—21no—
368C23×C53—22no—
369C23×C53—21no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—42no—
375C23×C53—42no—
376C23×C53—44no—
377C23×C53—42no—
378C23×C53—42no—
379C23×C53—81no—
380C23×C53—82no—
381C23×C53—82no—
382C23×C53#12011yescharacteristic
383C23×C53#12011yescharacteristic
384C23×C53C22×D411yescharacteristic
385Q8×C53—21no—
386Q8×C53—21no—
387Q8×C53—21no—
388Q8×C53—21no—
389Q8×C53—21no—
390Q8×C53—42no—
391Q8×C53—41no—
392Q8×C53—41no—
393Q8×C53—41no—
394Q8×C53—41no—
395Q8×C53#12112yes—
396D4×C53—22no—
397D4×C53—22no—
398D4×C53—21no—
399D4×C53—21no—
400D4×C53—21no—
401D4×C53—21no—
402D4×C53—21no—
403D4×C53—42no—
404D4×C53—42no—
405D4×C53—44no—
406D4×C53—42no—
407D4×C53—44no—
408D4×C53—44no—
409D4×C53—42no—
410D4×C53—41no—
411D4×C53—41no—
412D4×C53—41no—
413D4×C53—41no—
414D4×C53—41no—
415D4×C53—41no—
416D4×C53—41no—
417D4×C53—41no—
418D4×C53—81no—
419D4×C53—82no—
420D4×C53—82no—
421D4×C53—82no—
422D4×C53—82no—
423D4×C53#12112yes—
424C2×C4×C53—21no—
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—22no—
434C2×C4×C53—21no—
435C2×C4×C53—21no—
436C2×C4×C53—22no—
437C2×C4×C53—21no—
438C2×C4×C53—21no—
439C2×C4×C53—21no—
440C2×C4×C53—22no—
441C2×C4×C53—21no—
442C2×C4×C53—22no—
443C2×C4×C53—42no—
444C2×C4×C53—42no—
445C2×C4×C53—42no—
446C2×C4×C53—44no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—42no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—42no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53—41no—
461C2×C4×C53—41no—
462C2×C4×C53—82no—
463C2×C4×C53#12011yescharacteristic
464C2×C4×C53#12011yescharacteristic
465C2×C4×C53C22×D411yescharacteristic
466C2×C4×C53C22×D411yescharacteristic
467C2×C4×C53C22×D411yescharacteristic
468C2×C4×C53C2×#4111yescharacteristic
469C2×C4×C53H(5,𝔽2)11yescharacteristic
470C2×C4×C53H(5,𝔽2)11yescharacteristic
471C8×C53—22no—
472C8×C53—41no—
473C8×C53—41no—
474C8×C53—41no—
475#24471C5311yesmaximal, characteristic, direct product factor, Sylow
476C22×C53—21no—
477C22×C53—21no—
478C22×C53—21no—
479C22×C53—21no—
480C22×C53—22no—
481C22×C53—21no—
482C22×C53—21no—
483C22×C53—21no—
484C22×C53—21no—
485C22×C53—41no—
486C22×C53—41no—
487C22×C53—41no—
488C22×C53—41no—
489C22×C53—42no—
490C22×C53—42no—
491C22×C53—41no—
492C22×C53—41no—
493C22×C53—41no—
494C22×C53—42no—
495C22×C53—41no—
496C22×C53—81no—
497C22×C53—81no—
498C22×C53—82no—
499C22×C53—82no—
500C22×C53—84no—
501C22×C53—164no—
502C22×C53C2×#12011yescharacteristic
503C22×C53D4211yescharacteristic
504C22×C53#54611yescharacteristic
505C4×C53—21no—
506C4×C53—21no—
507C4×C53—22no—
508C4×C53—42no—
509C4×C53—41no—
510C4×C53—41no—
511C4×C53—42no—
512C4×C53—41no—
513C4×C53—41no—
514C4×C53—81no—
515C4×C53—81no—
516C4×C53—81no—
517C4×C53C2×#12111yescharacteristic
518C4×C53#53411yescharacteristic
519C4×C53D4211yescharacteristic
520C4×C53#54611yescharacteristic
521#3488C2×C5311yescharacteristic
522#3056C2×C5311yescharacteristic, complemented
523C2×#455C2×C5311yescharacteristic, complemented
524#3007C2×C5311yescharacteristic, complemented
525C2×#421C2×C5311yescharacteristic, complemented
526#2620C2×C5311yescharacteristic, complemented
527#2039C2×C5311yescharacteristic, complemented
528#2037C2×C5311yescharacteristic, complemented
529#2007C2×C5311yescharacteristic, complemented
530#2004C2×C5311yescharacteristic, complemented
531#1900C2×C5311yescharacteristic, complemented
532#1897C2×C5311yescharacteristic, complemented
533#1882C2×C5311yescharacteristic, complemented
534#1859C2×C5311yescharacteristic, complemented
535#1792C2×C5311yescharacteristic, complemented
536C2×C53—21no—
537C2×C53—21no—
538C2×C53—41no—
539C2×C53—41no—
540C2×C53—42no—
541C2×C53—81no—
542C2×C53—82no—
543C2×C53—81no—
544C2×C53#241011yescharacteristic
545C2×C53#301911yescharacteristic
546C2×C53#302211yescharacteristic
547C2×H(5,𝔽2)C22×C5311yescharacteristic
548C22×#41C22×C5311yescharacteristic
549C2×#137C22×C5311yescharacteristic
550C2×#137C22×C5311yescharacteristic, complemented
551C2×#137C22×C5311yescharacteristic, complemented
552C22×M16C22×C5311yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C5311yescharacteristic
561#535—21no—
562#535C22×C5311yescharacteristic
563C2×#124C22×C5311yescharacteristic, complemented
564#525—21no—
565#525C22×C5311yescharacteristic
566C2×C22⋊Q8C22×C5311yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C5311yescharacteristic
569#520C22×C5311yescharacteristic
570C2×#117C22×C5311yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C5311yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C5311yescharacteristic
583C2×#104C22×C5311yescharacteristic
584C2×#104C22×C5311yescharacteristic, complemented
585C2×#104C22×C5311yescharacteristic, complemented
586C2×#104C22×C5311yescharacteristic, complemented
587C2×#104C22×C5311yescharacteristic, complemented
588#419C22×C5311yescharacteristic, complemented
589#417C22×C5311yescharacteristic
590#417C22×C5311yescharacteristic, complemented
591#417C22×C5311yescharacteristic, complemented
592C2×#100C22×C5311yescharacteristic, complemented
593C2×#100C22×C5311yescharacteristic, complemented
594#407C22×C5311yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C5311yescharacteristic, complemented
598#390C22×C5311yescharacteristic, complemented
599#384C22×C5311yescharacteristic, complemented
600#343C22×C5311yescharacteristic, complemented
601#343C22×C5311yescharacteristic, complemented
602#339C22×C5311yescharacteristic, complemented
603#339C22×C5311yescharacteristic, complemented
604C53#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C5311yescharacteristic
618C2×#41D4×C5311yescharacteristic
619C2×#41C23×C5311yescharacteristic
620C2×#41C23×C5311yescharacteristic
621C2×#41C23×C5311yescharacteristic
622C22×Q8D4×C5311yescharacteristic
623C22×Q8C23×C5311yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C5311yescharacteristic
630C22×D4D4×C5312yes—
631C22×D4C23×C5311yescharacteristic
632C23×C4—21no—
633C23×C4C23×C5311yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C5311yescharacteristic
650C2×M16C23×C5311yescharacteristic
651C2×M16C23×C5311yescharacteristic
652C2×M16C23×C5311yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C5311yescharacteristic
670C22⋊Q8D4×C5311yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C5311yescharacteristic
686#121D4×C5311yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C5311yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C5311yescharacteristic
708C2×C4⋊C4C23×C5311yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C5312yes—
715C2×C42C23×C5311yescharacteristic
716C2×C42C23×C5311yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C5314yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C5312yes—
741C24C2×D4×C5311yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C5312yes—
765#41#41×C5312yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C5311yescharacteristic
776C2×Q8C2×D4×C5311yescharacteristic
777C2×Q8C2×D4×C5311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C5311yescharacteristic
812C2×D4C2×D4×C5311yescharacteristic
813C2×D4C2×D4×C5311yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C5311yescharacteristic
833C22×C4C2×D4×C5311yescharacteristic
834C22×C4C2×D4×C5311yescharacteristic
835C22×C4C2×D4×C5311yescharacteristic
836C22×C4C2×D4×C5311yescharacteristic
837C22×C4C2×D4×C5312yes—
838C22×C4C24×C5311yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C5312yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C5311yescharacteristic
872C4⋊C4C2×D4×C5311yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C5312yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C5311yescharacteristic
915C23#120×C5311yescharacteristic
916C23C22×D4×C5311yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C5312yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C5312yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C5311yescharacteristic
996C2×C4#120×C5311yescharacteristic
997C2×C4C22×D4×C5311yescharacteristic
998C2×C4C22×D4×C5311yescharacteristic
999C2×C4C22×D4×C5311yescharacteristic
1000C2×C4C2×#41×C5311yescharacteristic
1001C2×C4H(5,𝔽2)×C5311yescharacteristic
1002C2×C4H(5,𝔽2)×C5311yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C5311yescharacteristic
1034C22D42×C5311yescharacteristic
1035C22C53×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C5311yescharacteristic
1049C4C53×#53411yescharacteristic
1050C4D42×C5311yescharacteristic
1051C4C53×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C53×#241011yescharacteristic
1061C2C53×#301911yescharacteristic
1062C2C53×#302211yescharacteristic
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. C2×C53×#421C2semidirect
6. C53×#2620C2semidirect
7. C53×#2039C2semidirect
8. C53×#2037C2semidirect
9. C53×#2007C2semidirect
10. C53×#2004C2semidirect
11. C53×#1900C2semidirect
12. C53×#1897C2semidirect
13. C53×#1882C2semidirect
14. C53×#1859C2semidirect
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. C2×#117×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
66. C53×#391C22semidirect
67. C53×#390C22semidirect
68. C53×#384C22semidirect
69. C53×#343C22semidirect
70. C53×#343C22semidirect
71. C53×#339C22semidirect
72. C53×#339C22semidirect
192. #104×C53D4semidirect
321. M16×C53C2×D4semidirect
363. C42×C53C2×D4semidirect
475. #24471C53direct (N × H)
522. #3056C2×C53semidirect
523. C2×#455C2×C53semidirect
524. #3007C2×C53semidirect
525. C2×#421C2×C53semidirect
526. #2620C2×C53semidirect
527. #2039C2×C53semidirect
528. #2037C2×C53semidirect
529. #2007C2×C53semidirect
530. #2004C2×C53semidirect
531. #1900C2×C53semidirect
532. #1897C2×C53semidirect
533. #1882C2×C53semidirect
534. #1859C2×C53semidirect
535. #1792C2×C53semidirect
550. C2×#137C22×C53semidirect
551. C2×#137C22×C53semidirect
552. C22×M16C22×C53semidirect
563. C2×#124C22×C53semidirect
566. C2×C22⋊Q8C22×C53semidirect
570. C2×#117C22×C53semidirect
580. #428C22×C53semidirect
584. C2×#104C22×C53semidirect
585. C2×#104C22×C53semidirect
586. C2×#104C22×C53semidirect
587. C2×#104C22×C53semidirect
588. #419C22×C53semidirect
590. #417C22×C53semidirect
591. #417C22×C53semidirect
592. C2×#100C22×C53semidirect
593. C2×#100C22×C53semidirect
594. #407C22×C53semidirect
597. #391C22×C53semidirect
598. #390C22×C53semidirect
599. #384C22×C53semidirect
600. #343C22×C53semidirect
601. #343C22×C53semidirect
602. #339C22×C53semidirect
603. #339C22×C53semidirect
604. C53#24471direct (N × H)
724. #104D4×C53semidirect
853. M16C2×D4×C53semidirect
895. C42C2×D4×C53semidirect

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
C2×C53×#4212
C53×#26202
C53×#20392
C53×#20372
C53×#20072
C53×#20042
C53×#19002
C53×#18972
C53×#18822
C53×#18592
C53×#17922
#2447153