Finite Group Databasebeta

← C53×#17597 #27225109

Subgroups — C53×#17597 #27225109

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3519C211yesmaximal, characteristic
2C53×#2974C211yesmaximal, characteristic, complemented
3C53×#2318C211yesmaximal, characteristic, complemented
4C53×#1521C211yesmaximal, characteristic, complemented
5C53×#1519C211yesmaximal, characteristic, complemented
6C53×#1517C211yesmaximal, characteristic, complemented
7C53×#1516C211yesmaximal, characteristic, complemented
8C53×#1514C211yesmaximal, characteristic, complemented
9C53×#1513C211yesmaximal, characteristic, complemented
10C53×#1512C211yesmaximal, characteristic, complemented
11C53×#1510C211yesmaximal, characteristic, complemented
12C53×#1507C211yesmaximal, characteristic, complemented
13C53×#1504C211yesmaximal, characteristic, complemented
14C53×#1501C211yesmaximal, characteristic, complemented
15C2×C53×#327C211yesmaximal, characteristic, complemented
16C53×#555C411yescharacteristic, complemented
17C53×#554C411yescharacteristic, complemented
18C53×#553—21no—
19C53×#553C411yescharacteristic, complemented
20C53×#553C411yescharacteristic, complemented
21C53×#550C411yescharacteristic, complemented
22C53×#546—21no—
23C53×#546—21no—
24C53×#546C411yescharacteristic, complemented
25C53×#546C411yescharacteristic, complemented
26D42×C53—21no—
27D42×C53C411yescharacteristic, complemented
28C53×#540—21no—
29C53×#538—21no—
30C53×#538—21no—
31C53×#532C2211yescharacteristic
32C53×#529C2211yescharacteristic
33C53×#525C2211yescharacteristic
34C53×#525C2211yescharacteristic
35C2×#121×C53C2211yescharacteristic
36C2×#121×C53C2211yescharacteristic
37C53×#518—21no—
38C2×C4×D4×C53C2211yescharacteristic
39C53×#436—21no—
40C53×#435—21no—
41C53×#435—21no—
42C8×D4×C53—21no—
43C53×#432C2211yescharacteristic, complemented
44C53×#431C2211yescharacteristic, complemented
45C53×#407C2211yescharacteristic, complemented
46C53×#407C2211yescharacteristic, complemented
47C2×C22⋊C8×C53C2211yescharacteristic, complemented
48C2×C22⋊C8×C53C2211yescharacteristic, complemented
49C53×#388—21no—
50C53×#387—21no—
51C53×#386—21no—
52C53×#385—21no—
53C53×#383C2211yescharacteristic, complemented
54C53×#382C2211yescharacteristic, complemented
55C53×#381C2211yescharacteristic, complemented
56C53×#380C2211yescharacteristic, complemented
57C4×C22⋊C4×C53C2211yescharacteristic, complemented
58C2×#95×C53C2211yescharacteristic, complemented
59C53×#328C2211yescharacteristic, complemented
60C53×#328C2211yescharacteristic, complemented
61C53×#328C2211yescharacteristic, complemented
62C53×#328C2211yescharacteristic, complemented
63C53×#327C2211yescharacteristic
64C53×#327C2211yescharacteristic
65C53×#327C2211yescharacteristic
66C53×#327C2211yescharacteristic
67C53×#327C2211yescharacteristic, complemented
68C53×#327C2211yescharacteristic, complemented
69C53×#327C2211yescharacteristic, complemented
70C53×#327C2211yescharacteristic, complemented
71C53×#327C2211yescharacteristic, complemented
72C53×#327C2211yescharacteristic, complemented
73C53×#327C2211yescharacteristic, complemented
74C53×#327C2211yescharacteristic, complemented
75C2×#41×C53—21no—
76C2×#41×C53C2×C411yescharacteristic
77C2×#41×C53C2×C411yescharacteristic, complemented
78C22×D4×C53—21no—
79C22×D4×C53—21no—
80C22×D4×C53—21no—
81C22×D4×C53C2×C411yescharacteristic
82C22×D4×C53C2×C411yescharacteristic, complemented
83C22×D4×C53D411yescharacteristic
84C23×C4×C53—21no—
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C2×M16×C53—21no—
88C2×M16×C53—21no—
89C22×C8×C53—21no—
90C22×C8×C53—21no—
91C4⋊Q8×C53C2×C411yescharacteristic, complemented
92#127×C53—21no—
93#127×C53C2×C411yescharacteristic, complemented
94#126×C53—21no—
95#126×C53—21no—
96#126×C53—21no—
97#125×C53—21no—
98#125×C53C2×C411yescharacteristic, complemented
99#124×C53—21no—
100#124×C53—21no—
101#124×C53—21no—
102#124×C53C2×C411yescharacteristic, complemented
103#123×C53—21no—
104#123×C53—21no—
105#123×C53—21no—
106#123×C53—21no—
107#123×C53—21no—
108#123×C53—21no—
109#123×C53—21no—
110C22⋊Q8×C53—21no—
111C22⋊Q8×C53—21no—
112C22⋊Q8×C53C2×C411yescharacteristic
113C22⋊Q8×C53C2×C411yescharacteristic, complemented
114C22⋊Q8×C53C2311yescharacteristic
115#121×C53—21no—
116#121×C53—21no—
117#121×C53—21no—
118#121×C53—21no—
119#121×C53—21no—
120#121×C53—21no—
121#121×C53—21no—
122#121×C53—21no—
123#121×C53—21no—
124#121×C53—21no—
125#121×C53—21no—
126#121×C53—21no—
127#121×C53—21no—
128#121×C53C2×C411yescharacteristic
129#121×C53C2×C411yescharacteristic
130#121×C53C2×C411yescharacteristic
131#121×C53C2×C411yescharacteristic, complemented
132#121×C53C2×C411yescharacteristic, complemented
133#121×C53C2×C411yescharacteristic, complemented
134#121×C53C2311yescharacteristic
135#121×C53C2311yescharacteristic
136#121×C53C2311yescharacteristic
137#120×C53—21no—
138#120×C53—21no—
139#120×C53—21no—
140#120×C53—21no—
141#120×C53—21no—
142#120×C53—21no—
143C4×Q8×C53C2×C411yescharacteristic, complemented
144C4×D4×C53—21no—
145C4×D4×C53—21no—
146C4×D4×C53—21no—
147C4×D4×C53—21no—
148C4×D4×C53—21no—
149C4×D4×C53—21no—
150C4×D4×C53—21no—
151C4×D4×C53—21no—
152C4×D4×C53—21no—
153C4×D4×C53—21no—
154C4×D4×C53C2×C411yescharacteristic
155C4×D4×C53C2×C411yescharacteristic
156C4×D4×C53C2×C411yescharacteristic
157C4×D4×C53C2×C411yescharacteristic
158C4×D4×C53C2×C411yescharacteristic, complemented
159C4×D4×C53C2×C411yescharacteristic, complemented
160C4×D4×C53C2×C411yescharacteristic, complemented
161C4×D4×C53D411yescharacteristic
162C4×D4×C53D411yescharacteristic
163C4×D4×C53D411yescharacteristic
164C4×D4×C53D411yescharacteristic
165#117×C53—21no—
166#117×C53—21no—
167#117×C53C2×C411yescharacteristic
168#117×C53C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2×C411yescharacteristic
172C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C4⋊C8×C53—21no—
186C4⋊C8×C53—21no—
187C22⋊C8×C53—21no—
188C22⋊C8×C53—21no—
189C22⋊C8×C53—21no—
190C22⋊C8×C53—21no—
191C22⋊C8×C53C2311yescharacteristic
192C22⋊C8×C53C2311yescharacteristic
193C22⋊C8×C53C2311yescharacteristic
194C22⋊C8×C53C2311yescharacteristic
195#97×C53—21no—
196C4×C8×C53—21no—
197#95×C53—21no—
198#95×C53—21no—
199#95×C53—21no—
200#95×C53—21no—
201#95×C53—21no—
202#95×C53C2311yescharacteristic
203#95×C53C2311yescharacteristic
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53—21no—
208C24×C53C2×D411yescharacteristic
209C24×C53C2×D411yescharacteristic
210#41×C53—81no—
211#41×C53—81no—
212#41×C53—81no—
213#41×C53—81no—
214C2×Q8×C53—21no—
215C2×Q8×C53C22×C411yescharacteristic
216C2×D4×C53—21no—
217C2×D4×C53—21no—
218C2×D4×C53—21no—
219C2×D4×C53—21no—
220C2×D4×C53—21no—
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53—21no—
225C2×D4×C53—21no—
226C2×D4×C53—21no—
227C2×D4×C53—21no—
228C2×D4×C53—21no—
229C2×D4×C53—21no—
230C2×D4×C53—21no—
231C2×D4×C53—42no—
232C2×D4×C53—44no—
233C2×D4×C53—81no—
234C2×D4×C53—81no—
235C2×D4×C53—81no—
236C2×D4×C53—81no—
237C2×D4×C53—81no—
238C2×D4×C53—81no—
239C2×D4×C53C22⋊C411yescharacteristic
240C2×D4×C53C22⋊C411yescharacteristic
241C2×D4×C53C22⋊C411yescharacteristic
242C2×D4×C53C22⋊C411yescharacteristic
243C2×D4×C53C22×C411yescharacteristic
244C2×D4×C53C22×C411yescharacteristic
245C2×D4×C53C22×C411yescharacteristic
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—21no—
256C22×C4×C53—21no—
257C22×C4×C53—42no—
258C22×C4×C53—81no—
259C22×C4×C53—81no—
260C22×C4×C53—81no—
261C22×C4×C53—81no—
262C22×C4×C53C22×C411yescharacteristic
263C22×C4×C53C22×C411yescharacteristic
264C22×C4×C53C22×C411yescharacteristic
265C22×C4×C53C22×C411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2×D411yescharacteristic
274C22×C4×C53C2411yescharacteristic
275M16×C53—81no—
276M16×C53—81no—
277C2×C8×C53—21no—
278C2×C8×C53—21no—
279C2×C8×C53—21no—
280C2×C8×C53—21no—
281C2×C8×C53—81no—
282C2×C8×C53—81no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53—21no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53—21no—
288C4⋊C4×C53—21no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53—21no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53—81no—
293C4⋊C4×C53—81no—
294C4⋊C4×C53C22⋊C411yescharacteristic
295C4⋊C4×C53C22⋊C411yescharacteristic
296C4⋊C4×C53C22⋊C411yescharacteristic
297C4⋊C4×C53C22⋊C411yescharacteristic
298C4⋊C4×C53C22×C411yescharacteristic
299C4⋊C4×C53C22×C411yescharacteristic
300C4⋊C4×C53C22×C411yescharacteristic
301C4⋊C4×C53C22×C411yescharacteristic
302C22⋊C4×C53—21no—
303C22⋊C4×C53—21no—
304C22⋊C4×C53—21no—
305C22⋊C4×C53—21no—
306C22⋊C4×C53—21no—
307C22⋊C4×C53—21no—
308C22⋊C4×C53—21no—
309C22⋊C4×C53—21no—
310C22⋊C4×C53—21no—
311C22⋊C4×C53—21no—
312C22⋊C4×C53—21no—
313C22⋊C4×C53—21no—
314C22⋊C4×C53—21no—
315C22⋊C4×C53—21no—
316C22⋊C4×C53—21no—
317C22⋊C4×C53—21no—
318C22⋊C4×C53—21no—
319C22⋊C4×C53—21no—
320C22⋊C4×C53—21no—
321C22⋊C4×C53—42no—
322C22⋊C4×C53—81no—
323C22⋊C4×C53—81no—
324C22⋊C4×C53C22⋊C411yescharacteristic
325C22⋊C4×C53C22⋊C411yescharacteristic
326C22⋊C4×C53C22⋊C411yescharacteristic
327C22⋊C4×C53C22⋊C411yescharacteristic
328C22⋊C4×C53C22⋊C411yescharacteristic
329C22⋊C4×C53C22⋊C411yescharacteristic
330C22⋊C4×C53C22⋊C411yescharacteristic
331C22⋊C4×C53C22⋊C411yescharacteristic
332C42×C53—21no—
333C42×C53—21no—
334C42×C53—21no—
335C42×C53—81no—
336C42×C53C22×C411yescharacteristic
337C42×C53C22×C411yescharacteristic
338C42×C53C2×D411yescharacteristic
339C42×C53C2×D411yescharacteristic
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—22no—
343C23×C53—21no—
344C23×C53—21no—
345C23×C53—21no—
346C23×C53—21no—
347C23×C53—21no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—42no—
352C23×C53—42no—
353C23×C53—81no—
354C23×C53—81no—
355C23×C53—81no—
356C23×C53—81no—
357C23×C53C2×C22⋊C411yescharacteristic
358C23×C53C2×C22⋊C411yescharacteristic
359C23×C53C2×C22⋊C411yescharacteristic
360C23×C53C2×C22⋊C411yescharacteristic
361C23×C53C22×D411yescharacteristic
362Q8×C53—41no—
363Q8×C53—81no—
364D4×C53—22no—
365D4×C53—22no—
366D4×C53—41no—
367D4×C53—41no—
368D4×C53—41no—
369D4×C53—41no—
370D4×C53—41no—
371D4×C53—42no—
372D4×C53—42no—
373D4×C53—41no—
374D4×C53—41no—
375D4×C53—41no—
376D4×C53—41no—
377D4×C53—41no—
378D4×C53—41no—
379D4×C53—42no—
380D4×C53—81no—
381D4×C53—81no—
382D4×C53—81no—
383D4×C53—81no—
384D4×C53—81no—
385D4×C53—81no—
386D4×C53—81no—
387D4×C53—81no—
388D4×C53—81no—
389C2×C4×C53—21no—
390C2×C4×C53—21no—
391C2×C4×C53—21no—
392C2×C4×C53—21no—
393C2×C4×C53—21no—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—41no—
397C2×C4×C53—41no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—42no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—81no—
422C2×C4×C53—81no—
423C2×C4×C53—81no—
424C2×C4×C53—81no—
425C2×C4×C53—81no—
426C2×C4×C53—81no—
427C2×C4×C53—84no—
428C2×C4×C53C2×C22⋊C411yescharacteristic
429C2×C4×C53C2×C22⋊C411yescharacteristic
430C2×C4×C53C2×C22⋊C411yescharacteristic
431C2×C4×C53C2×C22⋊C411yescharacteristic
432C2×C4×C53C2×C22⋊C411yescharacteristic
433C2×C4×C53C2×C22⋊C411yescharacteristic
434C2×C4×C53C2×C22⋊C411yescharacteristic
435C2×C4×C53C2×C22⋊C411yescharacteristic
436C2×C4×C53C23×C411yescharacteristic
437C2×C4×C53C22×D411yescharacteristic
438C8×C53—41no—
439C8×C53—41no—
440C8×C53—41no—
441C8×C53—41no—
442#17597C5311yesmaximal, characteristic, direct product factor, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—21no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53—21no—
455C22×C53—21no—
456C22×C53—42no—
457C22×C53—42no—
458C22×C53—41no—
459C22×C53—41no—
460C22×C53—41no—
461C22×C53—41no—
462C22×C53—41no—
463C22×C53—41no—
464C22×C53—41no—
465C22×C53—41no—
466C22×C53—41no—
467C22×C53—81no—
468C22×C53—81no—
469C22×C53—162no—
470C22×C53—162no—
471C22×C53#42112yes—
472C22×C53C22×C22⋊C411yescharacteristic
473C22×C53#57611yescharacteristic
474C22×C53#57711yescharacteristic
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—21no—
480C4×C53—21no—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53—41no—
486C4×C53—41no—
487C4×C53—41no—
488C4×C53—41no—
489C4×C53—41no—
490C4×C53—81no—
491C4×C53—81no—
492C4×C53—81no—
493C4×C53—81no—
494#3519C2×C5311yescharacteristic
495#2974C2×C5311yescharacteristic, complemented
496#2318C2×C5311yescharacteristic, complemented
497#1521C2×C5311yescharacteristic, complemented
498#1519C2×C5311yescharacteristic, complemented
499#1517C2×C5311yescharacteristic, complemented
500#1516C2×C5311yescharacteristic, complemented
501#1514C2×C5311yescharacteristic, complemented
502#1513C2×C5311yescharacteristic, complemented
503#1512C2×C5311yescharacteristic, complemented
504#1510C2×C5311yescharacteristic, complemented
505#1507C2×C5311yescharacteristic, complemented
506#1504C2×C5311yescharacteristic, complemented
507#1501C2×C5311yescharacteristic, complemented
508C2×#327C2×C5311yescharacteristic, complemented
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—41no—
514C2×C53—41no—
515C2×C53—81no—
516C2×C53—81no—
517C2×C53—81no—
518C2×C53#288311yescharacteristic
519C2×C53#289711yescharacteristic
520C2×C53C2×#42111yescharacteristic
521#555C4×C5311yescharacteristic, complemented
522#554C4×C5311yescharacteristic, complemented
523#553—21no—
524#553C4×C5311yescharacteristic, complemented
525#553C4×C5311yescharacteristic, complemented
526#550C4×C5311yescharacteristic, complemented
527#546—21no—
528#546—21no—
529#546C4×C5311yescharacteristic, complemented
530#546C4×C5311yescharacteristic, complemented
531D42—21no—
532D42C4×C5311yescharacteristic, complemented
533#540—21no—
534#538—21no—
535#538—21no—
536#532C22×C5311yescharacteristic
537#529C22×C5311yescharacteristic
538#525C22×C5311yescharacteristic
539#525C22×C5311yescharacteristic
540C2×#121C22×C5311yescharacteristic
541C2×#121C22×C5311yescharacteristic
542#518—21no—
543C2×C4×D4C22×C5311yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C22×C5311yescharacteristic, complemented
549#431C22×C5311yescharacteristic, complemented
550#407C22×C5311yescharacteristic, complemented
551#407C22×C5311yescharacteristic, complemented
552C2×C22⋊C8C22×C5311yescharacteristic, complemented
553C2×C22⋊C8C22×C5311yescharacteristic, complemented
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C22×C5311yescharacteristic, complemented
559#382C22×C5311yescharacteristic, complemented
560#381C22×C5311yescharacteristic, complemented
561#380C22×C5311yescharacteristic, complemented
562C4×C22⋊C4C22×C5311yescharacteristic, complemented
563C2×#95C22×C5311yescharacteristic, complemented
564#328C22×C5311yescharacteristic, complemented
565#328C22×C5311yescharacteristic, complemented
566#328C22×C5311yescharacteristic, complemented
567#328C22×C5311yescharacteristic, complemented
568#327C22×C5311yescharacteristic
569#327C22×C5311yescharacteristic
570#327C22×C5311yescharacteristic
571#327C22×C5311yescharacteristic
572#327C22×C5311yescharacteristic, complemented
573#327C22×C5311yescharacteristic, complemented
574#327C22×C5311yescharacteristic, complemented
575#327C22×C5311yescharacteristic, complemented
576#327C22×C5311yescharacteristic, complemented
577#327C22×C5311yescharacteristic, complemented
578#327C22×C5311yescharacteristic, complemented
579#327C22×C5311yescharacteristic, complemented
580C53#1759711yescharacteristic, direct product factor, Sylow
581C2×#41—21no—
582C2×#41C2×C4×C5311yescharacteristic
583C2×#41C2×C4×C5311yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×C4×C5311yescharacteristic
588C22×D4C2×C4×C5311yescharacteristic, complemented
589C22×D4D4×C5311yescharacteristic
590C23×C4—21no—
591C23×C4C23×C5311yescharacteristic
592C23×C4C23×C5311yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8C2×C4×C5311yescharacteristic, complemented
598#127—21no—
599#127C2×C4×C5311yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×C4×C5311yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×C4×C5311yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×C4×C5311yescharacteristic
619C22⋊Q8C2×C4×C5311yescharacteristic, complemented
620C22⋊Q8C23×C5311yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×C4×C5311yescharacteristic
635#121C2×C4×C5311yescharacteristic
636#121C2×C4×C5311yescharacteristic
637#121C2×C4×C5311yescharacteristic, complemented
638#121C2×C4×C5311yescharacteristic, complemented
639#121C2×C4×C5311yescharacteristic, complemented
640#121C23×C5311yescharacteristic
641#121C23×C5311yescharacteristic
642#121C23×C5311yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×C4×C5311yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×C4×C5311yescharacteristic
661C4×D4C2×C4×C5311yescharacteristic
662C4×D4C2×C4×C5311yescharacteristic
663C4×D4C2×C4×C5311yescharacteristic
664C4×D4C2×C4×C5311yescharacteristic, complemented
665C4×D4C2×C4×C5311yescharacteristic, complemented
666C4×D4C2×C4×C5311yescharacteristic, complemented
667C4×D4D4×C5311yescharacteristic
668C4×D4D4×C5311yescharacteristic
669C4×D4D4×C5311yescharacteristic
670C4×D4D4×C5311yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×C4×C5311yescharacteristic
674#117C2×C4×C5311yescharacteristic, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C2×C4×C5311yescharacteristic
678C2×C4⋊C4C2×C4×C5311yescharacteristic, complemented
679C2×C4⋊C4D4×C5311yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4D4×C5311yescharacteristic
688C2×C22⋊C4D4×C5311yescharacteristic
689C2×C42—21no—
690C2×C42C23×C5311yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C23×C5311yescharacteristic
698C22⋊C8C23×C5311yescharacteristic
699C22⋊C8C23×C5311yescharacteristic
700C22⋊C8C23×C5311yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C23×C5311yescharacteristic
709#95C23×C5311yescharacteristic
710#95C23×C5311yescharacteristic
711#95C23×C5311yescharacteristic
712C24—21no—
713C24—21no—
714C24C2×D4×C5311yescharacteristic
715C24C2×D4×C5311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C5311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C5311yescharacteristic
746C2×D4C22⋊C4×C5311yescharacteristic
747C2×D4C22⋊C4×C5311yescharacteristic
748C2×D4C22⋊C4×C5311yescharacteristic
749C2×D4C22×C4×C5311yescharacteristic
750C2×D4C22×C4×C5311yescharacteristic
751C2×D4C22×C4×C5311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C5311yescharacteristic
769C22×C4C22×C4×C5311yescharacteristic
770C22×C4C22×C4×C5311yescharacteristic
771C22×C4C22×C4×C5311yescharacteristic
772C22×C4C2×D4×C5311yescharacteristic
773C22×C4C2×D4×C5311yescharacteristic
774C22×C4C2×D4×C5311yescharacteristic
775C22×C4C2×D4×C5311yescharacteristic
776C22×C4C2×D4×C5311yescharacteristic
777C22×C4C2×D4×C5311yescharacteristic
778C22×C4C2×D4×C5311yescharacteristic
779C22×C4C2×D4×C5311yescharacteristic
780C22×C4C24×C5311yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C5311yescharacteristic
801C4⋊C4C22⋊C4×C5311yescharacteristic
802C4⋊C4C22⋊C4×C5311yescharacteristic
803C4⋊C4C22⋊C4×C5311yescharacteristic
804C4⋊C4C22×C4×C5311yescharacteristic
805C4⋊C4C22×C4×C5311yescharacteristic
806C4⋊C4C22×C4×C5311yescharacteristic
807C4⋊C4C22×C4×C5311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C5311yescharacteristic
831C22⋊C4C22⋊C4×C5311yescharacteristic
832C22⋊C4C22⋊C4×C5311yescharacteristic
833C22⋊C4C22⋊C4×C5311yescharacteristic
834C22⋊C4C22⋊C4×C5311yescharacteristic
835C22⋊C4C22⋊C4×C5311yescharacteristic
836C22⋊C4C22⋊C4×C5311yescharacteristic
837C22⋊C4C22⋊C4×C5311yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C5311yescharacteristic
843C42C22×C4×C5311yescharacteristic
844C42C2×D4×C5311yescharacteristic
845C42C2×D4×C5311yescharacteristic
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C5311yescharacteristic
864C23C2×C22⋊C4×C5311yescharacteristic
865C23C2×C22⋊C4×C5311yescharacteristic
866C23C2×C22⋊C4×C5311yescharacteristic
867C23C22×D4×C5311yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—42no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C5311yescharacteristic
935C2×C4C2×C22⋊C4×C5311yescharacteristic
936C2×C4C2×C22⋊C4×C5311yescharacteristic
937C2×C4C2×C22⋊C4×C5311yescharacteristic
938C2×C4C2×C22⋊C4×C5311yescharacteristic
939C2×C4C2×C22⋊C4×C5311yescharacteristic
940C2×C4C2×C22⋊C4×C5311yescharacteristic
941C2×C4C2×C22⋊C4×C5311yescharacteristic
942C2×C4C23×C4×C5311yescharacteristic
943C2×C4C22×D4×C5311yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C53×#42112yes—
977C22C22×C22⋊C4×C5311yescharacteristic
978C22C53×#57611yescharacteristic
979C22C53×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C53×#288311yescharacteristic
1009C2C53×#289711yescharacteristic
1010C2C2×C53×#42111yescharacteristic
subgroupG/H
center, socleC22×C53C22×C22⋊C4
commutatorC2×C4C23×C4×C53
Frattini, cosocleC22×C4C24×C53
prime radicalC53×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C53 ◁ C2×C4×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#2974C2semidirect
3. C53×#2318C2semidirect
4. C53×#1521C2semidirect
5. C53×#1519C2semidirect
6. C53×#1517C2semidirect
7. C53×#1516C2semidirect
8. C53×#1514C2semidirect
9. C53×#1513C2semidirect
10. C53×#1512C2semidirect
11. C53×#1510C2semidirect
12. C53×#1507C2semidirect
13. C53×#1504C2semidirect
14. C53×#1501C2semidirect
15. C2×C53×#327C2semidirect
16. C53×#555C4semidirect
17. C53×#554C4semidirect
19. C53×#553C4semidirect
20. C53×#553C4semidirect
21. C53×#550C4semidirect
24. C53×#546C4semidirect
25. C53×#546C4semidirect
27. D42×C53C4semidirect
43. C53×#432C22semidirect
44. C53×#431C22semidirect
45. C53×#407C22semidirect
46. C53×#407C22semidirect
47. C2×C22⋊C8×C53C22semidirect
48. C2×C22⋊C8×C53C22semidirect
53. C53×#383C22semidirect
54. C53×#382C22semidirect
55. C53×#381C22semidirect
56. C53×#380C22semidirect
57. C4×C22⋊C4×C53C22semidirect
58. C2×#95×C53C22semidirect
59. C53×#328C22semidirect
60. C53×#328C22semidirect
61. C53×#328C22semidirect
62. C53×#328C22semidirect
67. C53×#327C22semidirect
68. C53×#327C22semidirect
69. C53×#327C22semidirect
70. C53×#327C22semidirect
71. C53×#327C22semidirect
72. C53×#327C22semidirect
73. C53×#327C22semidirect
74. C53×#327C22semidirect
77. C2×#41×C53C2×C4semidirect
82. C22×D4×C53C2×C4semidirect
91. C4⋊Q8×C53C2×C4semidirect
93. #127×C53C2×C4semidirect
98. #125×C53C2×C4semidirect
102. #124×C53C2×C4semidirect
113. C22⋊Q8×C53C2×C4semidirect
131. #121×C53C2×C4semidirect
132. #121×C53C2×C4semidirect
133. #121×C53C2×C4semidirect
143. C4×Q8×C53C2×C4semidirect
158. C4×D4×C53C2×C4semidirect
159. C4×D4×C53C2×C4semidirect
160. C4×D4×C53C2×C4semidirect
168. #117×C53C2×C4semidirect
172. C2×C4⋊C4×C53C2×C4semidirect
442. #17597C53direct (N × H)
495. #2974C2×C53semidirect
496. #2318C2×C53semidirect
497. #1521C2×C53semidirect
498. #1519C2×C53semidirect
499. #1517C2×C53semidirect
500. #1516C2×C53semidirect
501. #1514C2×C53semidirect
502. #1513C2×C53semidirect
503. #1512C2×C53semidirect
504. #1510C2×C53semidirect
505. #1507C2×C53semidirect
506. #1504C2×C53semidirect
507. #1501C2×C53semidirect
508. C2×#327C2×C53semidirect
521. #555C4×C53semidirect
522. #554C4×C53semidirect
524. #553C4×C53semidirect
525. #553C4×C53semidirect
526. #550C4×C53semidirect
529. #546C4×C53semidirect
530. #546C4×C53semidirect
532. D42C4×C53semidirect
548. #432C22×C53semidirect
549. #431C22×C53semidirect
550. #407C22×C53semidirect
551. #407C22×C53semidirect
552. C2×C22⋊C8C22×C53semidirect
553. C2×C22⋊C8C22×C53semidirect
558. #383C22×C53semidirect
559. #382C22×C53semidirect
560. #381C22×C53semidirect
561. #380C22×C53semidirect
562. C4×C22⋊C4C22×C53semidirect
563. C2×#95C22×C53semidirect
564. #328C22×C53semidirect
565. #328C22×C53semidirect
566. #328C22×C53semidirect
567. #328C22×C53semidirect
572. #327C22×C53semidirect
573. #327C22×C53semidirect
574. #327C22×C53semidirect
575. #327C22×C53semidirect
576. #327C22×C53semidirect
577. #327C22×C53semidirect
578. #327C22×C53semidirect
579. #327C22×C53semidirect
580. C53#17597direct (N × H)
583. C2×#41C2×C4×C53semidirect
588. C22×D4C2×C4×C53semidirect
597. C4⋊Q8C2×C4×C53semidirect
599. #127C2×C4×C53semidirect
604. #125C2×C4×C53semidirect
608. #124C2×C4×C53semidirect
619. C22⋊Q8C2×C4×C53semidirect
637. #121C2×C4×C53semidirect
638. #121C2×C4×C53semidirect
639. #121C2×C4×C53semidirect
649. C4×Q8C2×C4×C53semidirect
664. C4×D4C2×C4×C53semidirect
665. C4×D4C2×C4×C53semidirect
666. C4×D4C2×C4×C53semidirect
674. #117C2×C4×C53semidirect
678. C2×C4⋊C4C2×C4×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35192
C53×#29742
C53×#23182
C53×#15212
C53×#15192
C53×#15172
C53×#15162
C53×#15142
C53×#15132
C53×#15122
C53×#15102
C53×#15072
C53×#15042
C53×#15012
C2×C53×#3272
#1759753