Finite Group Databasebeta

← C53×#13876 #27221388

Subgroups — C53×#13876 #27221388

Order 13568.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#388C212yesmaximal
2C2×C53×#384C211yesmaximal, characteristic, complemented
3C2×C53×#380C211yesmaximal, characteristic
4C2×C53×#380C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
7C53×#1442C212yesmaximal, complemented
8C53×#1439C212yesmaximal
9C53×#1436C212yesmaximal, complemented
10C53×C4⋊#95C211yesmaximal, characteristic, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C53C2211yescharacteristic
13C22×C4⋊C4×C53C2211yescharacteristic
14C22×C4⋊C4×C53C2211yescharacteristic
15C22×C4⋊C4×C53C2212yes—
16C22×C4⋊C4×C53C2212yes—
17C22×C4⋊C4×C53C2211yescharacteristic
18C22×C4⋊C4×C53C2211yescharacteristic
19C22×C22⋊C4×C53C2212yes—
20C22×C22⋊C4×C53C2212yes—
21C22×C22⋊C4×C53C2211yescharacteristic
22C22×C22⋊C4×C53C2211yescharacteristic
23C22×C42×C53C2212yes—
24C22×C42×C53C2211yescharacteristic
25C22×C42×C53C2211yescharacteristic
26C53×#388—28no—
27C53×#384—24no—
28C53×#380—24no—
29C53×#380—24no—
30C4×C4⋊C4×C53—24no—
31C4×C22⋊C4×C53C418yescomplemented
32C2×#95×C53C2212yes—
33C2×#95×C53C2212yes—
34C2×#95×C53C2212yes—
35C2×#95×C53C2212yes—
36C2×#95×C53C2212yes—
37C2×#95×C53C2212yes—
38C2×#95×C53C2212yes—
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2211yescharacteristic
41C25×C53C2311yescharacteristic
42C23×C4×C53—22no—
43C23×C4×C53—22no—
44C23×C4×C53—22no—
45C23×C4×C53—22no—
46C23×C4×C53—22no—
47C23×C4×C53—22no—
48C23×C4×C53C2×C414yes—
49C23×C4×C53C2312yes—
50C23×C4×C53C2312yes—
51C23×C4×C53C2311yescharacteristic
52C23×C4×C53C2311yescharacteristic
53C23×C4×C53C2312yes—
54C23×C4×C53C2312yes—
55C23×C4×C53C2311yescharacteristic
56C23×C4×C53C2311yescharacteristic
57C23×C4×C53C2311yescharacteristic
58C23×C4×C53C2311yescharacteristic
59C2×C4⋊C4×C53—22no—
60C2×C4⋊C4×C53—22no—
61C2×C4⋊C4×C53—22no—
62C2×C4⋊C4×C53—24no—
63C2×C4⋊C4×C53—24no—
64C2×C4⋊C4×C53—22no—
65C2×C4⋊C4×C53—24no—
66C2×C4⋊C4×C53—22no—
67C2×C4⋊C4×C53—22no—
68C2×C4⋊C4×C53—22no—
69C2×C4⋊C4×C53—24no—
70C2×C4⋊C4×C53—22no—
71C2×C4⋊C4×C53—22no—
72C2×C4⋊C4×C53—22no—
73C2×C4⋊C4×C53—42no—
74C2×C4⋊C4×C53—42no—
75C2×C4⋊C4×C53D414yes—
76C2×C4⋊C4×C53D414yes—
77C2×C22⋊C4×C53—24no—
78C2×C22⋊C4×C53—24no—
79C2×C22⋊C4×C53—24no—
80C2×C22⋊C4×C53—24no—
81C2×C22⋊C4×C53—22no—
82C2×C22⋊C4×C53—22no—
83C2×C22⋊C4×C53—42no—
84C2×C22⋊C4×C53—42no—
85C2×C22⋊C4×C53C2×C414yes—
86C2×C22⋊C4×C53C2×C414yes—
87C2×C22⋊C4×C53D414yes—
88C2×C22⋊C4×C53Q814yes—
89C2×C42×C53—22no—
90C2×C42×C53—22no—
91C2×C42×C53—24no—
92C2×C42×C53—24no—
93C2×C42×C53—22no—
94C2×C42×C53—22no—
95C2×C42×C53—42no—
96C2×C42×C53C2×C414yes—
97C2×C42×C53C2×C414yes—
98#95×C53—24no—
99#95×C53—24no—
100#95×C53—24no—
101#95×C53—24no—
102#95×C53—24no—
103#95×C53—24no—
104#95×C53—42no—
105#95×C53C2×C414yes—
106#95×C53C2×C414yes—
107C24×C53—21no—
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53C22×C412yes—
120C24×C53C2×D412yes—
121C24×C53C2×Q812yes—
122C24×C53C2411yescharacteristic
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—21no—
158C22×C4×C53—22no—
159C22×C4×C53—28no—
160C22×C4×C53—28no—
161C22×C4×C53—28no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—44no—
177C22×C4×C53—44no—
178C22×C4×C53—44no—
179C22×C4×C53—44no—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C22×C412yes—
182C22×C4×C53C22×C412yes—
183C22×C4×C53C22×C412yes—
184C22×C4×C53C22×C412yes—
185C22×C4×C53C22×C412yes—
186C22×C4×C53C2×D414yes—
187C22×C4×C53C2×D414yes—
188C22×C4×C53C2×D412yes—
189C22×C4×C53C2×D412yes—
190C22×C4×C53C2×D412yes—
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2×Q812yes—
193C22×C4×C53C2×Q812yes—
194C22×C4×C53#4112yes—
195C22×C4×C53#4112yes—
196C22×C4×C53#4112yes—
197C22×C4×C53#4112yes—
198C22×C4×C53#4112yes—
199C22×C4×C53#4112yes—
200C4⋊C4×C53—28no—
201C4⋊C4×C53—28no—
202C4⋊C4×C53—48no—
203C4⋊C4×C53—48no—
204C4⋊C4×C53—44no—
205C4⋊C4×C53—44no—
206C22⋊C4×C53—28no—
207C22⋊C4×C53—48no—
208C22⋊C4×C53—48no—
209C22⋊C4×C53C4⋊C4116yescomplemented
210C42×C53—28no—
211C42×C53—28no—
212C42×C53—48no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—22no—
218C23×C53—22no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53C2×C4⋊C414yes—
248C23×C53C23×C411yescharacteristic
249C23×C53C22×D411yescharacteristic
250C23×C53C22×D411yescharacteristic
251C23×C53C22×D411yescharacteristic
252C23×C53C22×Q811yescharacteristic
253C23×C53C2×#4111yescharacteristic
254C23×C53C2×#4111yescharacteristic
255C23×C53C2×#4111yescharacteristic
256C23×C53C2×#4111yescharacteristic
257C23×C53C2×#4111yescharacteristic
258C23×C53C2×#4111yescharacteristic
259C23×C53H(5,𝔽2)11yescharacteristic
260C23×C53H(5,𝔽2)11yescharacteristic
261C23×C532−1+411yescharacteristic
262C23×C532−1+411yescharacteristic
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—24no—
288C2×C4×C53—24no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—41no—
303C2×C4×C53—42no—
304C2×C4×C53—41no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—416no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53C2×C4⋊C414yes—
325C2×C4×C53C2×C4⋊C414yes—
326C2×C4×C53#11714yes—
327C2×C4×C53#11714yes—
328C2×C4×C53C4×D414yes—
329C2×C4×C53C4×D414yes—
330C2×C4×C53#12114yes—
331C2×C4×C53#12314yes—
332C2×C4×C53#12414yes—
333C2×C4×C53#12614yes—
334#13876C5311yesmaximal, characteristic, direct product factor, Sylow
335C22×C53—24no—
336C22×C53—24no—
337C22×C53—24no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53C22×C4⋊C411yescharacteristic
351C22×C53C2×#11711yescharacteristic
352C22×C53C2×#11711yescharacteristic
353C22×C53C2×C4×D411yescharacteristic
354C22×C53C2×C4×D411yescharacteristic
355C22×C53#52011yescharacteristic
356C22×C53#52011yescharacteristic
357C22×C53C2×#12111yescharacteristic
358C22×C53C2×#12311yescharacteristic
359C22×C53C2×#12411yescharacteristic
360C22×C53C2×#12611yescharacteristic
361C22×C53#53211yescharacteristic
362C22×C53#53211yescharacteristic
363C22×C53#53311yescharacteristic
364C22×C53#53311yescharacteristic
365C22×C53#54011yescharacteristic
366C22×C53#54111yescharacteristic
367C22×C53#54211yescharacteristic
368C22×C53#54211yescharacteristic
369C22×C53D4211yescharacteristic
370C22×C53D4211yescharacteristic
371C22×C53#54611yescharacteristic
372C22×C53#54711yescharacteristic
373C22×C53#54711yescharacteristic
374C22×C53#54711yescharacteristic
375C22×C53#54811yescharacteristic
376C22×C53D4×Q811yescharacteristic
377C22×C53D4×Q811yescharacteristic
378C22×C53#55011yescharacteristic
379C22×C53#55211yescharacteristic
380C22×C53#55311yescharacteristic
381C22×C53#55411yescharacteristic
382C22×C53#55411yescharacteristic
383C22×C53#55511yescharacteristic
384C22×C53#55611yescharacteristic
385C4×C53—24no—
386C4×C53—24no—
387C4×C53—24no—
388C4×C53—42no—
389C4×C53—44no—
390C4×C53—44no—
391C4×C53—42no—
392C4×C53—82no—
393C4×C53—82no—
394C4×C53#38818yescomplemented
395C2×#388C2×C5312yes—
396C2×#384C2×C5311yescharacteristic, complemented
397C2×#380C2×C5311yescharacteristic
398C2×#380C2×C5311yescharacteristic
399C2×C4×C4⋊C4C2×C5311yescharacteristic, complemented
400C2×C4×C22⋊C4C2×C5311yescharacteristic
401#1442C2×C5312yescomplemented
402#1439C2×C5312yes—
403#1436C2×C5312yescomplemented
404C4⋊#95C2×C5311yescharacteristic, complemented
405C4⋊#95C2×C5311yescharacteristic, complemented
406C2×C53—44no—
407C2×C53#228511yescharacteristic
408C2×C53C2×#38811yescharacteristic
409C2×C53#231411yescharacteristic
410C2×C53D4×C4⋊C411yescharacteristic
411C2×C53D4×C4⋊C411yescharacteristic
412C2×C53#235211yescharacteristic
413C2×C53#235411yescharacteristic
414C2×C53#242211yescharacteristic
415C2×C53#242311yescharacteristic
416C2×C53#242811yescharacteristic
417C2×C53#242911yescharacteristic
418C2×C53#249111yescharacteristic
419C2×C53#249211yescharacteristic
420C2×C53#249611yescharacteristic
421C2×C53#249711yescharacteristic
422C24×C4C22×C5311yescharacteristic
423C22×C4⋊C4C22×C5311yescharacteristic
424C22×C4⋊C4C22×C5311yescharacteristic
425C22×C4⋊C4C22×C5312yes—
426C22×C4⋊C4C22×C5312yes—
427C22×C4⋊C4C22×C5311yescharacteristic
428C22×C4⋊C4C22×C5311yescharacteristic
429C22×C22⋊C4C22×C5312yes—
430C22×C22⋊C4C22×C5312yes—
431C22×C22⋊C4C22×C5311yescharacteristic
432C22×C22⋊C4C22×C5311yescharacteristic
433C22×C42C22×C5312yes—
434C22×C42C22×C5311yescharacteristic
435C22×C42C22×C5311yescharacteristic
436#388—28no—
437#384—24no—
438#380—24no—
439#380—24no—
440C4×C4⋊C4—24no—
441C4×C22⋊C4C4×C5318yescomplemented
442C2×#95C22×C5312yes—
443C2×#95C22×C5312yes—
444C2×#95C22×C5312yes—
445C2×#95C22×C5312yes—
446C2×#95C22×C5312yes—
447C2×#95C22×C5312yes—
448C2×#95C22×C5312yes—
449C2×#95C22×C5311yescharacteristic
450C2×#95C22×C5311yescharacteristic
451C53#1387611yescharacteristic, direct product factor, Sylow
452C25C23×C5311yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4C2×C4×C5314yes—
460C23×C4C23×C5312yes—
461C23×C4C23×C5312yes—
462C23×C4C23×C5311yescharacteristic
463C23×C4C23×C5311yescharacteristic
464C23×C4C23×C5312yes—
465C23×C4C23×C5312yes—
466C23×C4C23×C5311yescharacteristic
467C23×C4C23×C5311yescharacteristic
468C23×C4C23×C5311yescharacteristic
469C23×C4C23×C5311yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4D4×C5314yes—
487C2×C4⋊C4D4×C5314yes—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4C2×C4×C5314yes—
497C2×C22⋊C4C2×C4×C5314yes—
498C2×C22⋊C4D4×C5314yes—
499C2×C22⋊C4Q8×C5314yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—24no—
505C2×C42—24no—
506C2×C42—42no—
507C2×C42C2×C4×C5314yes—
508C2×C42C2×C4×C5314yes—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—24no—
515#95—42no—
516#95C2×C4×C5314yes—
517#95C2×C4×C5314yes—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C22×C4×C5312yes—
531C24C2×D4×C5312yes—
532C24C2×Q8×C5312yes—
533C24C24×C5311yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C22×C4×C5312yes—
592C22×C4C22×C4×C5312yes—
593C22×C4C22×C4×C5312yes—
594C22×C4C22×C4×C5312yes—
595C22×C4C22×C4×C5312yes—
596C22×C4C22×C4×C5312yes—
597C22×C4C2×D4×C5314yes—
598C22×C4C2×D4×C5314yes—
599C22×C4C2×D4×C5312yes—
600C22×C4C2×D4×C5312yes—
601C22×C4C2×D4×C5312yes—
602C22×C4C2×D4×C5312yes—
603C22×C4C2×Q8×C5312yes—
604C22×C4C2×Q8×C5312yes—
605C22×C4#41×C5312yes—
606C22×C4#41×C5312yes—
607C22×C4#41×C5312yes—
608C22×C4#41×C5312yes—
609C22×C4#41×C5312yes—
610C22×C4#41×C5312yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4C4⋊C4×C53116yescomplemented
621C42—28no—
622C42—28no—
623C42—48no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊C4×C5314yes—
659C23C23×C4×C5311yescharacteristic
660C23C22×D4×C5311yescharacteristic
661C23C22×D4×C5311yescharacteristic
662C23C22×D4×C5311yescharacteristic
663C23C22×Q8×C5311yescharacteristic
664C23C2×#41×C5311yescharacteristic
665C23C2×#41×C5311yescharacteristic
666C23C2×#41×C5311yescharacteristic
667C23C2×#41×C5311yescharacteristic
668C23C2×#41×C5311yescharacteristic
669C23C2×#41×C5311yescharacteristic
670C23H(5,𝔽2)×C5311yescharacteristic
671C23H(5,𝔽2)×C5311yescharacteristic
672C232−1+4×C5311yescharacteristic
673C232−1+4×C5311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C2×C4⋊C4×C5314yes—
736C2×C4C2×C4⋊C4×C5314yes—
737C2×C4#117×C5314yes—
738C2×C4#117×C5314yes—
739C2×C4C4×D4×C5314yes—
740C2×C4C4×D4×C5314yes—
741C2×C4#121×C5314yes—
742C2×C4#123×C5314yes—
743C2×C4#124×C5314yes—
744C2×C4#126×C5314yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊C4×C5311yescharacteristic
761C22C2×#117×C5311yescharacteristic
762C22C2×#117×C5311yescharacteristic
763C22C2×C4×D4×C5311yescharacteristic
764C22C2×C4×D4×C5311yescharacteristic
765C22C53×#52011yescharacteristic
766C22C53×#52011yescharacteristic
767C22C2×#121×C5311yescharacteristic
768C22C2×#123×C5311yescharacteristic
769C22C2×#124×C5311yescharacteristic
770C22C2×#126×C5311yescharacteristic
771C22C53×#53211yescharacteristic
772C22C53×#53211yescharacteristic
773C22C53×#53311yescharacteristic
774C22C53×#53311yescharacteristic
775C22C53×#54011yescharacteristic
776C22C53×#54111yescharacteristic
777C22C53×#54211yescharacteristic
778C22C53×#54211yescharacteristic
779C22D42×C5311yescharacteristic
780C22D42×C5311yescharacteristic
781C22C53×#54611yescharacteristic
782C22C53×#54711yescharacteristic
783C22C53×#54711yescharacteristic
784C22C53×#54711yescharacteristic
785C22C53×#54811yescharacteristic
786C22D4×Q8×C5311yescharacteristic
787C22D4×Q8×C5311yescharacteristic
788C22C53×#55011yescharacteristic
789C22C53×#55211yescharacteristic
790C22C53×#55311yescharacteristic
791C22C53×#55411yescharacteristic
792C22C53×#55411yescharacteristic
793C22C53×#55511yescharacteristic
794C22C53×#55611yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—44no—
799C4—42no—
800C4—42no—
801C4—44no—
802C4—82no—
803C4—82no—
804C4C53×#38818yescomplemented
805C2—44no—
806C2C53×#228511yescharacteristic
807C2C2×C53×#38811yescharacteristic
808C2C53×#231411yescharacteristic
809C2D4×C4⋊C4×C5311yescharacteristic
810C2D4×C4⋊C4×C5311yescharacteristic
811C2C53×#235211yescharacteristic
812C2C53×#235411yescharacteristic
813C2C53×#242211yescharacteristic
814C2C53×#242311yescharacteristic
815C2C53×#242811yescharacteristic
816C2C53×#242911yescharacteristic
817C2C53×#249111yescharacteristic
818C2C53×#249211yescharacteristic
819C2C53×#249611yescharacteristic
820C2C53×#249711yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC25×C53C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C53×#384C2semidirect
5. C2×C4×C4⋊C4×C53C2semidirect
7. C53×#1442C2semidirect
9. C53×#1436C2semidirect
10. C53×C4⋊#95C2semidirect
11. C53×C4⋊#95C2semidirect
31. C4×C22⋊C4×C53C4semidirect
209. C22⋊C4×C53C4⋊C4semidirect
334. #13876C53direct (N × H)
394. C4×C53#388semidirect
396. C2×#384C2×C53semidirect
399. C2×C4×C4⋊C4C2×C53semidirect
401. #1442C2×C53semidirect
403. #1436C2×C53semidirect
404. C4⋊#95C2×C53semidirect
405. C4⋊#95C2×C53semidirect
441. C4×C22⋊C4C4×C53semidirect
451. C53#13876direct (N × H)
620. C22⋊C4C4⋊C4×C53semidirect
804. C4C53×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3882
C2×C53×#3842
C2×C53×#3802
C2×C4×C4⋊C4×C532
C2×C4×C22⋊C4×C532
C53×#14422
C53×#14392
C53×#14362
C53×C4⋊#952
#1387653