Finite Group Databasebeta

← C53×#14408 #27221920

Subgroups — C53×#14408 #27221920

Order 13568.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#389C211yesmaximal, characteristic, complemented
2C2×C53×#388C211yesmaximal, characteristic
3C2×C53×#388C211yesmaximal, characteristic
4C2×C53×#385C211yesmaximal, characteristic
5C2×C53×#380C211yesmaximal, characteristic
6C53×#1444C211yesmaximal, characteristic, complemented
7C53×#1442C211yesmaximal, characteristic, complemented
8C53×#1441C211yesmaximal, characteristic, complemented
9C53×#1441C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic
11C53×#1439C211yesmaximal, characteristic
12C53×#1436C211yesmaximal, characteristic, complemented
13C53×#1436C211yesmaximal, characteristic, complemented
14C53×C4⋊#95C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C53C2211yescharacteristic
17C22×C4⋊C4×C53C2211yescharacteristic
18C22×C4⋊C4×C53C2211yescharacteristic
19C22×C4⋊C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C4⋊C4×C53C2211yescharacteristic
22C22×C4⋊C4×C53C2211yescharacteristic
23C22×C4⋊C4×C53C2211yescharacteristic
24C22×C4⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2211yescharacteristic
29C22×C22⋊C4×C53C2211yescharacteristic
30C22×C22⋊C4×C53C2211yescharacteristic
31C22×C42×C53C2211yescharacteristic
32C22×C42×C53C2211yescharacteristic
33C53×#389—24no—
34C53×#388—24no—
35C53×#388—24no—
36C53×#385C418yescomplemented
37C53×#380—24no—
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2211yescharacteristic
41C2×#95×C53C2211yescharacteristic
42C2×#95×C53C2211yescharacteristic
43C2×#95×C53C2211yescharacteristic
44C2×#95×C53C2211yescharacteristic
45C2×#95×C53C2211yescharacteristic
46C2×#95×C53C2211yescharacteristic
47C2×#95×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C25×C53C2311yescharacteristic
57C23×C4×C53—22no—
58C23×C4×C53—22no—
59C23×C4×C53—41no—
60C23×C4×C53—41no—
61C23×C4×C53—41no—
62C23×C4×C53—41no—
63C23×C4×C53C2×C414yes—
64C23×C4×C53C2311yescharacteristic
65C23×C4×C53C2311yescharacteristic
66C23×C4×C53C2311yescharacteristic
67C23×C4×C53C2311yescharacteristic
68C23×C4×C53C2311yescharacteristic
69C23×C4×C53C2311yescharacteristic
70C23×C4×C53C2311yescharacteristic
71C23×C4×C53C2311yescharacteristic
72C23×C4×C53C2311yescharacteristic
73C23×C4×C53C2311yescharacteristic
74C23×C4×C53C2311yescharacteristic
75C23×C4×C53C2311yescharacteristic
76C23×C4×C53C2311yescharacteristic
77C23×C4×C53C2311yescharacteristic
78C2×C4⋊C4×C53—22no—
79C2×C4⋊C4×C53—22no—
80C2×C4⋊C4×C53—22no—
81C2×C4⋊C4×C53—22no—
82C2×C4⋊C4×C53—22no—
83C2×C4⋊C4×C53—22no—
84C2×C4⋊C4×C53—22no—
85C2×C4⋊C4×C53—22no—
86C2×C4⋊C4×C53—22no—
87C2×C4⋊C4×C53—41no—
88C2×C4⋊C4×C53—41no—
89C2×C4⋊C4×C53—41no—
90C2×C4⋊C4×C53—41no—
91C2×C4⋊C4×C53—41no—
92C2×C4⋊C4×C53—41no—
93C2×C4⋊C4×C53—41no—
94C2×C4⋊C4×C53—41no—
95C2×C4⋊C4×C53—41no—
96C2×C4⋊C4×C53—41no—
97C2×C4⋊C4×C53—41no—
98C2×C4⋊C4×C53—41no—
99C2×C4⋊C4×C53C2×C414yes—
100C2×C4⋊C4×C53C2×C414yes—
101C2×C4⋊C4×C53D414yes—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—22no—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—41no—
111C2×C22⋊C4×C53—41no—
112C2×C22⋊C4×C53—41no—
113C2×C22⋊C4×C53—41no—
114C2×C22⋊C4×C53—41no—
115C2×C22⋊C4×C53—41no—
116C2×C22⋊C4×C53C2×C414yes—
117C2×C22⋊C4×C53C2×C414yes—
118C2×C22⋊C4×C53D414yes—
119C2×C22⋊C4×C53Q814yes—
120C2×C42×C53—22no—
121C2×C42×C53—22no—
122C2×C42×C53—22no—
123C2×C42×C53—22no—
124C2×C42×C53—41no—
125C2×C42×C53—41no—
126#95×C53—22no—
127#95×C53—22no—
128#95×C53—22no—
129#95×C53—22no—
130#95×C53—22no—
131#95×C53—22no—
132#95×C53—22no—
133#95×C53—22no—
134#95×C53—22no—
135#95×C53—22no—
136#95×C53—41no—
137#95×C53—41no—
138#95×C53—41no—
139#95×C53—41no—
140#95×C53—41no—
141#95×C53—41no—
142#95×C53C2×C414yes—
143#95×C53C2×C414yes—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53C22×C412yes—
157C24×C53C2×D412yes—
158C24×C53C2×Q812yes—
159C24×C53C2411yescharacteristic
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—28no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—44no—
244C22×C4×C53—44no—
245C22×C4×C53—44no—
246C22×C4×C53—44no—
247C22×C4×C53—44no—
248C22×C4×C53—44no—
249C22×C4×C53C22×C412yes—
250C22×C4×C53C22×C412yes—
251C22×C4×C53C22×C412yes—
252C22×C4×C53C22×C412yes—
253C22×C4×C53C22×C412yes—
254C22×C4×C53C22×C412yes—
255C22×C4×C53C2×D412yes—
256C22×C4×C53C2×D412yes—
257C22×C4×C53C2×D412yes—
258C22×C4×C53C2×D412yes—
259C22×C4×C53C2×D412yes—
260C22×C4×C53C2×Q812yes—
261C22×C4×C53C2×Q812yes—
262C22×C4×C53#4112yes—
263C22×C4×C53#4112yes—
264C22×C4×C53#4112yes—
265C4⋊C4×C53—28no—
266C4⋊C4×C53—44no—
267C4⋊C4×C53—44no—
268C4⋊C4×C53—44no—
269C4⋊C4×C53—44no—
270C4⋊C4×C53—44no—
271C4⋊C4×C53—44no—
272C4⋊C4×C53—44no—
273C22⋊C4×C53—44no—
274C22⋊C4×C53—44no—
275C22⋊C4×C53—44no—
276C22⋊C4×C53—44no—
277C22⋊C4×C53—44no—
278C22⋊C4×C53C4⋊C4116yescomplemented
279C42×C53—44no—
280C42×C53—44no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53C2×C4⋊C414yes—
316C23×C53C23×C411yescharacteristic
317C23×C53C22×D411yescharacteristic
318C23×C53C22×D411yescharacteristic
319C23×C53C22×Q811yescharacteristic
320C23×C53C2×#4111yescharacteristic
321C23×C53C2×#4111yescharacteristic
322C23×C53C2×#4111yescharacteristic
323C23×C53H(5,𝔽2)11yescharacteristic
324C23×C53H(5,𝔽2)11yescharacteristic
325C23×C53H(5,𝔽2)11yescharacteristic
326C23×C53H(5,𝔽2)11yescharacteristic
327C23×C53H(5,𝔽2)11yescharacteristic
328C23×C532−1+411yescharacteristic
329C23×C532−1+411yescharacteristic
330C23×C532−1+411yescharacteristic
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—22no—
370C2×C4×C53—416no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—41no—
393C2×C4×C53—41no—
394C2×C4×C53—41no—
395C2×C4×C53—41no—
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—41no—
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—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53C2×C4⋊C414yes—
428C2×C4×C53C2×C4⋊C414yes—
429C2×C4×C53C4×D414yes—
430#14408C5311yesmaximal, characteristic, direct product factor, Sylow
431C22×C53—24no—
432C22×C53—24no—
433C22×C53—24no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—42no—
437C22×C53—42no—
438C22×C53—42no—
439C22×C53—42no—
440C22×C53—42no—
441C22×C53—42no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53C22×C4⋊C411yescharacteristic
447C22×C53C2×C4×D411yescharacteristic
448C22×C53C4×#4111yescharacteristic
449C22×C53#51811yescharacteristic
450C22×C53#51811yescharacteristic
451C22×C53#51911yescharacteristic
452C22×C53#52011yescharacteristic
453C22×C53#53411yescharacteristic
454C22×C53#53511yescharacteristic
455C22×C53#53711yescharacteristic
456C22×C53#53711yescharacteristic
457C22×C53#53811yescharacteristic
458C22×C53#53811yescharacteristic
459C22×C53#53811yescharacteristic
460C22×C53#53911yescharacteristic
461C22×C53#54011yescharacteristic
462C22×C53#54211yescharacteristic
463C22×C53#54411yescharacteristic
464C22×C53#54411yescharacteristic
465C22×C53D4211yescharacteristic
466C22×C53#54611yescharacteristic
467C22×C53#54611yescharacteristic
468C22×C53#54711yescharacteristic
469C22×C53#54711yescharacteristic
470C22×C53#54811yescharacteristic
471C22×C53D4×Q811yescharacteristic
472C22×C53#55211yescharacteristic
473C22×C53#55411yescharacteristic
474C22×C53#55411yescharacteristic
475C22×C53#55411yescharacteristic
476C22×C53#55611yescharacteristic
477C22×C53#56211yescharacteristic
478C22×C53#56211yescharacteristic
479C22×C53#56311yescharacteristic
480C22×C53#56311yescharacteristic
481C4×C53—24no—
482C4×C53—24no—
483C4×C53—24no—
484C4×C53—42no—
485C4×C53—42no—
486C4×C53—42no—
487C4×C53—42no—
488C4×C53—42no—
489C4×C53—42no—
490C4×C53—42no—
491C4×C53—81no—
492C4×C53—81no—
493C4×C53—81no—
494C4×C53—81no—
495C2×#389C2×C5311yescharacteristic, complemented
496C2×#388C2×C5311yescharacteristic
497C2×#388C2×C5311yescharacteristic
498C2×#385C2×C5311yescharacteristic
499C2×#380C2×C5311yescharacteristic
500#1444C2×C5311yescharacteristic, complemented
501#1442C2×C5311yescharacteristic, complemented
502#1441C2×C5311yescharacteristic, complemented
503#1441C2×C5311yescharacteristic, complemented
504#1439C2×C5311yescharacteristic
505#1439C2×C5311yescharacteristic
506#1436C2×C5311yescharacteristic, complemented
507#1436C2×C5311yescharacteristic, complemented
508C4⋊#95C2×C5311yescharacteristic, complemented
509C22⋊#95C2×C5311yescharacteristic
510C2×C53—44no—
511C2×C53#231611yescharacteristic
512C2×C53#232111yescharacteristic
513C2×C53#233511yescharacteristic
514C2×C53D4×C4⋊C411yescharacteristic
515C2×C53#234911yescharacteristic
516C2×C53#236211yescharacteristic
517C2×C53#237811yescharacteristic
518C2×C53#267111yescharacteristic
519C2×C53#267611yescharacteristic
520C2×C53#269511yescharacteristic
521C2×C53#271511yescharacteristic
522C2×C53#272011yescharacteristic
523C2×C53#272911yescharacteristic
524C2×C53#276811yescharacteristic
525C2×C53#278811yescharacteristic
526C24×C4C22×C5311yescharacteristic
527C22×C4⋊C4C22×C5311yescharacteristic
528C22×C4⋊C4C22×C5311yescharacteristic
529C22×C4⋊C4C22×C5311yescharacteristic
530C22×C4⋊C4C22×C5311yescharacteristic
531C22×C4⋊C4C22×C5311yescharacteristic
532C22×C4⋊C4C22×C5311yescharacteristic
533C22×C4⋊C4C22×C5311yescharacteristic
534C22×C4⋊C4C22×C5311yescharacteristic
535C22×C22⋊C4C22×C5311yescharacteristic
536C22×C22⋊C4C22×C5311yescharacteristic
537C22×C22⋊C4C22×C5311yescharacteristic
538C22×C22⋊C4C22×C5311yescharacteristic
539C22×C22⋊C4C22×C5311yescharacteristic
540C22×C22⋊C4C22×C5311yescharacteristic
541C22×C42C22×C5311yescharacteristic
542C22×C42C22×C5311yescharacteristic
543#389—24no—
544#388—24no—
545#388—24no—
546#385C4×C5318yescomplemented
547#380—24no—
548C2×#95C22×C5311yescharacteristic
549C2×#95C22×C5311yescharacteristic
550C2×#95C22×C5311yescharacteristic
551C2×#95C22×C5311yescharacteristic
552C2×#95C22×C5311yescharacteristic
553C2×#95C22×C5311yescharacteristic
554C2×#95C22×C5311yescharacteristic
555C2×#95C22×C5311yescharacteristic
556C2×#95C22×C5311yescharacteristic
557C2×#95C22×C5311yescharacteristic
558C2×#95C22×C5311yescharacteristic
559C2×#95C22×C5311yescharacteristic
560C2×#95C22×C5311yescharacteristic
561C2×#95C22×C5311yescharacteristic
562C2×#95C22×C5311yescharacteristic
563C2×#95C22×C5311yescharacteristic
564C2×#95C22×C5311yescharacteristic
565C2×#95C22×C5311yescharacteristic
566C53#1440811yescharacteristic, direct product factor, Sylow
567C25C23×C5311yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C5314yes—
575C23×C4C23×C5311yescharacteristic
576C23×C4C23×C5311yescharacteristic
577C23×C4C23×C5311yescharacteristic
578C23×C4C23×C5311yescharacteristic
579C23×C4C23×C5311yescharacteristic
580C23×C4C23×C5311yescharacteristic
581C23×C4C23×C5311yescharacteristic
582C23×C4C23×C5311yescharacteristic
583C23×C4C23×C5311yescharacteristic
584C23×C4C23×C5311yescharacteristic
585C23×C4C23×C5311yescharacteristic
586C23×C4C23×C5311yescharacteristic
587C23×C4C23×C5311yescharacteristic
588C23×C4C23×C5311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×C4×C5314yes—
611C2×C4⋊C4C2×C4×C5314yes—
612C2×C4⋊C4D4×C5314yes—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4C2×C4×C5314yes—
628C2×C22⋊C4C2×C4×C5314yes—
629C2×C22⋊C4D4×C5314yes—
630C2×C22⋊C4Q8×C5314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42—41no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C5314yes—
654#95C2×C4×C5314yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C5312yes—
668C24C2×D4×C5312yes—
669C24C2×Q8×C5312yes—
670C24C24×C5311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—28no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C5312yes—
761C22×C4C22×C4×C5312yes—
762C22×C4C22×C4×C5312yes—
763C22×C4C22×C4×C5312yes—
764C22×C4C22×C4×C5312yes—
765C22×C4C22×C4×C5312yes—
766C22×C4C2×D4×C5312yes—
767C22×C4C2×D4×C5312yes—
768C22×C4C2×D4×C5312yes—
769C22×C4C2×D4×C5312yes—
770C22×C4C2×D4×C5312yes—
771C22×C4C2×Q8×C5312yes—
772C22×C4C2×Q8×C5312yes—
773C22×C4#41×C5312yes—
774C22×C4#41×C5312yes—
775C22×C4#41×C5312yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C53116yescomplemented
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C5314yes—
827C23C23×C4×C5311yescharacteristic
828C23C22×D4×C5311yescharacteristic
829C23C22×D4×C5311yescharacteristic
830C23C22×Q8×C5311yescharacteristic
831C23C2×#41×C5311yescharacteristic
832C23C2×#41×C5311yescharacteristic
833C23C2×#41×C5311yescharacteristic
834C23H(5,𝔽2)×C5311yescharacteristic
835C23H(5,𝔽2)×C5311yescharacteristic
836C23H(5,𝔽2)×C5311yescharacteristic
837C23H(5,𝔽2)×C5311yescharacteristic
838C23H(5,𝔽2)×C5311yescharacteristic
839C232−1+4×C5311yescharacteristic
840C232−1+4×C5311yescharacteristic
841C232−1+4×C5311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
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—41no—
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—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C5314yes—
939C2×C4C2×C4⋊C4×C5314yes—
940C2×C4C4×D4×C5314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C5311yescharacteristic
957C22C2×C4×D4×C5311yescharacteristic
958C22C4×#41×C5311yescharacteristic
959C22C53×#51811yescharacteristic
960C22C53×#51811yescharacteristic
961C22C53×#51911yescharacteristic
962C22C53×#52011yescharacteristic
963C22C53×#53411yescharacteristic
964C22C53×#53511yescharacteristic
965C22C53×#53711yescharacteristic
966C22C53×#53711yescharacteristic
967C22C53×#53811yescharacteristic
968C22C53×#53811yescharacteristic
969C22C53×#53811yescharacteristic
970C22C53×#53911yescharacteristic
971C22C53×#54011yescharacteristic
972C22C53×#54211yescharacteristic
973C22C53×#54411yescharacteristic
974C22C53×#54411yescharacteristic
975C22D42×C5311yescharacteristic
976C22C53×#54611yescharacteristic
977C22C53×#54611yescharacteristic
978C22C53×#54711yescharacteristic
979C22C53×#54711yescharacteristic
980C22C53×#54811yescharacteristic
981C22D4×Q8×C5311yescharacteristic
982C22C53×#55211yescharacteristic
983C22C53×#55411yescharacteristic
984C22C53×#55411yescharacteristic
985C22C53×#55411yescharacteristic
986C22C53×#55611yescharacteristic
987C22C53×#56211yescharacteristic
988C22C53×#56211yescharacteristic
989C22C53×#56311yescharacteristic
990C22C53×#56311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C53×#231611yescharacteristic
1007C2C53×#232111yescharacteristic
1008C2C53×#233511yescharacteristic
1009C2D4×C4⋊C4×C5311yescharacteristic
1010C2C53×#234911yescharacteristic
1011C2C53×#236211yescharacteristic
1012C2C53×#237811yescharacteristic
1013C2C53×#267111yescharacteristic
1014C2C53×#267611yescharacteristic
1015C2C53×#269511yescharacteristic
1016C2C53×#271511yescharacteristic
1017C2C53×#272011yescharacteristic
1018C2C53×#272911yescharacteristic
1019C2C53×#276811yescharacteristic
1020C2C53×#278811yescharacteristic
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
1. C2×C53×#389C2semidirect
6. C53×#1444C2semidirect
7. C53×#1442C2semidirect
8. C53×#1441C2semidirect
9. C53×#1441C2semidirect
12. C53×#1436C2semidirect
13. C53×#1436C2semidirect
14. C53×C4⋊#95C2semidirect
36. C53×#385C4semidirect
278. C22⋊C4×C53C4⋊C4semidirect
430. #14408C53direct (N × H)
495. C2×#389C2×C53semidirect
500. #1444C2×C53semidirect
501. #1442C2×C53semidirect
502. #1441C2×C53semidirect
503. #1441C2×C53semidirect
506. #1436C2×C53semidirect
507. #1436C2×C53semidirect
508. C4⋊#95C2×C53semidirect
546. #385C4×C53semidirect
566. C53#14408direct (N × H)
789. C22⋊C4C4⋊C4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3892
C2×C53×#3882
C2×C53×#3852
C2×C53×#3802
C53×#14442
C53×#14422
C53×#14412
C53×#14392
C53×#14362
C53×C4⋊#952
C53×C22⋊#952
#1440853