Finite Group Databasebeta

← C53×#14488 #27222000

Subgroups — C53×#14488 #27222000

Order 13568.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#388C211yesmaximal, characteristic
2C2×C53×#388C211yesmaximal, characteristic
3C2×C53×#385C211yesmaximal, characteristic
4C53×#1444C211yesmaximal, characteristic, complemented
5C53×#1442C211yesmaximal, characteristic, complemented
6C53×#1442C211yesmaximal, characteristic, complemented
7C53×#1441C211yesmaximal, characteristic, complemented
8C53×#1439C211yesmaximal, characteristic
9C53×#1439C211yesmaximal, characteristic
10C53×#1436C211yesmaximal, characteristic, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C53×C4⋊#95C211yesmaximal, characteristic, complemented
13C53×#1434C211yesmaximal, characteristic, complemented
14C53×C22⋊#95C211yesmaximal, characteristic
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×C22⋊C4×C53C2211yescharacteristic
24C22×C22⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2211yescharacteristic
29C22×C42×C53C2211yescharacteristic
30C22×C42×C53C2211yescharacteristic
31C53×#388—24no—
32C53×#388C418yescomplemented
33C53×#385—24no—
34C2×#95×C53C2211yescharacteristic
35C2×#95×C53C2211yescharacteristic
36C2×#95×C53C2211yescharacteristic
37C2×#95×C53C2211yescharacteristic
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
54C25×C53C2311yescharacteristic
55C23×C4×C53—22no—
56C23×C4×C53—22no—
57C23×C4×C53—22no—
58C23×C4×C53—41no—
59C23×C4×C53—41no—
60C23×C4×C53—41no—
61C23×C4×C53—41no—
62C23×C4×C53C2311yescharacteristic
63C23×C4×C53C2311yescharacteristic
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
76C2×C4⋊C4×C53—22no—
77C2×C4⋊C4×C53—22no—
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—41no—
84C2×C4⋊C4×C53—41no—
85C2×C4⋊C4×C53—41no—
86C2×C4⋊C4×C53—41no—
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×C53C2×C414yescomplemented
94C2×C22⋊C4×C53—22no—
95C2×C22⋊C4×C53—22no—
96C2×C22⋊C4×C53—22no—
97C2×C22⋊C4×C53—22no—
98C2×C22⋊C4×C53—22no—
99C2×C22⋊C4×C53—41no—
100C2×C22⋊C4×C53—41no—
101C2×C22⋊C4×C53—41no—
102C2×C22⋊C4×C53—41no—
103C2×C22⋊C4×C53—41no—
104C2×C22⋊C4×C53—41no—
105C2×C22⋊C4×C53—41no—
106C2×C22⋊C4×C53—41no—
107C2×C22⋊C4×C53C2×C414yes—
108C2×C22⋊C4×C53C2×C414yes—
109C2×C22⋊C4×C53C2×C414yes—
110C2×C22⋊C4×C53D414yes—
111C2×C22⋊C4×C53Q814yes—
112C2×C42×C53—22no—
113C2×C42×C53—22no—
114C2×C42×C53—41no—
115C2×C42×C53—41no—
116C2×C42×C53—41no—
117C2×C42×C53C2×C414yescomplemented
118#95×C53—22no—
119#95×C53—22no—
120#95×C53—22no—
121#95×C53—22no—
122#95×C53—22no—
123#95×C53—22no—
124#95×C53—22no—
125#95×C53—41no—
126#95×C53—41no—
127#95×C53—41no—
128#95×C53—41no—
129#95×C53—41no—
130#95×C53—41no—
131#95×C53—41no—
132#95×C53—41no—
133#95×C53—41no—
134#95×C53—41no—
135#95×C53—41no—
136#95×C53C2×C414yescomplemented
137#95×C53C2×C414yescomplemented
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—21no—
142C24×C53—21no—
143C24×C53—21no—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53C22×C412yes—
151C24×C53C2×D412yes—
152C24×C53C2×Q812yes—
153C24×C53C2411yescharacteristic
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
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—21no—
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—44no—
239C22×C4×C53—44no—
240C22×C4×C53—44no—
241C22×C4×C53—44no—
242C22×C4×C53—44no—
243C22×C4×C53—44no—
244C22×C4×C53—44no—
245C22×C4×C53C22×C412yes—
246C22×C4×C53C22×C412yes—
247C22×C4×C53C22×C412yes—
248C22×C4×C53C22×C412yes—
249C22×C4×C53C22×C412yes—
250C22×C4×C53C22×C412yes—
251C22×C4×C53C2×D412yes—
252C22×C4×C53C2×D412yes—
253C22×C4×C53C2×Q812yes—
254C22×C4×C53C2×Q812yes—
255C22×C4×C53#4112yes—
256C22×C4×C53#4112yes—
257C22×C4×C53#4112yes—
258C22×C4×C53#4112yes—
259C4⋊C4×C53—44no—
260C4⋊C4×C53—44no—
261C4⋊C4×C53—44no—
262C4⋊C4×C53—44no—
263C4⋊C4×C53—44no—
264C4⋊C4×C53—44no—
265C22⋊C4×C53—44no—
266C22⋊C4×C53—44no—
267C22⋊C4×C53—44no—
268C22⋊C4×C53—44no—
269C22⋊C4×C53—44no—
270C22⋊C4×C53C4⋊C4116yescomplemented
271C42×C53—44no—
272C42×C53—44no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
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—41no—
292C23×C53—41no—
293C23×C53—41no—
294C23×C53—41no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—41no—
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×C53C2×C4⋊C414yes—
308C23×C53C23×C411yescharacteristic
309C23×C53C22×D411yescharacteristic
310C23×C53C22×Q811yescharacteristic
311C23×C53C2×#4111yescharacteristic
312C23×C53C2×#4111yescharacteristic
313C23×C53C2×#4111yescharacteristic
314C23×C53C2×#4111yescharacteristic
315C23×C53H(5,𝔽2)11yescharacteristic
316C23×C53H(5,𝔽2)11yescharacteristic
317C23×C53H(5,𝔽2)11yescharacteristic
318C23×C53H(5,𝔽2)11yescharacteristic
319C23×C53H(5,𝔽2)11yescharacteristic
320C23×C53H(5,𝔽2)11yescharacteristic
321C23×C532−1+411yescharacteristic
322C23×C532−1+411yescharacteristic
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
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—416no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
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×C53C2×C4⋊C414yes—
421C2×C4×C53C2×C4⋊C414yes—
422#14488C5311yesmaximal, characteristic, direct product factor, Sylow
423C22×C53—24no—
424C22×C53—24no—
425C22×C53—24no—
426C22×C53—42no—
427C22×C53—42no—
428C22×C53—42no—
429C22×C53—42no—
430C22×C53—42no—
431C22×C53—42no—
432C22×C53—42no—
433C22×C53—42no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—42no—
437C22×C53—42no—
438C22×C53C22×C4⋊C411yescharacteristic
439C22×C53C4×#4111yescharacteristic
440C22×C53C4×#4111yescharacteristic
441C22×C53#51811yescharacteristic
442C22×C53#51811yescharacteristic
443C22×C53#52011yescharacteristic
444C22×C53#52011yescharacteristic
445C22×C53#53511yescharacteristic
446C22×C53#53611yescharacteristic
447C22×C53#53811yescharacteristic
448C22×C53#53811yescharacteristic
449C22×C53#53811yescharacteristic
450C22×C53#53911yescharacteristic
451C22×C53#54011yescharacteristic
452C22×C53#54211yescharacteristic
453C22×C53#54211yescharacteristic
454C22×C53#54211yescharacteristic
455C22×C53#54411yescharacteristic
456C22×C53#54411yescharacteristic
457C22×C53#54611yescharacteristic
458C22×C53#54611yescharacteristic
459C22×C53#54611yescharacteristic
460C22×C53#54611yescharacteristic
461C22×C53#55111yescharacteristic
462C22×C53#55211yescharacteristic
463C22×C53#55311yescharacteristic
464C22×C53#55411yescharacteristic
465C22×C53#55411yescharacteristic
466C22×C53#55411yescharacteristic
467C22×C53#55411yescharacteristic
468C22×C53#55611yescharacteristic
469C22×C53#56011yescharacteristic
470C22×C53#56011yescharacteristic
471C22×C53#56211yescharacteristic
472C22×C53#56211yescharacteristic
473C4×C53—24no—
474C4×C53—24no—
475C4×C53—42no—
476C4×C53—42no—
477C4×C53—42no—
478C4×C53—42no—
479C4×C53—42no—
480C4×C53—42no—
481C4×C53—42no—
482C4×C53—42no—
483C4×C53—81no—
484C4×C53—81no—
485C4×C53—81no—
486C4×C53—81no—
487C2×#388C2×C5311yescharacteristic
488C2×#388C2×C5311yescharacteristic
489C2×#385C2×C5311yescharacteristic
490#1444C2×C5311yescharacteristic, complemented
491#1442C2×C5311yescharacteristic, complemented
492#1442C2×C5311yescharacteristic, complemented
493#1441C2×C5311yescharacteristic, complemented
494#1439C2×C5311yescharacteristic
495#1439C2×C5311yescharacteristic
496#1436C2×C5311yescharacteristic, complemented
497C4⋊#95C2×C5311yescharacteristic, complemented
498C4⋊#95C2×C5311yescharacteristic, complemented
499#1434C2×C5311yescharacteristic, complemented
500C22⋊#95C2×C5311yescharacteristic
501C22⋊#95C2×C5311yescharacteristic
502C2×C53—44no—
503C2×C53#231711yescharacteristic
504C2×C53#233511yescharacteristic
505C2×C53#233711yescharacteristic
506C2×C53#234911yescharacteristic
507C2×C53#234911yescharacteristic
508C2×C53#237311yescharacteristic
509C2×C53#237711yescharacteristic
510C2×C53#268511yescharacteristic
511C2×C53#268711yescharacteristic
512C2×C53#270011yescharacteristic
513C2×C53#270311yescharacteristic
514C2×C53#274211yescharacteristic
515C2×C53#276811yescharacteristic
516C2×C53#278811yescharacteristic
517C2×C53#279011yescharacteristic
518C24×C4C22×C5311yescharacteristic
519C22×C4⋊C4C22×C5311yescharacteristic
520C22×C4⋊C4C22×C5311yescharacteristic
521C22×C4⋊C4C22×C5311yescharacteristic
522C22×C4⋊C4C22×C5311yescharacteristic
523C22×C4⋊C4C22×C5311yescharacteristic
524C22×C4⋊C4C22×C5311yescharacteristic
525C22×C22⋊C4C22×C5311yescharacteristic
526C22×C22⋊C4C22×C5311yescharacteristic
527C22×C22⋊C4C22×C5311yescharacteristic
528C22×C22⋊C4C22×C5311yescharacteristic
529C22×C22⋊C4C22×C5311yescharacteristic
530C22×C22⋊C4C22×C5311yescharacteristic
531C22×C42C22×C5311yescharacteristic
532C22×C42C22×C5311yescharacteristic
533#388—24no—
534#388C4×C5318yescomplemented
535#385—24no—
536C2×#95C22×C5311yescharacteristic
537C2×#95C22×C5311yescharacteristic
538C2×#95C22×C5311yescharacteristic
539C2×#95C22×C5311yescharacteristic
540C2×#95C22×C5311yescharacteristic
541C2×#95C22×C5311yescharacteristic
542C2×#95C22×C5311yescharacteristic
543C2×#95C22×C5311yescharacteristic
544C2×#95C22×C5311yescharacteristic
545C2×#95C22×C5311yescharacteristic
546C2×#95C22×C5311yescharacteristic
547C2×#95C22×C5311yescharacteristic
548C2×#95C22×C5311yescharacteristic
549C2×#95C22×C5311yescharacteristic
550C2×#95C22×C5311yescharacteristic
551C2×#95C22×C5311yescharacteristic
552C2×#95C22×C5311yescharacteristic
553C2×#95C22×C5311yescharacteristic
554C2×#95C22×C5311yescharacteristic
555C2×#95C22×C5311yescharacteristic
556C53#1448811yescharacteristic, direct product factor, Sylow
557C25C23×C5311yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C5311yescharacteristic
566C23×C4C23×C5311yescharacteristic
567C23×C4C23×C5311yescharacteristic
568C23×C4C23×C5311yescharacteristic
569C23×C4C23×C5311yescharacteristic
570C23×C4C23×C5311yescharacteristic
571C23×C4C23×C5311yescharacteristic
572C23×C4C23×C5311yescharacteristic
573C23×C4C23×C5311yescharacteristic
574C23×C4C23×C5311yescharacteristic
575C23×C4C23×C5311yescharacteristic
576C23×C4C23×C5311yescharacteristic
577C23×C4C23×C5311yescharacteristic
578C23×C4C23×C5311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C2×C4×C5314yescomplemented
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4C2×C4×C5314yes—
611C2×C22⋊C4C2×C4×C5314yes—
612C2×C22⋊C4C2×C4×C5314yes—
613C2×C22⋊C4D4×C5314yes—
614C2×C22⋊C4Q8×C5314yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C5314yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C5314yescomplemented
640#95C2×C4×C5314yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C5312yes—
654C24C2×D4×C5312yes—
655C24C2×Q8×C5312yes—
656C24C24×C5311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—21no—
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—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4C22×C4×C5312yes—
749C22×C4C22×C4×C5312yes—
750C22×C4C22×C4×C5312yes—
751C22×C4C22×C4×C5312yes—
752C22×C4C22×C4×C5312yes—
753C22×C4C22×C4×C5312yes—
754C22×C4C2×D4×C5312yes—
755C22×C4C2×D4×C5312yes—
756C22×C4C2×Q8×C5312yes—
757C22×C4C2×Q8×C5312yes—
758C22×C4#41×C5312yes—
759C22×C4#41×C5312yes—
760C22×C4#41×C5312yes—
761C22×C4#41×C5312yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4C4⋊C4×C53116yescomplemented
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C5314yes—
811C23C23×C4×C5311yescharacteristic
812C23C22×D4×C5311yescharacteristic
813C23C22×Q8×C5311yescharacteristic
814C23C2×#41×C5311yescharacteristic
815C23C2×#41×C5311yescharacteristic
816C23C2×#41×C5311yescharacteristic
817C23C2×#41×C5311yescharacteristic
818C23H(5,𝔽2)×C5311yescharacteristic
819C23H(5,𝔽2)×C5311yescharacteristic
820C23H(5,𝔽2)×C5311yescharacteristic
821C23H(5,𝔽2)×C5311yescharacteristic
822C23H(5,𝔽2)×C5311yescharacteristic
823C23H(5,𝔽2)×C5311yescharacteristic
824C232−1+4×C5311yescharacteristic
825C232−1+4×C5311yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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×C4C2×C4⋊C4×C5314yes—
924C2×C4C2×C4⋊C4×C5314yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C5311yescharacteristic
941C22C4×#41×C5311yescharacteristic
942C22C4×#41×C5311yescharacteristic
943C22C53×#51811yescharacteristic
944C22C53×#51811yescharacteristic
945C22C53×#52011yescharacteristic
946C22C53×#52011yescharacteristic
947C22C53×#53511yescharacteristic
948C22C53×#53611yescharacteristic
949C22C53×#53811yescharacteristic
950C22C53×#53811yescharacteristic
951C22C53×#53811yescharacteristic
952C22C53×#53911yescharacteristic
953C22C53×#54011yescharacteristic
954C22C53×#54211yescharacteristic
955C22C53×#54211yescharacteristic
956C22C53×#54211yescharacteristic
957C22C53×#54411yescharacteristic
958C22C53×#54411yescharacteristic
959C22C53×#54611yescharacteristic
960C22C53×#54611yescharacteristic
961C22C53×#54611yescharacteristic
962C22C53×#54611yescharacteristic
963C22C53×#55111yescharacteristic
964C22C53×#55211yescharacteristic
965C22C53×#55311yescharacteristic
966C22C53×#55411yescharacteristic
967C22C53×#55411yescharacteristic
968C22C53×#55411yescharacteristic
969C22C53×#55411yescharacteristic
970C22C53×#55611yescharacteristic
971C22C53×#56011yescharacteristic
972C22C53×#56011yescharacteristic
973C22C53×#56211yescharacteristic
974C22C53×#56211yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C53×#231711yescharacteristic
991C2C53×#233511yescharacteristic
992C2C53×#233711yescharacteristic
993C2C53×#234911yescharacteristic
994C2C53×#234911yescharacteristic
995C2C53×#237311yescharacteristic
996C2C53×#237711yescharacteristic
997C2C53×#268511yescharacteristic
998C2C53×#268711yescharacteristic
999C2C53×#270011yescharacteristic
1000C2C53×#270311yescharacteristic
1001C2C53×#274211yescharacteristic
1002C2C53×#276811yescharacteristic
1003C2C53×#278811yescharacteristic
1004C2C53×#279011yescharacteristic
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
4. C53×#1444C2semidirect
5. C53×#1442C2semidirect
6. C53×#1442C2semidirect
7. C53×#1441C2semidirect
10. C53×#1436C2semidirect
11. C53×C4⋊#95C2semidirect
12. C53×C4⋊#95C2semidirect
13. C53×#1434C2semidirect
32. C53×#388C4semidirect
93. C2×C4⋊C4×C53C2×C4semidirect
117. C2×C42×C53C2×C4semidirect
136. #95×C53C2×C4semidirect
137. #95×C53C2×C4semidirect
270. C22⋊C4×C53C4⋊C4semidirect
422. #14488C53direct (N × H)
490. #1444C2×C53semidirect
491. #1442C2×C53semidirect
492. #1442C2×C53semidirect
493. #1441C2×C53semidirect
496. #1436C2×C53semidirect
497. C4⋊#95C2×C53semidirect
498. C4⋊#95C2×C53semidirect
499. #1434C2×C53semidirect
534. #388C4×C53semidirect
556. C53#14488direct (N × H)
596. C2×C4⋊C4C2×C4×C53semidirect
620. C2×C42C2×C4×C53semidirect
639. #95C2×C4×C53semidirect
640. #95C2×C4×C53semidirect
773. 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×#3882
C2×C53×#3852
C53×#14442
C53×#14422
C53×#14412
C53×#14392
C53×#14362
C53×C4⋊#952
C53×#14342
C53×C22⋊#952
#1448853