Finite Group Databasebeta

← C53×#14112 #27221624

Subgroups — C53×#14112 #27221624

Order 13568.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 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×#385C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
8C53×#1444C211yesmaximal, characteristic, complemented
9C53×#1441C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic
11C53×#1439C211yesmaximal, characteristic
12C53×#1436C211yesmaximal, characteristic, complemented
13C53×#1436C211yesmaximal, characteristic, complemented
14C53×#1436C211yesmaximal, characteristic, complemented
15C53×C4⋊#95C211yesmaximal, characteristic, complemented
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
33C22×C42×C53C2211yescharacteristic
34C22×C42×C53C2211yescharacteristic
35C53×#389—24no—
36C53×#388—24no—
37C53×#388C418yescomplemented
38C53×#385—24no—
39C53×#385—24no—
40C4×C4⋊C4×C53—24no—
41C4×C22⋊C4×C53—24no—
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
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C25×C53C2311yescharacteristic
59C23×C4×C53—22no—
60C23×C4×C53—22no—
61C23×C4×C53—22no—
62C23×C4×C53—22no—
63C23×C4×C53—22no—
64C23×C4×C53—41no—
65C23×C4×C53—41no—
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
78C23×C4×C53C2311yescharacteristic
79C23×C4×C53C2311yescharacteristic
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—22no—
88C2×C4⋊C4×C53—22no—
89C2×C4⋊C4×C53—22no—
90C2×C4⋊C4×C53—22no—
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—41no—
99C2×C4⋊C4×C53—41no—
100C2×C4⋊C4×C53—41no—
101C2×C4⋊C4×C53—41no—
102C2×C4⋊C4×C53C2×C414yescomplemented
103C2×C4⋊C4×C53D414yes—
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—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53—22no—
115C2×C22⋊C4×C53—41no—
116C2×C22⋊C4×C53—41no—
117C2×C22⋊C4×C53C2×C414yes—
118C2×C22⋊C4×C53C2×C414yes—
119C2×C22⋊C4×C53C2×C414yes—
120C2×C22⋊C4×C53D414yes—
121C2×C22⋊C4×C53Q814yes—
122C2×C42×C53—22no—
123C2×C42×C53—22no—
124C2×C42×C53—22no—
125C2×C42×C53—22no—
126C2×C42×C53—22no—
127C2×C42×C53—22no—
128C2×C42×C53—22no—
129C2×C42×C53—22no—
130C2×C42×C53—41no—
131C2×C42×C53—41no—
132C2×C42×C53—41no—
133C2×C42×C53C2×C414yescomplemented
134#95×C53—22no—
135#95×C53—22no—
136#95×C53—22no—
137#95×C53—22no—
138#95×C53—22no—
139#95×C53—22no—
140#95×C53—22no—
141#95×C53—22no—
142#95×C53—22no—
143#95×C53—22no—
144#95×C53—22no—
145#95×C53—22no—
146#95×C53—41no—
147#95×C53C2×C414yescomplemented
148#95×C53C2×C414yescomplemented
149#95×C53D414yes—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53C22×C412yes—
163C24×C53C2×D412yes—
164C24×C53C2×Q812yes—
165C24×C53C2411yescharacteristic
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—28no—
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—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×D412yes—
261C22×C4×C53C2×D412yes—
262C22×C4×C53C2×D412yes—
263C22×C4×C53C2×Q812yes—
264C22×C4×C53C2×Q812yes—
265C22×C4×C53#4112yes—
266C22×C4×C53#4112yes—
267C22×C4×C53#4112yes—
268C22×C4×C53#4112yes—
269C22×C4×C53#4112yes—
270C22×C4×C53#4112yes—
271C4⋊C4×C53—28no—
272C4⋊C4×C53—28no—
273C4⋊C4×C53—28no—
274C4⋊C4×C53—44no—
275C4⋊C4×C53—44no—
276C4⋊C4×C53—44no—
277C4⋊C4×C53—44no—
278C4⋊C4×C53—44no—
279C22⋊C4×C53—28no—
280C22⋊C4×C53—28no—
281C22⋊C4×C53—28no—
282C22⋊C4×C53—44no—
283C22⋊C4×C53—44no—
284C22⋊C4×C53C4⋊C4116yescomplemented
285C42×C53—28no—
286C42×C53—44no—
287C42×C53—44no—
288C42×C53—44no—
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—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
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×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—41no—
322C23×C53—41no—
323C23×C53C2×C4⋊C414yes—
324C23×C53C23×C411yescharacteristic
325C23×C53C22×D411yescharacteristic
326C23×C53C22×D411yescharacteristic
327C23×C53C22×D411yescharacteristic
328C23×C53C22×Q811yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53C2×#4111yescharacteristic
331C23×C53C2×#4111yescharacteristic
332C23×C53C2×#4111yescharacteristic
333C23×C53C2×#4111yescharacteristic
334C23×C53C2×#4111yescharacteristic
335C23×C53H(5,𝔽2)11yescharacteristic
336C23×C53H(5,𝔽2)11yescharacteristic
337C23×C532−1+411yescharacteristic
338C23×C532−1+411yescharacteristic
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—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—22no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53—22no—
386C2×C4×C53—22no—
387C2×C4×C53—22no—
388C2×C4×C53—22no—
389C2×C4×C53—22no—
390C2×C4×C53—416no—
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×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53C2×C4⋊C414yes—
434C2×C4×C53C2×C4⋊C414yes—
435C2×C4×C53C4×D414yes—
436C2×C4×C53C4×D414yes—
437C2×C4×C53#12114yes—
438#14112C5311yesmaximal, characteristic, direct product factor, Sylow
439C22×C53—24no—
440C22×C53—24no—
441C22×C53—24no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—42no—
448C22×C53—42no—
449C22×C53—42no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—42no—
453C22×C53—42no—
454C22×C53C22×C4⋊C411yescharacteristic
455C22×C53C2×C4×D411yescharacteristic
456C22×C53C2×C4×D411yescharacteristic
457C22×C53C4×#4111yescharacteristic
458C22×C53C4×#4111yescharacteristic
459C22×C53#52011yescharacteristic
460C22×C53#52011yescharacteristic
461C22×C53C2×#12111yescharacteristic
462C22×C53#52511yescharacteristic
463C22×C53#52511yescharacteristic
464C22×C53#52511yescharacteristic
465C22×C53#52911yescharacteristic
466C22×C53#53211yescharacteristic
467C22×C53#53311yescharacteristic
468C22×C53#53311yescharacteristic
469C22×C53#53811yescharacteristic
470C22×C53#53911yescharacteristic
471C22×C53#54111yescharacteristic
472C22×C53#54211yescharacteristic
473C22×C53D4211yescharacteristic
474C22×C53D4211yescharacteristic
475C22×C53#54611yescharacteristic
476C22×C53#54611yescharacteristic
477C22×C53#54711yescharacteristic
478C22×C53#54711yescharacteristic
479C22×C53#54711yescharacteristic
480C22×C53#54811yescharacteristic
481C22×C53D4×Q811yescharacteristic
482C22×C53D4×Q811yescharacteristic
483C22×C53#55111yescharacteristic
484C22×C53#55211yescharacteristic
485C22×C53#55411yescharacteristic
486C22×C53#55411yescharacteristic
487C22×C53#55611yescharacteristic
488C22×C53#55911yescharacteristic
489C4×C53—24no—
490C4×C53—24no—
491C4×C53—24no—
492C4×C53—24no—
493C4×C53—24no—
494C4×C53—42no—
495C4×C53—42no—
496C4×C53—42no—
497C4×C53—42no—
498C4×C53—42no—
499C4×C53—42no—
500C4×C53—42no—
501C4×C53—81no—
502C4×C53—81no—
503C2×#389C2×C5311yescharacteristic, complemented
504C2×#388C2×C5311yescharacteristic
505C2×#388C2×C5311yescharacteristic
506C2×#385C2×C5311yescharacteristic
507C2×#385C2×C5311yescharacteristic
508C2×C4×C4⋊C4C2×C5311yescharacteristic, complemented
509C2×C4×C22⋊C4C2×C5311yescharacteristic
510#1444C2×C5311yescharacteristic, complemented
511#1441C2×C5311yescharacteristic, complemented
512#1439C2×C5311yescharacteristic
513#1439C2×C5311yescharacteristic
514#1436C2×C5311yescharacteristic, complemented
515#1436C2×C5311yescharacteristic, complemented
516#1436C2×C5311yescharacteristic, complemented
517C4⋊#95C2×C5311yescharacteristic, complemented
518C2×C53—44no—
519C2×C53#229611yescharacteristic
520C2×C53C4×#12111yescharacteristic
521C2×C53#233411yescharacteristic
522C2×C53D4×C4⋊C411yescharacteristic
523C2×C53D4×C4⋊C411yescharacteristic
524C2×C53#235911yescharacteristic
525C2×C53#236711yescharacteristic
526C2×C53#242411yescharacteristic
527C2×C53#242911yescharacteristic
528C2×C53#245511yescharacteristic
529C2×C53#246111yescharacteristic
530C2×C53#246511yescharacteristic
531C2×C53#247811yescharacteristic
532C2×C53#255611yescharacteristic
533C2×C53#258911yescharacteristic
534C24×C4C22×C5311yescharacteristic
535C22×C4⋊C4C22×C5311yescharacteristic
536C22×C4⋊C4C22×C5311yescharacteristic
537C22×C4⋊C4C22×C5311yescharacteristic
538C22×C4⋊C4C22×C5311yescharacteristic
539C22×C4⋊C4C22×C5311yescharacteristic
540C22×C4⋊C4C22×C5311yescharacteristic
541C22×C4⋊C4C22×C5311yescharacteristic
542C22×C4⋊C4C22×C5311yescharacteristic
543C22×C22⋊C4C22×C5311yescharacteristic
544C22×C22⋊C4C22×C5311yescharacteristic
545C22×C22⋊C4C22×C5311yescharacteristic
546C22×C22⋊C4C22×C5311yescharacteristic
547C22×C22⋊C4C22×C5311yescharacteristic
548C22×C22⋊C4C22×C5311yescharacteristic
549C22×C42C22×C5311yescharacteristic
550C22×C42C22×C5311yescharacteristic
551C22×C42C22×C5311yescharacteristic
552C22×C42C22×C5311yescharacteristic
553#389—24no—
554#388—24no—
555#388C4×C5318yescomplemented
556#385—24no—
557#385—24no—
558C4×C4⋊C4—24no—
559C4×C22⋊C4—24no—
560C2×#95C22×C5311yescharacteristic
561C2×#95C22×C5311yescharacteristic
562C2×#95C22×C5311yescharacteristic
563C2×#95C22×C5311yescharacteristic
564C2×#95C22×C5311yescharacteristic
565C2×#95C22×C5311yescharacteristic
566C2×#95C22×C5311yescharacteristic
567C2×#95C22×C5311yescharacteristic
568C2×#95C22×C5311yescharacteristic
569C2×#95C22×C5311yescharacteristic
570C2×#95C22×C5311yescharacteristic
571C2×#95C22×C5311yescharacteristic
572C2×#95C22×C5311yescharacteristic
573C2×#95C22×C5311yescharacteristic
574C2×#95C22×C5311yescharacteristic
575C2×#95C22×C5311yescharacteristic
576C53#1411211yescharacteristic, direct product factor, Sylow
577C25C23×C5311yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C5311yescharacteristic
586C23×C4C23×C5311yescharacteristic
587C23×C4C23×C5311yescharacteristic
588C23×C4C23×C5311yescharacteristic
589C23×C4C23×C5311yescharacteristic
590C23×C4C23×C5311yescharacteristic
591C23×C4C23×C5311yescharacteristic
592C23×C4C23×C5311yescharacteristic
593C23×C4C23×C5311yescharacteristic
594C23×C4C23×C5311yescharacteristic
595C23×C4C23×C5311yescharacteristic
596C23×C4C23×C5311yescharacteristic
597C23×C4C23×C5311yescharacteristic
598C23×C4C23×C5311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×C4×C5314yescomplemented
622C2×C4⋊C4D4×C5314yes—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4C2×C4×C5314yes—
637C2×C22⋊C4C2×C4×C5314yes—
638C2×C22⋊C4C2×C4×C5314yes—
639C2×C22⋊C4D4×C5314yes—
640C2×C22⋊C4Q8×C5314yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42C2×C4×C5314yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—41no—
666#95C2×C4×C5314yescomplemented
667#95C2×C4×C5314yescomplemented
668#95D4×C5314yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C5312yes—
682C24C2×D4×C5312yes—
683C24C2×Q8×C5312yes—
684C24C24×C5311yescharacteristic
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—28no—
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—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—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C5312yes—
769C22×C4C22×C4×C5312yes—
770C22×C4C22×C4×C5312yes—
771C22×C4C22×C4×C5312yes—
772C22×C4C22×C4×C5312yes—
773C22×C4C22×C4×C5312yes—
774C22×C4C2×D4×C5312yes—
775C22×C4C2×D4×C5312yes—
776C22×C4C2×D4×C5312yes—
777C22×C4C2×D4×C5312yes—
778C22×C4C2×D4×C5312yes—
779C22×C4C2×D4×C5312yes—
780C22×C4C2×D4×C5312yes—
781C22×C4C2×D4×C5312yes—
782C22×C4C2×Q8×C5312yes—
783C22×C4C2×Q8×C5312yes—
784C22×C4#41×C5312yes—
785C22×C4#41×C5312yes—
786C22×C4#41×C5312yes—
787C22×C4#41×C5312yes—
788C22×C4#41×C5312yes—
789C22×C4#41×C5312yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C4⋊C4×C53116yescomplemented
804C42—28no—
805C42—44no—
806C42—44no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C5314yes—
843C23C23×C4×C5311yescharacteristic
844C23C22×D4×C5311yescharacteristic
845C23C22×D4×C5311yescharacteristic
846C23C22×D4×C5311yescharacteristic
847C23C22×Q8×C5311yescharacteristic
848C23C2×#41×C5311yescharacteristic
849C23C2×#41×C5311yescharacteristic
850C23C2×#41×C5311yescharacteristic
851C23C2×#41×C5311yescharacteristic
852C23C2×#41×C5311yescharacteristic
853C23C2×#41×C5311yescharacteristic
854C23H(5,𝔽2)×C5311yescharacteristic
855C23H(5,𝔽2)×C5311yescharacteristic
856C232−1+4×C5311yescharacteristic
857C232−1+4×C5311yescharacteristic
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—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—416no—
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×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4C2×C4⋊C4×C5314yes—
953C2×C4C2×C4⋊C4×C5314yes—
954C2×C4C4×D4×C5314yes—
955C2×C4C4×D4×C5314yes—
956C2×C4#121×C5314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C5311yescharacteristic
973C22C2×C4×D4×C5311yescharacteristic
974C22C2×C4×D4×C5311yescharacteristic
975C22C4×#41×C5311yescharacteristic
976C22C4×#41×C5311yescharacteristic
977C22C53×#52011yescharacteristic
978C22C53×#52011yescharacteristic
979C22C2×#121×C5311yescharacteristic
980C22C53×#52511yescharacteristic
981C22C53×#52511yescharacteristic
982C22C53×#52511yescharacteristic
983C22C53×#52911yescharacteristic
984C22C53×#53211yescharacteristic
985C22C53×#53311yescharacteristic
986C22C53×#53311yescharacteristic
987C22C53×#53811yescharacteristic
988C22C53×#53911yescharacteristic
989C22C53×#54111yescharacteristic
990C22C53×#54211yescharacteristic
991C22D42×C5311yescharacteristic
992C22D42×C5311yescharacteristic
993C22C53×#54611yescharacteristic
994C22C53×#54611yescharacteristic
995C22C53×#54711yescharacteristic
996C22C53×#54711yescharacteristic
997C22C53×#54711yescharacteristic
998C22C53×#54811yescharacteristic
999C22D4×Q8×C5311yescharacteristic
1000C22D4×Q8×C5311yescharacteristic
1001C22C53×#55111yescharacteristic
1002C22C53×#55211yescharacteristic
1003C22C53×#55411yescharacteristic
1004C22C53×#55411yescharacteristic
1005C22C53×#55611yescharacteristic
1006C22C53×#55911yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C53×#229611yescharacteristic
1023C2C4×#121×C5311yescharacteristic
1024C2C53×#233411yescharacteristic
1025C2D4×C4⋊C4×C5311yescharacteristic
1026C2D4×C4⋊C4×C5311yescharacteristic
1027C2C53×#235911yescharacteristic
1028C2C53×#236711yescharacteristic
1029C2C53×#242411yescharacteristic
1030C2C53×#242911yescharacteristic
1031C2C53×#245511yescharacteristic
1032C2C53×#246111yescharacteristic
1033C2C53×#246511yescharacteristic
1034C2C53×#247811yescharacteristic
1035C2C53×#255611yescharacteristic
1036C2C53×#258911yescharacteristic
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. C2×C4×C4⋊C4×C53C2semidirect
8. C53×#1444C2semidirect
9. C53×#1441C2semidirect
12. C53×#1436C2semidirect
13. C53×#1436C2semidirect
14. C53×#1436C2semidirect
15. C53×C4⋊#95C2semidirect
37. C53×#388C4semidirect
102. C2×C4⋊C4×C53C2×C4semidirect
133. C2×C42×C53C2×C4semidirect
147. #95×C53C2×C4semidirect
148. #95×C53C2×C4semidirect
284. C22⋊C4×C53C4⋊C4semidirect
438. #14112C53direct (N × H)
503. C2×#389C2×C53semidirect
508. C2×C4×C4⋊C4C2×C53semidirect
510. #1444C2×C53semidirect
511. #1441C2×C53semidirect
514. #1436C2×C53semidirect
515. #1436C2×C53semidirect
516. #1436C2×C53semidirect
517. C4⋊#95C2×C53semidirect
555. #388C4×C53semidirect
576. C53#14112direct (N × H)
621. C2×C4⋊C4C2×C4×C53semidirect
652. C2×C42C2×C4×C53semidirect
666. #95C2×C4×C53semidirect
667. #95C2×C4×C53semidirect
803. 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×C4×C4⋊C4×C532
C2×C4×C22⋊C4×C532
C53×#14442
C53×#14412
C53×#14392
C53×#14362
C53×C4⋊#952
#1411253