Finite Group Databasebeta

← C53×#16535 #27224047

Subgroups — C53×#16535 #27224047

Order 13568.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#397C211yesmaximal, characteristic, complemented
2C2×C53×#394C211yesmaximal, characteristic, complemented
3C2×C53×#392C211yesmaximal, characteristic
4C2×C53×#388C211yesmaximal, characteristic, complemented
5C53×#1443C211yesmaximal, characteristic, complemented
6C53×#1442C211yesmaximal, characteristic, complemented
7C53×#1439C211yesmaximal, characteristic, complemented
8C53×#1439C211yesmaximal, characteristic, complemented
9C53×#1438C211yesmaximal, characteristic, complemented
10C53×#1438C211yesmaximal, characteristic, complemented
11C53×#1438C211yesmaximal, characteristic, complemented
12C53×#1438C211yesmaximal, characteristic, complemented
13C53×#1438C211yesmaximal, characteristic, complemented
14C53×#1437C211yesmaximal, characteristic, complemented
15C53×#1437C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C22×C4⋊C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C22⋊C4×C53C2211yescharacteristic
22C22×C22⋊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×C22⋊C4×C53C2211yescharacteristic
30C22×C22⋊C4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2211yescharacteristic
33C22×C22⋊C4×C53C2211yescharacteristic
34C22×C22⋊C4×C53C2211yescharacteristic
35C22×C22⋊C4×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C53×#397—24no—
38C53×#394—24no—
39C53×#392—24no—
40C53×#388—24no—
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
55C25×C53C2311yescharacteristic
56C25×C53C2311yescharacteristic
57C25×C53C2311yescharacteristic
58C22×D4×C53—22no—
59C22×D4×C53—22no—
60C22×D4×C53—22no—
61C22×D4×C53—22no—
62C22×D4×C53—22no—
63C22×D4×C53—22no—
64C22×D4×C53—22no—
65C22×D4×C53—22no—
66C22×D4×C53—22no—
67C22×D4×C53—41no—
68C22×D4×C53—41no—
69C22×D4×C53—41no—
70C22×D4×C53—41no—
71C22×D4×C53—41no—
72C22×D4×C53—41no—
73C22×D4×C53—41no—
74C22×D4×C53—41no—
75C22×D4×C53—41no—
76C22×D4×C53—41no—
77C22×D4×C53—41no—
78C22×D4×C53—41no—
79C23×C4×C53C2311yescharacteristic
80C23×C4×C53C2311yescharacteristic
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—41no—
95C2×C4⋊C4×C53—41no—
96C2×C4⋊C4×C53—41no—
97C2×C22⋊C4×C53—22no—
98C2×C22⋊C4×C53—22no—
99C2×C22⋊C4×C53—22no—
100C2×C22⋊C4×C53—22no—
101C2×C22⋊C4×C53—22no—
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—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—22no—
116C2×C22⋊C4×C53—22no—
117C2×C22⋊C4×C53—41no—
118C2×C22⋊C4×C53—41no—
119C2×C22⋊C4×C53—41no—
120C2×C22⋊C4×C53—41no—
121C2×C22⋊C4×C53—41no—
122C2×C22⋊C4×C53—41no—
123C2×C22⋊C4×C53—41no—
124C2×C22⋊C4×C53—41no—
125C2×C22⋊C4×C53—41no—
126C2×C22⋊C4×C53—41no—
127C2×C22⋊C4×C53—41no—
128C2×C22⋊C4×C53—41no—
129C2×C22⋊C4×C53—41no—
130C2×C22⋊C4×C53—41no—
131C2×C22⋊C4×C53—41no—
132C2×C22⋊C4×C53—41no—
133C2×C22⋊C4×C53—41no—
134C2×C22⋊C4×C53—41no—
135C2×C22⋊C4×C53—41no—
136C2×C22⋊C4×C53—41no—
137C2×C22⋊C4×C53—41no—
138C2×C22⋊C4×C53—41no—
139C2×C22⋊C4×C53—41no—
140C2×C22⋊C4×C53—41no—
141C2×C22⋊C4×C53D414yes—
142C2×C42×C53—22no—
143C2×C42×C53—41no—
144C2×C42×C53—41no—
145#95×C53—22no—
146#95×C53—22no—
147#95×C53—22no—
148#95×C53—22no—
149#95×C53—22no—
150#95×C53—22no—
151#95×C53—41no—
152#95×C53—41no—
153#95×C53—41no—
154#95×C53—41no—
155#95×C53—41no—
156#95×C53—41no—
157#95×C53—41no—
158#95×C53D414yescomplemented
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C24×C53—21no—
190C24×C53—21no—
191C24×C53—21no—
192C24×C53—21no—
193C24×C53—21no—
194C24×C53—21no—
195C24×C53—21no—
196C24×C53—21no—
197C24×C53—21no—
198C24×C53—21no—
199C24×C53—21no—
200C24×C53—21no—
201C24×C53C2×D412yes—
202C24×C53#4112yes—
203C24×C53#4112yes—
204C24×C53C2411yescharacteristic
205C2×D4×C53—44no—
206C2×D4×C53—44no—
207C2×D4×C53—44no—
208C2×D4×C53—44no—
209C2×D4×C53—44no—
210C2×D4×C53—44no—
211C2×D4×C53—44no—
212C2×D4×C53—44no—
213C2×D4×C53—44no—
214C2×D4×C53—44no—
215C2×D4×C53—44no—
216C2×D4×C53—44no—
217C2×D4×C53—44no—
218C2×D4×C53—44no—
219C2×D4×C53—44no—
220C2×D4×C53—44no—
221C2×D4×C53—44no—
222C2×D4×C53—44no—
223C2×D4×C53—44no—
224C2×D4×C53—44no—
225C2×D4×C53—44no—
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—21no—
244C22×C4×C53—21no—
245C22×C4×C53—21no—
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—21no—
256C22×C4×C53—21no—
257C22×C4×C53—21no—
258C22×C4×C53—21no—
259C22×C4×C53—21no—
260C22×C4×C53—21no—
261C22×C4×C53—21no—
262C22×C4×C53—21no—
263C22×C4×C53—21no—
264C22×C4×C53—21no—
265C22×C4×C53—21no—
266C22×C4×C53—21no—
267C22×C4×C53—21no—
268C22×C4×C53—21no—
269C22×C4×C53—21no—
270C22×C4×C53—21no—
271C22×C4×C53—21no—
272C22×C4×C53—21no—
273C22×C4×C53—21no—
274C22×C4×C53—21no—
275C22×C4×C53—21no—
276C22×C4×C53—21no—
277C22×C4×C53—21no—
278C22×C4×C53—21no—
279C22×C4×C53—21no—
280C22×C4×C53—21no—
281C22×C4×C53—21no—
282C22×C4×C53—21no—
283C22×C4×C53—21no—
284C22×C4×C53—21no—
285C22×C4×C53—21no—
286C22×C4×C53—21no—
287C22×C4×C53—21no—
288C22×C4×C53—21no—
289C22×C4×C53—21no—
290C22×C4×C53—21no—
291C22×C4×C53—21no—
292C22×C4×C53—21no—
293C22×C4×C53—21no—
294C22×C4×C53—21no—
295C22×C4×C53—21no—
296C22×C4×C53—21no—
297C22×C4×C53—21no—
298C22×C4×C53—21no—
299C22×C4×C53—21no—
300C22×C4×C53—21no—
301C22×C4×C53—21no—
302C22×C4×C53C2×D412yes—
303C22×C4×C53C2×D412yes—
304C22×C4×C53C2×D412yes—
305C22×C4×C53C2×D412yes—
306C22×C4×C53C2×D412yes—
307C22×C4×C53#4112yes—
308C22×C4×C53#4112yes—
309C22×C4×C53#4112yes—
310C4⋊C4×C53—44no—
311C4⋊C4×C53—44no—
312C22⋊C4×C53—28no—
313C22⋊C4×C53—44no—
314C22⋊C4×C53—44no—
315C22⋊C4×C53—44no—
316C22⋊C4×C53—44no—
317C22⋊C4×C53—44no—
318C22⋊C4×C53—44no—
319C22⋊C4×C53—44no—
320C22⋊C4×C53—44no—
321C22⋊C4×C53—44no—
322C22⋊C4×C53—44no—
323C22⋊C4×C53—44no—
324C22⋊C4×C53—44no—
325C22⋊C4×C53—44no—
326C22⋊C4×C53—44no—
327C42×C53—44no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53—41no—
384C23×C53—41no—
385C23×C53—41no—
386C23×C53—41no—
387C23×C53—41no—
388C23×C53—41no—
389C23×C53—41no—
390C23×C53—41no—
391C23×C53—41no—
392C23×C53—41no—
393C23×C53—41no—
394C23×C53—41no—
395C23×C53—41no—
396C23×C53—41no—
397C23×C53—41no—
398C23×C53—41no—
399C23×C53—41no—
400C23×C53—41no—
401C23×C53—41no—
402C23×C53—41no—
403C23×C53—41no—
404C23×C53—41no—
405C23×C53—41no—
406C23×C53—41no—
407C23×C53—41no—
408C23×C53—41no—
409C23×C53—41no—
410C23×C53—41no—
411C23×C53—41no—
412C23×C53—41no—
413C23×C53—41no—
414C23×C53—41no—
415C23×C53—41no—
416C23×C53—41no—
417C23×C53—41no—
418C23×C53—41no—
419C23×C53—41no—
420C23×C53—41no—
421C23×C53—41no—
422C23×C53—41no—
423C23×C53—41no—
424C23×C53—41no—
425C23×C53—41no—
426C23×C53—41no—
427C23×C53—41no—
428C23×C53—41no—
429C23×C53—41no—
430C23×C53—41no—
431C23×C53—41no—
432C23×C53—41no—
433C23×C53C22×D411yescharacteristic
434C23×C53C22×D411yescharacteristic
435C23×C53C2×#4111yescharacteristic
436C23×C53C2×#4111yescharacteristic
437C23×C53C2×#4111yescharacteristic
438C23×C53C2×#4111yescharacteristic
439C23×C53C2×#4111yescharacteristic
440C23×C53H(5,𝔽2)11yescharacteristic
441C23×C53H(5,𝔽2)11yescharacteristic
442C23×C53H(5,𝔽2)11yescharacteristic
443C23×C53H(5,𝔽2)11yescharacteristic
444C23×C53H(5,𝔽2)11yescharacteristic
445C23×C53H(5,𝔽2)11yescharacteristic
446C23×C53H(5,𝔽2)11yescharacteristic
447C23×C53H(5,𝔽2)11yescharacteristic
448D4×C53—416no—
449D4×C53—416no—
450D4×C53—416no—
451C2×C4×C53—22no—
452C2×C4×C53—22no—
453C2×C4×C53—22no—
454C2×C4×C53—22no—
455C2×C4×C53—22no—
456C2×C4×C53—22no—
457C2×C4×C53—22no—
458C2×C4×C53—22no—
459C2×C4×C53—22no—
460C2×C4×C53—22no—
461C2×C4×C53—22no—
462C2×C4×C53—22no—
463C2×C4×C53—22no—
464C2×C4×C53—22no—
465C2×C4×C53—22no—
466C2×C4×C53—22no—
467C2×C4×C53—22no—
468C2×C4×C53—22no—
469C2×C4×C53—22no—
470C2×C4×C53—22no—
471C2×C4×C53—22no—
472C2×C4×C53—22no—
473C2×C4×C53—22no—
474C2×C4×C53—22no—
475C2×C4×C53—41no—
476C2×C4×C53—41no—
477C2×C4×C53—41no—
478C2×C4×C53—41no—
479C2×C4×C53—41no—
480C2×C4×C53—41no—
481C2×C4×C53—41no—
482C2×C4×C53—41no—
483C2×C4×C53—41no—
484C2×C4×C53—41no—
485C2×C4×C53—41no—
486C2×C4×C53—41no—
487C2×C4×C53—41no—
488C2×C4×C53—41no—
489C2×C4×C53—41no—
490C2×C4×C53—41no—
491C2×C4×C53—41no—
492C2×C4×C53—41no—
493C2×C4×C53—41no—
494C2×C4×C53—41no—
495C2×C4×C53—41no—
496C2×C4×C53—41no—
497C2×C4×C53—41no—
498C2×C4×C53—41no—
499C2×C4×C53—41no—
500C2×C4×C53—41no—
501C2×C4×C53—41no—
502C2×C4×C53—41no—
503C2×C4×C53—41no—
504C2×C4×C53—41no—
505C2×C4×C53—41no—
506C2×C4×C53—41no—
507C2×C4×C53—41no—
508C2×C4×C53—41no—
509C2×C4×C53—41no—
510C2×C4×C53—41no—
511C2×C4×C53—41no—
512C2×C4×C53—41no—
513C2×C4×C53—41no—
514C2×C4×C53—41no—
515C2×C4×C53—41no—
516C2×C4×C53—41no—
517C2×C4×C53—41no—
518C2×C4×C53—41no—
519C2×C4×C53—41no—
520C2×C4×C53—41no—
521C2×C4×C53—41no—
522C2×C4×C53—41no—
523C2×C4×C53—41no—
524C2×C4×C53—41no—
525C2×C4×C53—41no—
526C2×C4×C53—41no—
527C2×C4×C53—41no—
528C2×C4×C53—41no—
529C2×C4×C53—41no—
530C2×C4×C53—41no—
531C2×C4×C53—41no—
532C2×C4×C53—41no—
533C2×C4×C53—41no—
534C2×C4×C53—41no—
535#16535C5311yesmaximal, characteristic, direct product factor, Sylow
536C22×C53—42no—
537C22×C53—42no—
538C22×C53—42no—
539C22×C53—42no—
540C22×C53—42no—
541C22×C53—42no—
542C22×C53—42no—
543C22×C53—42no—
544C22×C53—42no—
545C22×C53—42no—
546C22×C53—42no—
547C22×C53—42no—
548C22×C53—42no—
549C22×C53—42no—
550C22×C53—42no—
551C22×C53—42no—
552C22×C53—42no—
553C22×C53—42no—
554C22×C53—42no—
555C22×C53—42no—
556C22×C53—42no—
557C22×C53—81no—
558C22×C53—81no—
559C22×C53—81no—
560C22×C53—81no—
561C22×C53—81no—
562C22×C53—81no—
563C22×C53—81no—
564C22×C53—81no—
565C22×C53—81no—
566C22×C53—81no—
567C22×C53—81no—
568C22×C53—81no—
569C22×C53—81no—
570C22×C53—81no—
571C22×C53—81no—
572C22×C53—81no—
573C22×C53—81no—
574C22×C53—81no—
575C22×C53—81no—
576C22×C53—81no—
577C22×C53—81no—
578C22×C53—81no—
579C22×C53—81no—
580C22×C53—81no—
581C22×C53#52511yescharacteristic
582C22×C53#52911yescharacteristic
583C22×C53#53211yescharacteristic
584C22×C53#53411yescharacteristic
585C22×C53#53511yescharacteristic
586C22×C53#53511yescharacteristic
587C22×C53#53511yescharacteristic
588C22×C53#53811yescharacteristic
589C22×C53#53811yescharacteristic
590C22×C53#53811yescharacteristic
591C22×C53#53811yescharacteristic
592C22×C53#53811yescharacteristic
593C22×C53#53811yescharacteristic
594C22×C53#53811yescharacteristic
595C22×C53#53811yescharacteristic
596C22×C53#54011yescharacteristic
597C22×C53#54011yescharacteristic
598C22×C53#54011yescharacteristic
599C22×C53#54011yescharacteristic
600C22×C53D4211yescharacteristic
601C22×C53#54611yescharacteristic
602C22×C53#54611yescharacteristic
603C22×C53#54611yescharacteristic
604C22×C53#54611yescharacteristic
605C22×C53#54611yescharacteristic
606C22×C53#55011yescharacteristic
607C22×C53#55111yescharacteristic
608C22×C53#55111yescharacteristic
609C22×C53#55311yescharacteristic
610C22×C53#55311yescharacteristic
611C22×C53#55311yescharacteristic
612C22×C53#56011yescharacteristic
613C22×C53#56011yescharacteristic
614C22×C53#56011yescharacteristic
615C22×C53H(3,𝔽4)11yescharacteristic
616C4×C53—42no—
617C4×C53—42no—
618C4×C53—42no—
619C4×C53—42no—
620C4×C53—42no—
621C4×C53—42no—
622C4×C53—42no—
623C4×C53—42no—
624C4×C53—81no—
625C4×C53—81no—
626C4×C53—81no—
627C4×C53—81no—
628C2×#397C2×C5311yescharacteristic, complemented
629C2×#394C2×C5311yescharacteristic, complemented
630C2×#392C2×C5311yescharacteristic
631C2×#388C2×C5311yescharacteristic, complemented
632#1443C2×C5311yescharacteristic, complemented
633#1442C2×C5311yescharacteristic, complemented
634#1439C2×C5311yescharacteristic, complemented
635#1439C2×C5311yescharacteristic, complemented
636#1438C2×C5311yescharacteristic, complemented
637#1438C2×C5311yescharacteristic, complemented
638#1438C2×C5311yescharacteristic, complemented
639#1438C2×C5311yescharacteristic, complemented
640#1438C2×C5311yescharacteristic, complemented
641#1437C2×C5311yescharacteristic, complemented
642#1437C2×C5311yescharacteristic, complemented
643C2×C53—82no—
644C2×C53—82no—
645C2×C53—82no—
646C2×C53#246411yescharacteristic
647C2×C53#247111yescharacteristic
648C2×C53#255911yescharacteristic
649C2×C53#263111yescharacteristic
650C2×C53#264811yescharacteristic
651C2×C53#266111yescharacteristic
652C2×C53#267011yescharacteristic
653C2×C53#267311yescharacteristic
654C2×C53#268511yescharacteristic
655C2×C53#269711yescharacteristic
656C2×C53#270311yescharacteristic
657C2×C53#271411yescharacteristic
658C2×C53#275311yescharacteristic
659C2×C53#277811yescharacteristic
660C2×C53#282811yescharacteristic
661C23×D4C22×C5311yescharacteristic
662C23×D4C22×C5311yescharacteristic
663C23×D4C22×C5311yescharacteristic
664C22×C4⋊C4C22×C5311yescharacteristic
665C22×C4⋊C4C22×C5311yescharacteristic
666C22×C22⋊C4C22×C5311yescharacteristic
667C22×C22⋊C4C22×C5311yescharacteristic
668C22×C22⋊C4C22×C5311yescharacteristic
669C22×C22⋊C4C22×C5311yescharacteristic
670C22×C22⋊C4C22×C5311yescharacteristic
671C22×C22⋊C4C22×C5311yescharacteristic
672C22×C22⋊C4C22×C5311yescharacteristic
673C22×C22⋊C4C22×C5311yescharacteristic
674C22×C22⋊C4C22×C5311yescharacteristic
675C22×C22⋊C4C22×C5311yescharacteristic
676C22×C22⋊C4C22×C5311yescharacteristic
677C22×C22⋊C4C22×C5311yescharacteristic
678C22×C22⋊C4C22×C5311yescharacteristic
679C22×C22⋊C4C22×C5311yescharacteristic
680C22×C22⋊C4C22×C5311yescharacteristic
681C22×C42C22×C5311yescharacteristic
682#397—24no—
683#394—24no—
684#392—24no—
685#388—24no—
686C2×#95C22×C5311yescharacteristic
687C2×#95C22×C5311yescharacteristic
688C2×#95C22×C5311yescharacteristic
689C2×#95C22×C5311yescharacteristic
690C2×#95C22×C5311yescharacteristic
691C2×#95C22×C5311yescharacteristic
692C2×#95C22×C5311yescharacteristic
693C2×#95C22×C5311yescharacteristic
694C2×#95C22×C5311yescharacteristic
695C2×#95C22×C5311yescharacteristic
696C2×#95C22×C5311yescharacteristic
697C2×#95C22×C5311yescharacteristic
698C2×#95C22×C5311yescharacteristic
699C2×#95C22×C5311yescharacteristic
700C53#1653511yescharacteristic, direct product factor, Sylow
701C25C23×C5311yescharacteristic
702C25C23×C5311yescharacteristic
703C25C23×C5311yescharacteristic
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C23×C4C23×C5311yescharacteristic
726C23×C4C23×C5311yescharacteristic
727C23×C4C23×C5311yescharacteristic
728C23×C4C23×C5311yescharacteristic
729C23×C4C23×C5311yescharacteristic
730C23×C4C23×C5311yescharacteristic
731C23×C4C23×C5311yescharacteristic
732C23×C4C23×C5311yescharacteristic
733C23×C4C23×C5311yescharacteristic
734C23×C4C23×C5311yescharacteristic
735C23×C4C23×C5311yescharacteristic
736C23×C4C23×C5311yescharacteristic
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C4⋊C4—41no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4D4×C5314yes—
788C2×C42—22no—
789C2×C42—41no—
790C2×C42—41no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95D4×C5314yescomplemented
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24C2×D4×C5312yes—
848C24#41×C5312yes—
849C24#41×C5312yes—
850C24C24×C5311yescharacteristic
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4C2×D4×C5312yes—
949C22×C4C2×D4×C5312yes—
950C22×C4C2×D4×C5312yes—
951C22×C4C2×D4×C5312yes—
952C22×C4C2×D4×C5312yes—
953C22×C4#41×C5312yes—
954C22×C4#41×C5312yes—
955C22×C4#41×C5312yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C22⋊C4—28no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C42—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C22×D4×C5311yescharacteristic
1080C23C22×D4×C5311yescharacteristic
1081C23C2×#41×C5311yescharacteristic
1082C23C2×#41×C5311yescharacteristic
1083C23C2×#41×C5311yescharacteristic
1084C23C2×#41×C5311yescharacteristic
1085C23C2×#41×C5311yescharacteristic
1086C23H(5,𝔽2)×C5311yescharacteristic
1087C23H(5,𝔽2)×C5311yescharacteristic
1088C23H(5,𝔽2)×C5311yescharacteristic
1089C23H(5,𝔽2)×C5311yescharacteristic
1090C23H(5,𝔽2)×C5311yescharacteristic
1091C23H(5,𝔽2)×C5311yescharacteristic
1092C23H(5,𝔽2)×C5311yescharacteristic
1093C23H(5,𝔽2)×C5311yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C53×#52511yescharacteristic
1227C22C53×#52911yescharacteristic
1228C22C53×#53211yescharacteristic
1229C22C53×#53411yescharacteristic
1230C22C53×#53511yescharacteristic
1231C22C53×#53511yescharacteristic
1232C22C53×#53511yescharacteristic
1233C22C53×#53811yescharacteristic
1234C22C53×#53811yescharacteristic
1235C22C53×#53811yescharacteristic
1236C22C53×#53811yescharacteristic
1237C22C53×#53811yescharacteristic
1238C22C53×#53811yescharacteristic
1239C22C53×#53811yescharacteristic
1240C22C53×#53811yescharacteristic
1241C22C53×#54011yescharacteristic
1242C22C53×#54011yescharacteristic
1243C22C53×#54011yescharacteristic
1244C22C53×#54011yescharacteristic
1245C22D42×C5311yescharacteristic
1246C22C53×#54611yescharacteristic
1247C22C53×#54611yescharacteristic
1248C22C53×#54611yescharacteristic
1249C22C53×#54611yescharacteristic
1250C22C53×#54611yescharacteristic
1251C22C53×#55011yescharacteristic
1252C22C53×#55111yescharacteristic
1253C22C53×#55111yescharacteristic
1254C22C53×#55311yescharacteristic
1255C22C53×#55311yescharacteristic
1256C22C53×#55311yescharacteristic
1257C22C53×#56011yescharacteristic
1258C22C53×#56011yescharacteristic
1259C22C53×#56011yescharacteristic
1260C22C53×H(3,𝔽4)11yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C53×#246411yescharacteristic
1277C2C53×#247111yescharacteristic
1278C2C53×#255911yescharacteristic
1279C2C53×#263111yescharacteristic
1280C2C53×#264811yescharacteristic
1281C2C53×#266111yescharacteristic
1282C2C53×#267011yescharacteristic
1283C2C53×#267311yescharacteristic
1284C2C53×#268511yescharacteristic
1285C2C53×#269711yescharacteristic
1286C2C53×#270311yescharacteristic
1287C2C53×#271411yescharacteristic
1288C2C53×#275311yescharacteristic
1289C2C53×#277811yescharacteristic
1290C2C53×#282811yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
prime radicalC2×C53×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#397C2semidirect
2. C2×C53×#394C2semidirect
4. C2×C53×#388C2semidirect
5. C53×#1443C2semidirect
6. C53×#1442C2semidirect
7. C53×#1439C2semidirect
8. C53×#1439C2semidirect
9. C53×#1438C2semidirect
10. C53×#1438C2semidirect
11. C53×#1438C2semidirect
12. C53×#1438C2semidirect
13. C53×#1438C2semidirect
14. C53×#1437C2semidirect
15. C53×#1437C2semidirect
158. #95×C53D4semidirect
535. #16535C53direct (N × H)
628. C2×#397C2×C53semidirect
629. C2×#394C2×C53semidirect
631. C2×#388C2×C53semidirect
632. #1443C2×C53semidirect
633. #1442C2×C53semidirect
634. #1439C2×C53semidirect
635. #1439C2×C53semidirect
636. #1438C2×C53semidirect
637. #1438C2×C53semidirect
638. #1438C2×C53semidirect
639. #1438C2×C53semidirect
640. #1438C2×C53semidirect
641. #1437C2×C53semidirect
642. #1437C2×C53semidirect
700. C53#16535direct (N × H)
804. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3972
C2×C53×#3942
C2×C53×#3922
C2×C53×#3882
C53×#14432
C53×#14422
C53×#14392
C53×#14382
C53×#14372
#1653553