Finite Group Databasebeta

← C53×#16274 #27223786

Subgroups — C53×#16274 #27223786

Order 13568.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1308 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×#394C211yesmaximal, characteristic, complemented
4C2×C53×#392C211yesmaximal, characteristic
5C2×C53×#390C211yesmaximal, characteristic, complemented
6C2×C53×#388C211yesmaximal, characteristic, complemented
7C53×#1441C211yesmaximal, characteristic, complemented
8C53×#1439C211yesmaximal, characteristic, complemented
9C53×#1439C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C53×#1438C211yesmaximal, characteristic, complemented
13C53×#1438C211yesmaximal, characteristic, complemented
14C53×#1438C211yesmaximal, characteristic, complemented
15C53×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×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×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×C22⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C53×#397—24no—
40C53×#394—24no—
41C53×#394—24no—
42C53×#392—24no—
43C53×#390—24no—
44C53×#388—24no—
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
57C25×C53C2311yescharacteristic
58C25×C53C2311yescharacteristic
59C25×C53C2311yescharacteristic
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—22no—
68C22×D4×C53—22no—
69C22×D4×C53—22no—
70C22×D4×C53—22no—
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—
79C22×D4×C53—41no—
80C22×D4×C53—41no—
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
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
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—22no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—41no—
101C2×C4⋊C4×C53—41no—
102C2×C4⋊C4×C53—41no—
103C2×C4⋊C4×C53—41no—
104C2×C4⋊C4×C53—41no—
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—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53—22no—
124C2×C22⋊C4×C53—22no—
125C2×C22⋊C4×C53—22no—
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×C53—41no—
142C2×C22⋊C4×C53—41no—
143C2×C22⋊C4×C53—41no—
144C2×C22⋊C4×C53—41no—
145C2×C22⋊C4×C53—41no—
146C2×C22⋊C4×C53—41no—
147C2×C22⋊C4×C53—41no—
148C2×C22⋊C4×C53D414yes—
149C2×C22⋊C4×C53D414yescomplemented
150C2×C42×C53—22no—
151C2×C42×C53—22no—
152C2×C42×C53—41no—
153#95×C53—22no—
154#95×C53—22no—
155#95×C53—22no—
156#95×C53—22no—
157#95×C53—22no—
158#95×C53—22no—
159#95×C53—22no—
160#95×C53—41no—
161#95×C53—41no—
162#95×C53—41no—
163#95×C53—41no—
164#95×C53D414yescomplemented
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×C53—21no—
202C24×C53—21no—
203C24×C53—21no—
204C24×C53—21no—
205C24×C53—21no—
206C24×C53—21no—
207C24×C53C2×D412yes—
208C24×C53C2×D412yes—
209C24×C53#4112yes—
210C24×C53C2411yescharacteristic
211C2×D4×C53—28no—
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—
226C2×D4×C53—44no—
227C2×D4×C53—44no—
228C2×D4×C53—44no—
229C2×D4×C53—44no—
230C2×D4×C53—44no—
231C2×D4×C53—44no—
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×C53—21no—
303C22×C4×C53—21no—
304C22×C4×C53—21no—
305C22×C4×C53—21no—
306C22×C4×C53C2×D412yes—
307C22×C4×C53C2×D412yes—
308C22×C4×C53C2×D412yes—
309C22×C4×C53C2×D412yes—
310C22×C4×C53C2×D412yes—
311C22×C4×C53C2×D412yes—
312C22×C4×C53C2×D412yes—
313C22×C4×C53#4112yes—
314C22×C4×C53#4112yes—
315C22×C4×C53#4112yes—
316C4⋊C4×C53—44no—
317C4⋊C4×C53—44no—
318C4⋊C4×C53—44no—
319C4⋊C4×C53—44no—
320C22⋊C4×C53—28no—
321C22⋊C4×C53—44no—
322C22⋊C4×C53—44no—
323C22⋊C4×C53—44no—
324C22⋊C4×C53—44no—
325C22⋊C4×C53—44no—
326C22⋊C4×C53—44no—
327C22⋊C4×C53—44no—
328C22⋊C4×C53—44no—
329C22⋊C4×C53—44no—
330C22⋊C4×C53—44no—
331C22⋊C4×C53—44no—
332C22⋊C4×C53—44no—
333C22⋊C4×C53—44no—
334C22⋊C4×C53—44no—
335C42×C53—44no—
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—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
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×C53—41no—
434C23×C53—41no—
435C23×C53—41no—
436C23×C53—41no—
437C23×C53—41no—
438C23×C53—41no—
439C23×C53—41no—
440C23×C53—41no—
441C23×C53C22×D411yescharacteristic
442C23×C53C22×D411yescharacteristic
443C23×C53C22×D411yescharacteristic
444C23×C53C2×#4111yescharacteristic
445C23×C53C2×#4111yescharacteristic
446C23×C53C2×#4111yescharacteristic
447C23×C53C2×#4111yescharacteristic
448C23×C53H(5,𝔽2)11yescharacteristic
449C23×C53H(5,𝔽2)11yescharacteristic
450C23×C53H(5,𝔽2)11yescharacteristic
451C23×C53H(5,𝔽2)11yescharacteristic
452C23×C53H(5,𝔽2)11yescharacteristic
453C23×C53H(5,𝔽2)11yescharacteristic
454C23×C53H(5,𝔽2)11yescharacteristic
455C23×C532−1+411yescharacteristic
456D4×C53—416no—
457D4×C53—416no—
458D4×C53—416no—
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—22no—
476C2×C4×C53—22no—
477C2×C4×C53—22no—
478C2×C4×C53—22no—
479C2×C4×C53—22no—
480C2×C4×C53—22no—
481C2×C4×C53—22no—
482C2×C4×C53—22no—
483C2×C4×C53—22no—
484C2×C4×C53—22no—
485C2×C4×C53—22no—
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—
535C2×C4×C53—41no—
536C2×C4×C53—41no—
537C2×C4×C53—41no—
538C2×C4×C53—41no—
539C2×C4×C53—41no—
540C2×C4×C53—41no—
541C2×C4×C53—41no—
542C2×C4×C53#12314yes—
543#16274C5311yesmaximal, characteristic, direct product factor, Sylow
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—42no—
558C22×C53—42no—
559C22×C53—42no—
560C22×C53—42no—
561C22×C53—42no—
562C22×C53—42no—
563C22×C53—42no—
564C22×C53—42no—
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—81no—
582C22×C53—81no—
583C22×C53—81no—
584C22×C53—81no—
585C22×C53—81no—
586C22×C53—81no—
587C22×C53—81no—
588C22×C53—81no—
589C22×C53C2×#12311yescharacteristic
590C22×C53#52511yescharacteristic
591C22×C53#53211yescharacteristic
592C22×C53#53411yescharacteristic
593C22×C53#53511yescharacteristic
594C22×C53#53511yescharacteristic
595C22×C53#53711yescharacteristic
596C22×C53#53711yescharacteristic
597C22×C53#53711yescharacteristic
598C22×C53#53811yescharacteristic
599C22×C53#53811yescharacteristic
600C22×C53#53811yescharacteristic
601C22×C53#53911yescharacteristic
602C22×C53#54011yescharacteristic
603C22×C53#54011yescharacteristic
604C22×C53#54011yescharacteristic
605C22×C53#54211yescharacteristic
606C22×C53#54211yescharacteristic
607C22×C53#54211yescharacteristic
608C22×C53D4211yescharacteristic
609C22×C53D4211yescharacteristic
610C22×C53D4211yescharacteristic
611C22×C53#54611yescharacteristic
612C22×C53#54611yescharacteristic
613C22×C53#54611yescharacteristic
614C22×C53#54611yescharacteristic
615C22×C53#54611yescharacteristic
616C22×C53#55011yescharacteristic
617C22×C53#55111yescharacteristic
618C22×C53#55311yescharacteristic
619C22×C53#55911yescharacteristic
620C22×C53#56011yescharacteristic
621C22×C53#56011yescharacteristic
622C22×C53#56011yescharacteristic
623C22×C53H(3,𝔽4)11yescharacteristic
624C4×C53—24no—
625C4×C53—42no—
626C4×C53—42no—
627C4×C53—42no—
628C4×C53—42no—
629C4×C53—42no—
630C4×C53—42no—
631C4×C53—42no—
632C4×C53—81no—
633C4×C53—81no—
634C4×C53—81no—
635C4×C53—81no—
636C2×#397C2×C5311yescharacteristic, complemented
637C2×#394C2×C5311yescharacteristic, complemented
638C2×#394C2×C5311yescharacteristic, complemented
639C2×#392C2×C5311yescharacteristic
640C2×#390C2×C5311yescharacteristic, complemented
641C2×#388C2×C5311yescharacteristic, complemented
642#1441C2×C5311yescharacteristic, complemented
643#1439C2×C5311yescharacteristic, complemented
644#1439C2×C5311yescharacteristic, complemented
645#1439C2×C5311yescharacteristic, complemented
646#1439C2×C5311yescharacteristic, complemented
647#1438C2×C5311yescharacteristic, complemented
648#1438C2×C5311yescharacteristic, complemented
649#1438C2×C5311yescharacteristic, complemented
650#1436C2×C5311yescharacteristic, complemented
651C2×C53—82no—
652C2×C53—82no—
653C2×C53—82no—
654C2×C53#241811yescharacteristic
655C2×C53#244511yescharacteristic
656C2×C53#246411yescharacteristic
657C2×C53#262411yescharacteristic
658C2×C53#263011yescharacteristic
659C2×C53#266211yescharacteristic
660C2×C53#267011yescharacteristic
661C2×C53#267311yescharacteristic
662C2×C53#267511yescharacteristic
663C2×C53#267811yescharacteristic
664C2×C53#269111yescharacteristic
665C2×C53#270511yescharacteristic
666C2×C53#271211yescharacteristic
667C2×C53#279711yescharacteristic
668C2×C53#282811yescharacteristic
669C23×D4C22×C5311yescharacteristic
670C23×D4C22×C5311yescharacteristic
671C23×D4C22×C5311yescharacteristic
672C22×C4⋊C4C22×C5311yescharacteristic
673C22×C4⋊C4C22×C5311yescharacteristic
674C22×C4⋊C4C22×C5311yescharacteristic
675C22×C4⋊C4C22×C5311yescharacteristic
676C22×C22⋊C4C22×C5311yescharacteristic
677C22×C22⋊C4C22×C5311yescharacteristic
678C22×C22⋊C4C22×C5311yescharacteristic
679C22×C22⋊C4C22×C5311yescharacteristic
680C22×C22⋊C4C22×C5311yescharacteristic
681C22×C22⋊C4C22×C5311yescharacteristic
682C22×C22⋊C4C22×C5311yescharacteristic
683C22×C22⋊C4C22×C5311yescharacteristic
684C22×C22⋊C4C22×C5311yescharacteristic
685C22×C22⋊C4C22×C5311yescharacteristic
686C22×C22⋊C4C22×C5311yescharacteristic
687C22×C22⋊C4C22×C5311yescharacteristic
688C22×C22⋊C4C22×C5311yescharacteristic
689C22×C22⋊C4C22×C5311yescharacteristic
690C22×C22⋊C4C22×C5311yescharacteristic
691C22×C42C22×C5311yescharacteristic
692#397—24no—
693#394—24no—
694#394—24no—
695#392—24no—
696#390—24no—
697#388—24no—
698C2×#95C22×C5311yescharacteristic
699C2×#95C22×C5311yescharacteristic
700C2×#95C22×C5311yescharacteristic
701C2×#95C22×C5311yescharacteristic
702C2×#95C22×C5311yescharacteristic
703C2×#95C22×C5311yescharacteristic
704C2×#95C22×C5311yescharacteristic
705C2×#95C22×C5311yescharacteristic
706C2×#95C22×C5311yescharacteristic
707C2×#95C22×C5311yescharacteristic
708C2×#95C22×C5311yescharacteristic
709C2×#95C22×C5311yescharacteristic
710C53#1627411yescharacteristic, direct product factor, Sylow
711C25C23×C5311yescharacteristic
712C25C23×C5311yescharacteristic
713C25C23×C5311yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C23×C4C23×C5311yescharacteristic
736C23×C4C23×C5311yescharacteristic
737C23×C4C23×C5311yescharacteristic
738C23×C4C23×C5311yescharacteristic
739C23×C4C23×C5311yescharacteristic
740C23×C4C23×C5311yescharacteristic
741C23×C4C23×C5311yescharacteristic
742C23×C4C23×C5311yescharacteristic
743C23×C4C23×C5311yescharacteristic
744C23×C4C23×C5311yescharacteristic
745C23×C4C23×C5311yescharacteristic
746C23×C4C23×C5311yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
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⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4D4×C5314yes—
803C2×C22⋊C4D4×C5314yescomplemented
804C2×C42—22no—
805C2×C42—22no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C5314yescomplemented
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—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C5312yes—
862C24C2×D4×C5312yes—
863C24#41×C5312yes—
864C24C24×C5311yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
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×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4C2×D4×C5312yes—
961C22×C4C2×D4×C5312yes—
962C22×C4C2×D4×C5312yes—
963C22×C4C2×D4×C5312yes—
964C22×C4C2×D4×C5312yes—
965C22×C4C2×D4×C5312yes—
966C22×C4C2×D4×C5312yes—
967C22×C4#41×C5312yes—
968C22×C4#41×C5312yes—
969C22×C4#41×C5312yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—28no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
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—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C5311yescharacteristic
1096C23C22×D4×C5311yescharacteristic
1097C23C22×D4×C5311yescharacteristic
1098C23C2×#41×C5311yescharacteristic
1099C23C2×#41×C5311yescharacteristic
1100C23C2×#41×C5311yescharacteristic
1101C23C2×#41×C5311yescharacteristic
1102C23H(5,𝔽2)×C5311yescharacteristic
1103C23H(5,𝔽2)×C5311yescharacteristic
1104C23H(5,𝔽2)×C5311yescharacteristic
1105C23H(5,𝔽2)×C5311yescharacteristic
1106C23H(5,𝔽2)×C5311yescharacteristic
1107C23H(5,𝔽2)×C5311yescharacteristic
1108C23H(5,𝔽2)×C5311yescharacteristic
1109C232−1+4×C5311yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
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—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
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—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4#123×C5314yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C5311yescharacteristic
1243C22C53×#52511yescharacteristic
1244C22C53×#53211yescharacteristic
1245C22C53×#53411yescharacteristic
1246C22C53×#53511yescharacteristic
1247C22C53×#53511yescharacteristic
1248C22C53×#53711yescharacteristic
1249C22C53×#53711yescharacteristic
1250C22C53×#53711yescharacteristic
1251C22C53×#53811yescharacteristic
1252C22C53×#53811yescharacteristic
1253C22C53×#53811yescharacteristic
1254C22C53×#53911yescharacteristic
1255C22C53×#54011yescharacteristic
1256C22C53×#54011yescharacteristic
1257C22C53×#54011yescharacteristic
1258C22C53×#54211yescharacteristic
1259C22C53×#54211yescharacteristic
1260C22C53×#54211yescharacteristic
1261C22D42×C5311yescharacteristic
1262C22D42×C5311yescharacteristic
1263C22D42×C5311yescharacteristic
1264C22C53×#54611yescharacteristic
1265C22C53×#54611yescharacteristic
1266C22C53×#54611yescharacteristic
1267C22C53×#54611yescharacteristic
1268C22C53×#54611yescharacteristic
1269C22C53×#55011yescharacteristic
1270C22C53×#55111yescharacteristic
1271C22C53×#55311yescharacteristic
1272C22C53×#55911yescharacteristic
1273C22C53×#56011yescharacteristic
1274C22C53×#56011yescharacteristic
1275C22C53×#56011yescharacteristic
1276C22C53×H(3,𝔽4)11yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C53×#241811yescharacteristic
1293C2C53×#244511yescharacteristic
1294C2C53×#246411yescharacteristic
1295C2C53×#262411yescharacteristic
1296C2C53×#263011yescharacteristic
1297C2C53×#266211yescharacteristic
1298C2C53×#267011yescharacteristic
1299C2C53×#267311yescharacteristic
1300C2C53×#267511yescharacteristic
1301C2C53×#267811yescharacteristic
1302C2C53×#269111yescharacteristic
1303C2C53×#270511yescharacteristic
1304C2C53×#271211yescharacteristic
1305C2C53×#279711yescharacteristic
1306C2C53×#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
3. C2×C53×#394C2semidirect
5. C2×C53×#390C2semidirect
6. C2×C53×#388C2semidirect
7. C53×#1441C2semidirect
8. C53×#1439C2semidirect
9. C53×#1439C2semidirect
10. C53×#1439C2semidirect
11. C53×#1439C2semidirect
12. C53×#1438C2semidirect
13. C53×#1438C2semidirect
14. C53×#1438C2semidirect
15. C53×#1436C2semidirect
149. C2×C22⋊C4×C53D4semidirect
164. #95×C53D4semidirect
543. #16274C53direct (N × H)
636. C2×#397C2×C53semidirect
637. C2×#394C2×C53semidirect
638. C2×#394C2×C53semidirect
640. C2×#390C2×C53semidirect
641. C2×#388C2×C53semidirect
642. #1441C2×C53semidirect
643. #1439C2×C53semidirect
644. #1439C2×C53semidirect
645. #1439C2×C53semidirect
646. #1439C2×C53semidirect
647. #1438C2×C53semidirect
648. #1438C2×C53semidirect
649. #1438C2×C53semidirect
650. #1436C2×C53semidirect
710. C53#16274direct (N × H)
803. C2×C22⋊C4D4×C53semidirect
818. #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×#3902
C2×C53×#3882
C53×#14412
C53×#14392
C53×#14382
C53×#14362
#1627453