Finite Group Databasebeta

← C2×C53×#2424 #27242162

Subgroups — C2×C53×#2424 #27242162

Order 13568.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C53C211yesmaximal, characteristic, complemented
2C22×#121×C53C211yesmaximal, characteristic, complemented
3C22×#120×C53C211yesmaximal, characteristic, complemented
4C22×#120×C53C211yesmaximal, characteristic, complemented
5C22×C4×D4×C53C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C53C211yesmaximal, characteristic, complemented
7C53×#2424C2116yesmaximal, direct product factor
8C2×C53×#396C211yesmaximal, characteristic, complemented
9C2×C53×#394C211yesmaximal, characteristic, complemented
10C2×C53×#394C211yesmaximal, characteristic, complemented
11C2×C53×#392C211yesmaximal, characteristic, complemented
12C2×C53×#390C211yesmaximal, characteristic, complemented
13C2×C53×#388C211yesmaximal, characteristic, complemented
14C2×C53×#386C211yesmaximal, characteristic, complemented
15C2×C53×#386C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic, complemented
17C26×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C23×D4×C53C2211yescharacteristic
20C23×D4×C53C2211yescharacteristic
21C23×D4×C53C2211yescharacteristic
22C23×D4×C53C2211yescharacteristic
23C23×D4×C53C2211yescharacteristic
24C23×D4×C53C2211yescharacteristic, complemented
25C24×C4×C53C2211yescharacteristic
26C24×C4×C53C2211yescharacteristic
27C24×C4×C53C2211yescharacteristic, complemented
28C2×#121×C53—28no—
29C2×#121×C53—28no—
30C2×#121×C53C2218yescomplemented
31C2×#121×C53C2218yescomplemented
32C2×#120×C53—28no—
33C2×#120×C53—28no—
34C2×#120×C53C2218yescomplemented
35C2×#120×C53C2218yescomplemented
36C2×C4×D4×C53—28no—
37C2×C4×D4×C53C2218yescomplemented
38C22×C4⋊C4×C53C2211yescharacteristic, complemented
39C22×C4⋊C4×C53C2211yescharacteristic, complemented
40C22×C4⋊C4×C53C2211yescharacteristic, complemented
41C22×C4⋊C4×C53C2211yescharacteristic, complemented
42C22×C22⋊C4×C53—28no—
43C22×C22⋊C4×C53C2211yescharacteristic
44C22×C22⋊C4×C53C2211yescharacteristic
45C22×C22⋊C4×C53C2211yescharacteristic
46C22×C22⋊C4×C53C2211yescharacteristic
47C22×C22⋊C4×C53C2211yescharacteristic
48C22×C22⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2218yescomplemented
54C22×C22⋊C4×C53C2211yescharacteristic, complemented
55C22×C22⋊C4×C53C2211yescharacteristic, complemented
56C22×C22⋊C4×C53C2211yescharacteristic, complemented
57C22×C22⋊C4×C53C2211yescharacteristic, complemented
58C22×C22⋊C4×C53C2211yescharacteristic, complemented
59C22×C42×C53C2211yescharacteristic, complemented
60C53×#396C2218yescomplemented
61C53×#394C2218yescomplemented
62C53×#394C2218yescomplemented
63C53×#392C2218yescomplemented
64C53×#390C2218yescomplemented
65C53×#388C2218yescomplemented
66C53×#386C2218yescomplemented
67C53×#386C2218yescomplemented
68C53×#385C2218yescomplemented
69C2×#95×C53C2211yescharacteristic, complemented
70C2×#95×C53C2211yescharacteristic, complemented
71C2×#95×C53C2211yescharacteristic, complemented
72C2×#95×C53C2211yescharacteristic, complemented
73C25×C53—24no—
74C25×C53—24no—
75C25×C53—24no—
76C25×C53—24no—
77C25×C53—24no—
78C25×C53—42no—
79C25×C53—42no—
80C25×C53C2311yescharacteristic
81C25×C53C2311yescharacteristic
82C25×C53C2311yescharacteristic
83C25×C53C2311yescharacteristic
84C25×C53C2314yes—
85C25×C53C2311yescharacteristic
86C22×D4×C53—24no—
87C22×D4×C53—24no—
88C22×D4×C53—24no—
89C22×D4×C53—24no—
90C22×D4×C53—24no—
91C22×D4×C53—24no—
92C22×D4×C53—24no—
93C22×D4×C53—24no—
94C22×D4×C53—24no—
95C22×D4×C53—24no—
96C22×D4×C53—24no—
97C22×D4×C53—24no—
98C22×D4×C53—24no—
99C22×D4×C53—24no—
100C22×D4×C53—24no—
101C22×D4×C53—42no—
102C22×D4×C53—42no—
103C22×D4×C53—42no—
104C22×D4×C53—42no—
105C22×D4×C53—42no—
106C22×D4×C53D418yescomplemented
107C22×D4×C53C2314yes—
108C22×D4×C53C2314yes—
109C22×D4×C53C2314yes—
110C22×D4×C53C2314yes—
111C22×D4×C53C2314yes—
112C22×D4×C53C2314yes—
113C22×D4×C53C2314yescomplemented
114C23×C4×C53—24no—
115C23×C4×C53—24no—
116C23×C4×C53—24no—
117C23×C4×C53—24no—
118C23×C4×C53—24no—
119C23×C4×C53—24no—
120C23×C4×C53—42no—
121C23×C4×C53—42no—
122C23×C4×C53—42no—
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2314yes—
129C23×C4×C53C2314yes—
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2314yescomplemented
136#121×C53—232no—
137#121×C53—232no—
138#120×C53—232no—
139#120×C53—232no—
140C4×D4×C53—232no—
141C2×C4⋊C4×C53—24no—
142C2×C4⋊C4×C53—24no—
143C2×C4⋊C4×C53—24no—
144C2×C4⋊C4×C53—42no—
145C2×C4⋊C4×C53C2314yescomplemented
146C2×C4⋊C4×C53C2314yescomplemented
147C2×C4⋊C4×C53C2314yescomplemented
148C2×C4⋊C4×C53C2314yescomplemented
149C2×C22⋊C4×C53—232no—
150C2×C22⋊C4×C53—24no—
151C2×C22⋊C4×C53—24no—
152C2×C22⋊C4×C53—24no—
153C2×C22⋊C4×C53—24no—
154C2×C22⋊C4×C53—24no—
155C2×C22⋊C4×C53—24no—
156C2×C22⋊C4×C53—24no—
157C2×C22⋊C4×C53—24no—
158C2×C22⋊C4×C53—24no—
159C2×C22⋊C4×C53—24no—
160C2×C22⋊C4×C53—24no—
161C2×C22⋊C4×C53—24no—
162C2×C22⋊C4×C53—42no—
163C2×C22⋊C4×C53D418yescomplemented
164C2×C22⋊C4×C53D418yescomplemented
165C2×C22⋊C4×C53C2314yes—
166C2×C22⋊C4×C53C2314yes—
167C2×C22⋊C4×C53C2314yes—
168C2×C22⋊C4×C53C2314yes—
169C2×C22⋊C4×C53C2314yes—
170C2×C22⋊C4×C53C2314yes—
171C2×C22⋊C4×C53C2314yes—
172C2×C22⋊C4×C53C2314yes—
173C2×C22⋊C4×C53C2314yes—
174C2×C22⋊C4×C53C2314yes—
175C2×C22⋊C4×C53C2314yescomplemented
176C2×C22⋊C4×C53C2314yescomplemented
177C2×C22⋊C4×C53C2314yescomplemented
178C2×C22⋊C4×C53C2314yescomplemented
179C2×C22⋊C4×C53C2314yescomplemented
180C2×C42×C53—24no—
181C2×C42×C53C2314yescomplemented
182#95×C53C2314yescomplemented
183#95×C53C2314yescomplemented
184#95×C53C2314yescomplemented
185#95×C53C2314yescomplemented
186C24×C53—22no—
187C24×C53—22no—
188C24×C53—22no—
189C24×C53—22no—
190C24×C53—232no—
191C24×C53—28no—
192C24×C53—22no—
193C24×C53—22no—
194C24×C53—22no—
195C24×C53—22no—
196C24×C53—22no—
197C24×C53—22no—
198C24×C53—22no—
199C24×C53—22no—
200C24×C53—22no—
201C24×C53—28no—
202C24×C53—28no—
203C24×C53—22no—
204C24×C53—22no—
205C24×C53—22no—
206C24×C53—22no—
207C24×C53—22no—
208C24×C53—22no—
209C24×C53—22no—
210C24×C53—22no—
211C24×C53—22no—
212C24×C53—22no—
213C24×C53—22no—
214C24×C53—28no—
215C24×C53—28no—
216C24×C53—22no—
217C24×C53—22no—
218C24×C53—22no—
219C24×C53—22no—
220C24×C53—22no—
221C24×C53—44no—
222C24×C53—44no—
223C24×C53—416no—
224C24×C53—416no—
225C24×C53—416no—
226C24×C53—416no—
227C24×C53—416no—
228C24×C53—416no—
229C24×C53C2×D414yes—
230C24×C53C2×D414yes—
231C24×C53C2×D414yes—
232C24×C53C2×D414yes—
233C24×C53#4114yes—
234C24×C53#4114yes—
235C24×C53C2412yes—
236C24×C53C2412yes—
237C24×C53C2412yes—
238C24×C53C2412yes—
239C24×C53C2412yes—
240C24×C53C2411yescharacteristic
241C2×D4×C53—232no—
242C2×D4×C53—28no—
243C2×D4×C53—28no—
244C2×D4×C53—28no—
245C2×D4×C53—28no—
246C2×D4×C53—28no—
247C2×D4×C53—28no—
248C2×D4×C53—28no—
249C2×D4×C53—28no—
250C2×D4×C53—28no—
251C2×D4×C53—28no—
252C2×D4×C53—28no—
253C2×D4×C53—28no—
254C2×D4×C53—28no—
255C2×D4×C53—28no—
256C2×D4×C53—28no—
257C2×D4×C53—44no—
258C2×D4×C53—44no—
259C2×D4×C53—44no—
260C2×D4×C53—44no—
261C2×D4×C53—44no—
262C2×D4×C53—416no—
263C2×D4×C53—416no—
264C2×D4×C53—416no—
265C2×D4×C53—416no—
266C2×D4×C53—416no—
267C2×D4×C53—416no—
268C2×D4×C53C2×D4116yescomplemented
269C22×C4×C53—22no—
270C22×C4×C53—22no—
271C22×C4×C53—22no—
272C22×C4×C53—22no—
273C22×C4×C53—22no—
274C22×C4×C53—22no—
275C22×C4×C53—22no—
276C22×C4×C53—22no—
277C22×C4×C53—22no—
278C22×C4×C53—22no—
279C22×C4×C53—22no—
280C22×C4×C53—22no—
281C22×C4×C53—22no—
282C22×C4×C53—22no—
283C22×C4×C53—22no—
284C22×C4×C53—22no—
285C22×C4×C53—22no—
286C22×C4×C53—22no—
287C22×C4×C53—22no—
288C22×C4×C53—28no—
289C22×C4×C53—28no—
290C22×C4×C53—22no—
291C22×C4×C53—22no—
292C22×C4×C53—22no—
293C22×C4×C53—22no—
294C22×C4×C53—22no—
295C22×C4×C53—22no—
296C22×C4×C53—28no—
297C22×C4×C53—28no—
298C22×C4×C53—28no—
299C22×C4×C53—28no—
300C22×C4×C53—44no—
301C22×C4×C53—44no—
302C22×C4×C53—44no—
303C22×C4×C53—416no—
304C22×C4×C53—416no—
305C22×C4×C53—416no—
306C22×C4×C53C2×D414yes—
307C22×C4×C53C2×D414yes—
308C22×C4×C53C2×D414yes—
309C22×C4×C53C2×D414yes—
310C22×C4×C53C2×D414yes—
311C22×C4×C53C2412yes—
312C22×C4×C53C2412yes—
313C22×C4×C53C2412yes—
314C22×C4×C53C2412yes—
315C22×C4×C53C2412yes—
316C22×C4×C53C2412yes—
317C22×C4×C53C2412yes—
318C22×C4×C53C2412yes—
319C22×C4×C53C2412yes—
320C22×C4×C53C2412yes—
321C4⋊C4×C53—28no—
322C4⋊C4×C53—28no—
323C4⋊C4×C53—28no—
324C4⋊C4×C53—44no—
325C22⋊C4×C53—28no—
326C22⋊C4×C53—28no—
327C22⋊C4×C53—28no—
328C22⋊C4×C53—28no—
329C22⋊C4×C53—28no—
330C22⋊C4×C53—28no—
331C22⋊C4×C53—28no—
332C22⋊C4×C53—28no—
333C22⋊C4×C53—28no—
334C22⋊C4×C53—28no—
335C22⋊C4×C53—28no—
336C22⋊C4×C53—28no—
337C22⋊C4×C53—44no—
338C22⋊C4×C53C2×D4116yescomplemented
339C22⋊C4×C53C2×D4116yescomplemented
340C42×C53—28no—
341C23×C53—28no—
342C23×C53—28no—
343C23×C53—28no—
344C23×C53—28no—
345C23×C53—28no—
346C23×C53—28no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—232no—
352C23×C53—28no—
353C23×C53—28no—
354C23×C53—28no—
355C23×C53—28no—
356C23×C53—28no—
357C23×C53—28no—
358C23×C53—28no—
359C23×C53—28no—
360C23×C53—28no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—22no—
373C23×C53—22no—
374C23×C53—22no—
375C23×C53—22no—
376C23×C53—22no—
377C23×C53—22no—
378C23×C53—22no—
379C23×C53—22no—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—22no—
386C23×C53—416no—
387C23×C53—416no—
388C23×C53—416no—
389C23×C53—416no—
390C23×C53—4128no—
391C23×C53—416no—
392C23×C53—44no—
393C23×C53—44no—
394C23×C53—416no—
395C23×C53—44no—
396C23×C53—44no—
397C23×C53—44no—
398C23×C53—44no—
399C23×C53—44no—
400C23×C53—44no—
401C23×C53—44no—
402C23×C53—44no—
403C23×C53—44no—
404C23×C53—44no—
405C23×C53—44no—
406C23×C53—44no—
407C23×C53—44no—
408C23×C53—44no—
409C23×C53—44no—
410C23×C53—44no—
411C23×C53—44no—
412C23×C53#121116yescomplemented
413C23×C53C22×D414yes—
414C23×C53C22×D414yes—
415C23×C53C22×D414yes—
416C23×C53C22×D414yes—
417C23×C53C22×D412yes—
418C23×C53C22×D412yes—
419C23×C53C22×D412yes—
420C23×C53C2×#4114yes—
421C23×C53C2×#4114yes—
422C23×C53C2×#4112yes—
423C23×C53C2×#4112yes—
424C23×C53H(5,𝔽2)12yes—
425C23×C53H(5,𝔽2)12yes—
426C23×C53C2511yescharacteristic
427D4×C53—232no—
428D4×C53—416no—
429D4×C53—416no—
430D4×C53—416no—
431D4×C53—416no—
432D4×C53—416no—
433D4×C53—416no—
434C2×C4×C53—28no—
435C2×C4×C53—28no—
436C2×C4×C53—28no—
437C2×C4×C53—28no—
438C2×C4×C53—28no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53—22no—
447C2×C4×C53—22no—
448C2×C4×C53—22no—
449C2×C4×C53—22no—
450C2×C4×C53—22no—
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—416no—
465C2×C4×C53—416no—
466C2×C4×C53—416no—
467C2×C4×C53—44no—
468C2×C4×C53—44no—
469C2×C4×C53—44no—
470C2×C4×C53—44no—
471C2×C4×C53—44no—
472C2×C4×C53C22×D414yes—
473C2×C4×C53C22×D414yes—
474C2×C4×C53C22×D414yes—
475C2×C4×C53C22×D414yes—
476C2×C4×C53C22×D414yes—
477C2×#2424C5311yesmaximal, characteristic, direct product factor, Sylow
478C22×C53—24no—
479C22×C53—232no—
480C22×C53—24no—
481C22×C53—24no—
482C22×C53—24no—
483C22×C53—24no—
484C22×C53—24no—
485C22×C53—24no—
486C22×C53—24no—
487C22×C53—24no—
488C22×C53—24no—
489C22×C53—24no—
490C22×C53—24no—
491C22×C53—24no—
492C22×C53—24no—
493C22×C53—24no—
494C22×C53—464no—
495C22×C53—42no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—416no—
499C22×C53—416no—
500C22×C53—416no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—42no—
516C22×C53—42no—
517C22×C53—88no—
518C22×C53C2×#12114yes—
519C22×C53C2×#12118yescomplemented
520C22×C53#52514yes—
521C22×C53#53814yes—
522C22×C53D4214yes—
523C22×C53D4214yes—
524C22×C53#54614yes—
525C22×C53#54614yes—
526C22×C53C23×D411yescharacteristic
527C22×C53C23×D411yescharacteristic
528C22×C53C23×D411yescharacteristic
529C22×C53C22×#4111yescharacteristic
530C22×C53C22×#4111yescharacteristic
531C22×C53C2×H(5,𝔽2)11yescharacteristic
532C22×C53C2×H(5,𝔽2)11yescharacteristic
533C4×C53—24no—
534C4×C53—24no—
535C4×C53—24no—
536C4×C53—24no—
537C4×C53—24no—
538C4×C53—42no—
539C4×C53—42no—
540C4×C53—42no—
541C4×C53—42no—
542C4×C53—42no—
543C22×#121C2×C5311yescharacteristic, complemented
544C22×#121C2×C5311yescharacteristic, complemented
545C22×#120C2×C5311yescharacteristic, complemented
546C22×#120C2×C5311yescharacteristic, complemented
547C22×C4×D4C2×C5311yescharacteristic, complemented
548C23×C22⋊C4C2×C5311yescharacteristic, complemented
549#2424C2×C53116yesdirect product factor
550C2×#396C2×C5311yescharacteristic, complemented
551C2×#394C2×C5311yescharacteristic, complemented
552C2×#394C2×C5311yescharacteristic, complemented
553C2×#392C2×C5311yescharacteristic, complemented
554C2×#390C2×C5311yescharacteristic, complemented
555C2×#388C2×C5311yescharacteristic, complemented
556C2×#386C2×C5311yescharacteristic, complemented
557C2×#386C2×C5311yescharacteristic, complemented
558C2×#385C2×C5311yescharacteristic, complemented
559C2×C53—28no—
560C2×C53—44no—
561C2×C53—44no—
562C2×C53—44no—
563C2×C53—82no—
564C2×C53#242418yesdirect product factor
565C2×C53C22×#12111yescharacteristic
566C2×C53C2×#52511yescharacteristic
567C2×C53C2×#53811yescharacteristic
568C2×C53C2×D4211yescharacteristic
569C2×C53C2×D4211yescharacteristic
570C2×C53C2×#54611yescharacteristic
571C2×C53C2×#54611yescharacteristic
572C26C22×C5311yescharacteristic
573C23×D4C22×C5311yescharacteristic
574C23×D4C22×C5311yescharacteristic
575C23×D4C22×C5311yescharacteristic
576C23×D4C22×C5311yescharacteristic
577C23×D4C22×C5311yescharacteristic
578C23×D4C22×C5311yescharacteristic
579C23×D4C22×C5311yescharacteristic, complemented
580C24×C4C22×C5311yescharacteristic
581C24×C4C22×C5311yescharacteristic
582C24×C4C22×C5311yescharacteristic, complemented
583C2×#121—28no—
584C2×#121—28no—
585C2×#121C22×C5318yescomplemented
586C2×#121C22×C5318yescomplemented
587C2×#120—28no—
588C2×#120—28no—
589C2×#120C22×C5318yescomplemented
590C2×#120C22×C5318yescomplemented
591C2×C4×D4—28no—
592C2×C4×D4C22×C5318yescomplemented
593C22×C4⋊C4C22×C5311yescharacteristic, complemented
594C22×C4⋊C4C22×C5311yescharacteristic, complemented
595C22×C4⋊C4C22×C5311yescharacteristic, complemented
596C22×C4⋊C4C22×C5311yescharacteristic, complemented
597C22×C22⋊C4—28no—
598C22×C22⋊C4C22×C5311yescharacteristic
599C22×C22⋊C4C22×C5311yescharacteristic
600C22×C22⋊C4C22×C5311yescharacteristic
601C22×C22⋊C4C22×C5311yescharacteristic
602C22×C22⋊C4C22×C5311yescharacteristic
603C22×C22⋊C4C22×C5311yescharacteristic
604C22×C22⋊C4C22×C5311yescharacteristic
605C22×C22⋊C4C22×C5311yescharacteristic
606C22×C22⋊C4C22×C5311yescharacteristic
607C22×C22⋊C4C22×C5311yescharacteristic
608C22×C22⋊C4C22×C5318yescomplemented
609C22×C22⋊C4C22×C5311yescharacteristic, complemented
610C22×C22⋊C4C22×C5311yescharacteristic, complemented
611C22×C22⋊C4C22×C5311yescharacteristic, complemented
612C22×C22⋊C4C22×C5311yescharacteristic, complemented
613C22×C22⋊C4C22×C5311yescharacteristic, complemented
614C22×C42C22×C5311yescharacteristic, complemented
615#396C22×C5318yescomplemented
616#394C22×C5318yescomplemented
617#394C22×C5318yescomplemented
618#392C22×C5318yescomplemented
619#390C22×C5318yescomplemented
620#388C22×C5318yescomplemented
621#386C22×C5318yescomplemented
622#386C22×C5318yescomplemented
623#385C22×C5318yescomplemented
624C2×#95C22×C5311yescharacteristic, complemented
625C2×#95C22×C5311yescharacteristic, complemented
626C2×#95C22×C5311yescharacteristic, complemented
627C2×#95C22×C5311yescharacteristic, complemented
628C53C2×#242411yescharacteristic, direct product factor, Sylow
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—24no—
634C25—42no—
635C25—42no—
636C25C23×C5311yescharacteristic
637C25C23×C5311yescharacteristic
638C25C23×C5311yescharacteristic
639C25C23×C5311yescharacteristic
640C25C23×C5314yes—
641C25C23×C5311yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—24no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4D4×C5318yescomplemented
663C22×D4C23×C5314yes—
664C22×D4C23×C5314yes—
665C22×D4C23×C5314yes—
666C22×D4C23×C5314yes—
667C22×D4C23×C5314yes—
668C22×D4C23×C5314yes—
669C22×D4C23×C5314yescomplemented
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—42no—
679C23×C4C23×C5311yescharacteristic
680C23×C4C23×C5311yescharacteristic
681C23×C4C23×C5311yescharacteristic
682C23×C4C23×C5311yescharacteristic
683C23×C4C23×C5311yescharacteristic
684C23×C4C23×C5314yes—
685C23×C4C23×C5314yes—
686C23×C4C23×C5311yescharacteristic
687C23×C4C23×C5311yescharacteristic
688C23×C4C23×C5311yescharacteristic
689C23×C4C23×C5311yescharacteristic
690C23×C4C23×C5311yescharacteristic
691C23×C4C23×C5314yescomplemented
692#121—232no—
693#121—232no—
694#120—232no—
695#120—232no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4C23×C5314yescomplemented
702C2×C4⋊C4C23×C5314yescomplemented
703C2×C4⋊C4C23×C5314yescomplemented
704C2×C4⋊C4C23×C5314yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—232no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4D4×C5318yescomplemented
720C2×C22⋊C4D4×C5318yescomplemented
721C2×C22⋊C4C23×C5314yes—
722C2×C22⋊C4C23×C5314yes—
723C2×C22⋊C4C23×C5314yes—
724C2×C22⋊C4C23×C5314yes—
725C2×C22⋊C4C23×C5314yes—
726C2×C22⋊C4C23×C5314yes—
727C2×C22⋊C4C23×C5314yes—
728C2×C22⋊C4C23×C5314yes—
729C2×C22⋊C4C23×C5314yes—
730C2×C22⋊C4C23×C5314yes—
731C2×C22⋊C4C23×C5314yescomplemented
732C2×C22⋊C4C23×C5314yescomplemented
733C2×C22⋊C4C23×C5314yescomplemented
734C2×C22⋊C4C23×C5314yescomplemented
735C2×C22⋊C4C23×C5314yescomplemented
736C2×C42—24no—
737C2×C42C23×C5314yescomplemented
738#95C23×C5314yescomplemented
739#95C23×C5314yescomplemented
740#95C23×C5314yescomplemented
741#95C23×C5314yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C5314yes—
786C24C2×D4×C5314yes—
787C24C2×D4×C5314yes—
788C24C2×D4×C5314yes—
789C24#41×C5314yes—
790C24#41×C5314yes—
791C24C24×C5312yes—
792C24C24×C5312yes—
793C24C24×C5312yes—
794C24C24×C5312yes—
795C24C24×C5312yes—
796C24C24×C5311yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C53116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C5314yes—
863C22×C4C2×D4×C5314yes—
864C22×C4C2×D4×C5314yes—
865C22×C4C2×D4×C5314yes—
866C22×C4C2×D4×C5314yes—
867C22×C4C24×C5312yes—
868C22×C4C24×C5312yes—
869C22×C4C24×C5312yes—
870C22×C4C24×C5312yes—
871C22×C4C24×C5312yes—
872C22×C4C24×C5312yes—
873C22×C4C24×C5312yes—
874C22×C4C24×C5312yes—
875C22×C4C24×C5312yes—
876C22×C4C24×C5312yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C53116yescomplemented
895C22⋊C4C2×D4×C53116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—4128no—
947C23—416no—
948C23—44no—
949C23—44no—
950C23—416no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23#121×C53116yescomplemented
969C23C22×D4×C5314yes—
970C23C22×D4×C5314yes—
971C23C22×D4×C5314yes—
972C23C22×D4×C5314yes—
973C23C22×D4×C5312yes—
974C23C22×D4×C5312yes—
975C23C22×D4×C5312yes—
976C23C2×#41×C5314yes—
977C23C2×#41×C5314yes—
978C23C2×#41×C5312yes—
979C23C2×#41×C5312yes—
980C23H(5,𝔽2)×C5312yes—
981C23H(5,𝔽2)×C5312yes—
982C23C25×C5311yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C5314yes—
1029C2×C4C22×D4×C5314yes—
1030C2×C4C22×D4×C5314yes—
1031C2×C4C22×D4×C5314yes—
1032C2×C4C22×D4×C5314yes—
1033C22—232no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—416no—
1051C22—416no—
1052C22—416no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×#121×C5314yes—
1074C22C2×#121×C5318yescomplemented
1075C22C53×#52514yes—
1076C22C53×#53814yes—
1077C22D42×C5314yes—
1078C22D42×C5314yes—
1079C22C53×#54614yes—
1080C22C53×#54614yes—
1081C22C23×D4×C5311yescharacteristic
1082C22C23×D4×C5311yescharacteristic
1083C22C23×D4×C5311yescharacteristic
1084C22C22×#41×C5311yescharacteristic
1085C22C22×#41×C5311yescharacteristic
1086C22C2×H(5,𝔽2)×C5311yescharacteristic
1087C22C2×H(5,𝔽2)×C5311yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C53×#242418yesdirect product factor
1104C2C22×#121×C5311yescharacteristic
1105C2C2×C53×#52511yescharacteristic
1106C2C2×C53×#53811yescharacteristic
1107C2C2×D42×C5311yescharacteristic
1108C2C2×D42×C5311yescharacteristic
1109C2C2×C53×#54611yescharacteristic
1110C2C2×C53×#54611yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC23C25×C53
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C53C2semidirect
2. C22×#121×C53C2semidirect
3. C22×#120×C53C2semidirect
4. C22×#120×C53C2semidirect
5. C22×C4×D4×C53C2semidirect
6. C23×C22⋊C4×C53C2semidirect
7. C53×#2424C2direct (N × H)
8. C2×C53×#396C2semidirect
9. C2×C53×#394C2semidirect
10. C2×C53×#394C2semidirect
11. C2×C53×#392C2semidirect
12. C2×C53×#390C2semidirect
13. C2×C53×#388C2semidirect
14. C2×C53×#386C2semidirect
15. C2×C53×#386C2semidirect
16. C2×C53×#385C2semidirect
24. C23×D4×C53C22semidirect
27. C24×C4×C53C22semidirect
30. C2×#121×C53C22semidirect
31. C2×#121×C53C22semidirect
34. C2×#120×C53C22semidirect
35. C2×#120×C53C22semidirect
37. C2×C4×D4×C53C22semidirect
38. C22×C4⋊C4×C53C22semidirect
39. C22×C4⋊C4×C53C22semidirect
40. C22×C4⋊C4×C53C22semidirect
41. C22×C4⋊C4×C53C22semidirect
53. C22×C22⋊C4×C53C22semidirect
54. C22×C22⋊C4×C53C22semidirect
55. C22×C22⋊C4×C53C22semidirect
56. C22×C22⋊C4×C53C22semidirect
57. C22×C22⋊C4×C53C22semidirect
58. C22×C22⋊C4×C53C22semidirect
59. C22×C42×C53C22semidirect
60. C53×#396C22semidirect
61. C53×#394C22semidirect
62. C53×#394C22semidirect
63. C53×#392C22semidirect
64. C53×#390C22semidirect
65. C53×#388C22semidirect
66. C53×#386C22semidirect
67. C53×#386C22semidirect
68. C53×#385C22semidirect
69. C2×#95×C53C22semidirect
70. C2×#95×C53C22semidirect
71. C2×#95×C53C22semidirect
72. C2×#95×C53C22semidirect
106. C22×D4×C53D4semidirect
113. C22×D4×C53C23semidirect
135. C23×C4×C53C23semidirect
145. C2×C4⋊C4×C53C23semidirect
146. C2×C4⋊C4×C53C23semidirect
147. C2×C4⋊C4×C53C23semidirect
148. C2×C4⋊C4×C53C23semidirect
163. C2×C22⋊C4×C53D4semidirect
164. C2×C22⋊C4×C53D4semidirect
175. C2×C22⋊C4×C53C23semidirect
176. C2×C22⋊C4×C53C23semidirect
177. C2×C22⋊C4×C53C23semidirect
178. C2×C22⋊C4×C53C23semidirect
179. C2×C22⋊C4×C53C23semidirect
181. C2×C42×C53C23semidirect
182. #95×C53C23semidirect
183. #95×C53C23semidirect
184. #95×C53C23semidirect
185. #95×C53C23semidirect
268. C2×D4×C53C2×D4semidirect
338. C22⋊C4×C53C2×D4semidirect
339. C22⋊C4×C53C2×D4semidirect
412. C23×C53#121semidirect
477. C2×#2424C53direct (N × H)
519. C22×C53C2×#121semidirect
543. C22×#121C2×C53semidirect
544. C22×#121C2×C53semidirect
545. C22×#120C2×C53semidirect
546. C22×#120C2×C53semidirect
547. C22×C4×D4C2×C53semidirect
548. C23×C22⋊C4C2×C53semidirect
549. #2424C2×C53direct (N × H)
550. C2×#396C2×C53semidirect
551. C2×#394C2×C53semidirect
552. C2×#394C2×C53semidirect
553. C2×#392C2×C53semidirect
554. C2×#390C2×C53semidirect
555. C2×#388C2×C53semidirect
556. C2×#386C2×C53semidirect
557. C2×#386C2×C53semidirect
558. C2×#385C2×C53semidirect
564. C2×C53#2424direct (N × H)
579. C23×D4C22×C53semidirect
582. C24×C4C22×C53semidirect
585. C2×#121C22×C53semidirect
586. C2×#121C22×C53semidirect
589. C2×#120C22×C53semidirect
590. C2×#120C22×C53semidirect
592. C2×C4×D4C22×C53semidirect
593. C22×C4⋊C4C22×C53semidirect
594. C22×C4⋊C4C22×C53semidirect
595. C22×C4⋊C4C22×C53semidirect
596. C22×C4⋊C4C22×C53semidirect
608. C22×C22⋊C4C22×C53semidirect
609. C22×C22⋊C4C22×C53semidirect
610. C22×C22⋊C4C22×C53semidirect
611. C22×C22⋊C4C22×C53semidirect
612. C22×C22⋊C4C22×C53semidirect
613. C22×C22⋊C4C22×C53semidirect
614. C22×C42C22×C53semidirect
615. #396C22×C53semidirect
616. #394C22×C53semidirect
617. #394C22×C53semidirect
618. #392C22×C53semidirect
619. #390C22×C53semidirect
620. #388C22×C53semidirect
621. #386C22×C53semidirect
622. #386C22×C53semidirect
623. #385C22×C53semidirect
624. C2×#95C22×C53semidirect
625. C2×#95C22×C53semidirect
626. C2×#95C22×C53semidirect
627. C2×#95C22×C53semidirect
628. C53C2×#2424direct (N × H)
662. C22×D4D4×C53semidirect
669. C22×D4C23×C53semidirect
691. C23×C4C23×C53semidirect
701. C2×C4⋊C4C23×C53semidirect
702. C2×C4⋊C4C23×C53semidirect
703. C2×C4⋊C4C23×C53semidirect
704. C2×C4⋊C4C23×C53semidirect
719. C2×C22⋊C4D4×C53semidirect
720. C2×C22⋊C4D4×C53semidirect
731. C2×C22⋊C4C23×C53semidirect
732. C2×C22⋊C4C23×C53semidirect
733. C2×C22⋊C4C23×C53semidirect
734. C2×C22⋊C4C23×C53semidirect
735. C2×C22⋊C4C23×C53semidirect
737. C2×C42C23×C53semidirect
738. #95C23×C53semidirect
739. #95C23×C53semidirect
740. #95C23×C53semidirect
741. #95C23×C53semidirect
824. C2×D4C2×D4×C53semidirect
894. C22⋊C4C2×D4×C53semidirect
895. C22⋊C4C2×D4×C53semidirect
968. C23#121×C53semidirect
1074. C22C2×#121×C53semidirect
1103. C2C53×#2424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C532
C22×#120×C532
C22×C4×D4×C532
C23×C22⋊C4×C532
C53×#24242
C2×C53×#3962
C2×C53×#3942
C2×C53×#3922
C2×C53×#3902
C2×C53×#3882
C2×C53×#3862
C2×C53×#3852
C2×#242453