Finite Group Databasebeta

← C53×#13967 #27221479

Subgroups — C53×#13967 #27221479

Order 13568.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C53C211yesmaximal, characteristic
2C22×C4×D4×C53C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C53C211yesmaximal, characteristic, complemented
4C2×C53×#386C212yesmaximal, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#379C211yesmaximal, characteristic, complemented
7C53×#1439C212yesmaximal, complemented
8C53×#1438C212yesmaximal, complemented
9C53×#1437C212yesmaximal, complemented
10C53×C22⋊#95C211yesmaximal, characteristic, complemented
11C53×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C53C2211yescharacteristic
13C23×D4×C53C2212yes—
14C23×D4×C53C2211yescharacteristic
15C24×C4×C53C2211yescharacteristic
16C24×C4×C53C2211yescharacteristic
17C24×C4×C53C2211yescharacteristic, complemented
18C2×#120×C53—24no—
19C2×#120×C53—24no—
20C2×#120×C53C418yescomplemented
21C2×C4×D4×C53—24no—
22C2×C4×D4×C53—24no—
23C2×C4×D4×C53—24no—
24C22×C4⋊C4×C53C2211yescharacteristic, complemented
25C22×C22⋊C4×C53—24no—
26C22×C22⋊C4×C53—28no—
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2212yes—
29C22×C22⋊C4×C53C2212yes—
30C22×C22⋊C4×C53C2212yes—
31C22×C22⋊C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2212yes—
33C22×C22⋊C4×C53C2211yescharacteristic
34C22×C22⋊C4×C53C2212yes—
35C22×C22⋊C4×C53C2211yescharacteristic, complemented
36C22×C22⋊C4×C53C2212yescomplemented
37C22×C42×C53C2211yescharacteristic, complemented
38C53×#386—24no—
39C53×#386—28no—
40C53×#379—24no—
41C2×#95×C53C2212yescomplemented
42C2×#95×C53C2212yescomplemented
43C2×#95×C53C2212yescomplemented
44C2×#95×C53C2212yescomplemented
45C2×#95×C53C2212yescomplemented
46C25×C53—24no—
47C25×C53—22no—
48C25×C53—24no—
49C25×C53—22no—
50C25×C53—22no—
51C25×C53—22no—
52C25×C53—22no—
53C25×C53—22no—
54C25×C53—42no—
55C25×C53—42no—
56C25×C53C2×C414yescomplemented
57C25×C53C2311yescharacteristic
58C25×C53C2312yes—
59C25×C53C2311yescharacteristic
60C22×D4×C53—22no—
61C22×D4×C53—22no—
62C22×D4×C53—22no—
63C22×D4×C53—22no—
64C22×D4×C53—24no—
65C22×D4×C53—24no—
66C22×D4×C53—24no—
67C22×D4×C53—24no—
68C22×D4×C53—42no—
69C22×D4×C53—42no—
70C22×D4×C53C2×C414yes—
71C22×D4×C53C2×C418yescomplemented
72C22×D4×C53D414yes—
73C22×D4×C53D414yes—
74C23×C4×C53—22no—
75C23×C4×C53—22no—
76C23×C4×C53—22no—
77C23×C4×C53—22no—
78C23×C4×C53—24no—
79C23×C4×C53—24no—
80C23×C4×C53—22no—
81C23×C4×C53—22no—
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53—24no—
85C23×C4×C53—42no—
86C23×C4×C53—42no—
87C23×C4×C53—42no—
88C23×C4×C53D414yescomplemented
89C23×C4×C53C2312yes—
90C23×C4×C53C2312yes—
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97#120×C53—232no—
98C4×D4×C53—232no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C22⋊C4×C53—232no—
103C2×C22⋊C4×C53—24no—
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—24no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53—24no—
114C2×C22⋊C4×C53—22no—
115C2×C22⋊C4×C53—24no—
116C2×C22⋊C4×C53—24no—
117C2×C22⋊C4×C53—24no—
118C2×C22⋊C4×C53—24no—
119C2×C22⋊C4×C53—24no—
120C2×C22⋊C4×C53—24no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53—24no—
124C2×C22⋊C4×C53—24no—
125C2×C22⋊C4×C53—24no—
126C2×C22⋊C4×C53—42no—
127C2×C22⋊C4×C53—42no—
128C2×C22⋊C4×C53—42no—
129C2×C22⋊C4×C53C2×C414yescomplemented
130C2×C22⋊C4×C53C2×C418yescomplemented
131C2×C22⋊C4×C53D418yescomplemented
132C2×C22⋊C4×C53D414yescomplemented
133C2×C42×C53—22no—
134C2×C42×C53—22no—
135C2×C42×C53—22no—
136#95×C53—24no—
137#95×C53—24no—
138#95×C53—24no—
139#95×C53—42no—
140#95×C53—42no—
141C24×C53—22no—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53—22no—
145C24×C53—28no—
146C24×C53—28no—
147C24×C53—216no—
148C24×C53—28no—
149C24×C53—216no—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53—22no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53—22no—
163C24×C53—22no—
164C24×C53—22no—
165C24×C53—22no—
166C24×C53—22no—
167C24×C53—22no—
168C24×C53—22no—
169C24×C53—22no—
170C24×C53—28no—
171C24×C53—28no—
172C24×C53—48no—
173C24×C53—48no—
174C24×C53—48no—
175C24×C53—48no—
176C24×C53—48no—
177C24×C53—48no—
178C24×C53—48no—
179C24×C53—48no—
180C24×C53—48no—
181C24×C53—44no—
182C24×C53—44no—
183C24×C53—48no—
184C24×C53—44no—
185C24×C53—44no—
186C24×C53—44no—
187C24×C53—44no—
188C24×C53C22×C412yes—
189C24×C53C22×C414yes—
190C24×C53C22×C412yes—
191C24×C53C2×D412yes—
192C24×C53C2×D412yes—
193C24×C53C2×D414yes—
194C24×C53C2×D412yes—
195C24×C53C2×D412yes—
196C24×C53C2×D412yes—
197C24×C53C2×D412yes—
198C24×C53#4114yes—
199C24×C53#4112yes—
200C24×C53#4112yes—
201C24×C53C2411yescharacteristic
202C2×D4×C53—28no—
203C2×D4×C53—28no—
204C2×D4×C53—28no—
205C2×D4×C53—28no—
206C2×D4×C53—28no—
207C2×D4×C53—28no—
208C2×D4×C53—216no—
209C2×D4×C53—216no—
210C2×D4×C53—48no—
211C2×D4×C53—48no—
212C2×D4×C53—48no—
213C2×D4×C53—48no—
214C2×D4×C53—48no—
215C2×D4×C53C22⋊C4116yescomplemented
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—22no—
223C22×C4×C53—28no—
224C22×C4×C53—28no—
225C22×C4×C53—28no—
226C22×C4×C53—22no—
227C22×C4×C53—22no—
228C22×C4×C53—22no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—22no—
232C22×C4×C53—22no—
233C22×C4×C53—22no—
234C22×C4×C53—22no—
235C22×C4×C53—22no—
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—22no—
241C22×C4×C53—22no—
242C22×C4×C53—22no—
243C22×C4×C53—22no—
244C22×C4×C53—22no—
245C22×C4×C53—22no—
246C22×C4×C53—22no—
247C22×C4×C53—22no—
248C22×C4×C53—22no—
249C22×C4×C53—22no—
250C22×C4×C53—28no—
251C22×C4×C53—22no—
252C22×C4×C53—22no—
253C22×C4×C53—22no—
254C22×C4×C53—22no—
255C22×C4×C53—22no—
256C22×C4×C53—22no—
257C22×C4×C53—22no—
258C22×C4×C53—44no—
259C22×C4×C53—48no—
260C22×C4×C53—48no—
261C22×C4×C53—48no—
262C22×C4×C53—48no—
263C22×C4×C53—48no—
264C22×C4×C53—48no—
265C22×C4×C53—44no—
266C22×C4×C53—44no—
267C22×C4×C53—44no—
268C22×C4×C53—44no—
269C22×C4×C53C22×C414yes—
270C22×C4×C53C22×C412yes—
271C22×C4×C53C2×D414yes—
272C22×C4×C53C2×D412yes—
273C22×C4×C53C2×D412yes—
274C22×C4×C53C2×D412yes—
275C22×C4×C53C2×D412yes—
276C22×C4×C53C2×D412yes—
277C22×C4×C53C2×D414yes—
278C22×C4×C53C2×D412yes—
279C4⋊C4×C53—28no—
280C22⋊C4×C53—216no—
281C22⋊C4×C53—28no—
282C22⋊C4×C53—28no—
283C22⋊C4×C53—28no—
284C22⋊C4×C53—216no—
285C22⋊C4×C53—216no—
286C22⋊C4×C53—48no—
287C22⋊C4×C53—48no—
288C22⋊C4×C53—48no—
289C22⋊C4×C53—44no—
290C42×C53—28no—
291C23×C53—24no—
292C23×C53—24no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—24no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—24no—
299C23×C53—24no—
300C23×C53—24no—
301C23×C53—24no—
302C23×C53—24no—
303C23×C53—24no—
304C23×C53—24no—
305C23×C53—24no—
306C23×C53—24no—
307C23×C53—232no—
308C23×C53—24no—
309C23×C53—24no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—24no—
313C23×C53—24no—
314C23×C53—24no—
315C23×C53—24no—
316C23×C53—24no—
317C23×C53—24no—
318C23×C53—22no—
319C23×C53—24no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—24no—
324C23×C53—24no—
325C23×C53—24no—
326C23×C53—24no—
327C23×C53—24no—
328C23×C53—24no—
329C23×C53—24no—
330C23×C53—24no—
331C23×C53—24no—
332C23×C53—24no—
333C23×C53—24no—
334C23×C53—24no—
335C23×C53—24no—
336C23×C53—24no—
337C23×C53—24no—
338C23×C53—432no—
339C23×C53—432no—
340C23×C53—416no—
341C23×C53—416no—
342C23×C53—416no—
343C23×C53—416no—
344C23×C53—432no—
345C23×C53—432no—
346C23×C53—416no—
347C23×C53—41no—
348C23×C53—42no—
349C23×C53—42no—
350C23×C53—42no—
351C23×C53—42no—
352C23×C53—41no—
353C23×C53—42no—
354C23×C53—41no—
355C23×C53—42no—
356C23×C53—41no—
357C23×C53—42no—
358C23×C53—42no—
359C23×C53—42no—
360C23×C53—42no—
361C23×C53—42no—
362C23×C53—42no—
363C23×C53—42no—
364C23×C53—42no—
365C23×C53—42no—
366C23×C53—42no—
367C23×C53—42no—
368C23×C53—42no—
369C23×C53—42no—
370C23×C53—42no—
371C23×C53—42no—
372C23×C53—42no—
373C23×C53—416no—
374C23×C53C2×C22⋊C414yes—
375C23×C53C2×C22⋊C414yescomplemented
376C23×C53C4×D414yes—
377C23×C53C4×D414yes—
378C23×C53C4×D418yescomplemented
379C23×C53#12014yes—
380C23×C53#12114yes—
381C23×C53#12114yes—
382C23×C53#12314yes—
383C23×C53C23×C411yescharacteristic
384C23×C53C22×D411yescharacteristic
385C23×C53C22×D411yescharacteristic
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C23×C53C22×D412yes—
389C23×C53C2×#4111yescharacteristic
390C23×C53C2×#4111yescharacteristic
391C23×C53C2×#4112yes—
392C23×C53H(5,𝔽2)12yes—
393C23×C53H(5,𝔽2)12yes—
394D4×C53—232no—
395D4×C53—432no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—22no—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—24no—
405C2×C4×C53—24no—
406C2×C4×C53—24no—
407C2×C4×C53—24no—
408C2×C4×C53—24no—
409C2×C4×C53—22no—
410C2×C4×C53—24no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—24no—
416C2×C4×C53—24no—
417C2×C4×C53—24no—
418C2×C4×C53—24no—
419C2×C4×C53—416no—
420C2×C4×C53—416no—
421C2×C4×C53—416no—
422C2×C4×C53—41no—
423C2×C4×C53—42no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—42no—
428C2×C4×C53—42no—
429C2×C4×C53—42no—
430C2×C4×C53—42no—
431C2×C4×C53—42no—
432C2×C4×C53—42no—
433C2×C4×C53—42no—
434C2×C4×C53—42no—
435C2×C4×C53—42no—
436C2×C4×C53—42no—
437C2×C4×C53—42no—
438C2×C4×C53—42no—
439C2×C4×C53—42no—
440C2×C4×C53—42no—
441C2×C4×C53—42no—
442C2×C4×C53—42no—
443C2×C4×C53—42no—
444C2×C4×C53—42no—
445C2×C4×C53C2×C22⋊C414yescomplemented
446C2×C4×C53#12014yescomplemented
447#13967C5311yesmaximal, characteristic, direct product factor, Sylow
448C22×C53—24no—
449C22×C53—28no—
450C22×C53—28no—
451C22×C53—24no—
452C22×C53—24no—
453C22×C53—24no—
454C22×C53—28no—
455C22×C53—28no—
456C22×C53—24no—
457C22×C53—24no—
458C22×C53—28no—
459C22×C53—28no—
460C22×C53—28no—
461C22×C53—24no—
462C22×C53—28no—
463C22×C53—464no—
464C22×C53—42no—
465C22×C53—44no—
466C22×C53—44no—
467C22×C53—44no—
468C22×C53—44no—
469C22×C53—42no—
470C22×C53—44no—
471C22×C53—42no—
472C22×C53—44no—
473C22×C53—42no—
474C22×C53—44no—
475C22×C53—44no—
476C22×C53—44no—
477C22×C53—44no—
478C22×C53—44no—
479C22×C53—44no—
480C22×C53—44no—
481C22×C53—42no—
482C22×C53—44no—
483C22×C53—44no—
484C22×C53—42no—
485C22×C53#38618yescomplemented
486C22×C53C22×C22⋊C411yescharacteristic
487C22×C53C2×C4×D411yescharacteristic
488C22×C53C2×C4×D412yes—
489C22×C53C2×C4×D411yescharacteristic
490C22×C53#51812yes—
491C22×C53C2×#12011yescharacteristic
492C22×C53C2×#12011yescharacteristic
493C22×C53C2×#12111yescharacteristic
494C22×C53C2×#12111yescharacteristic
495C22×C53C2×#12311yescharacteristic
496C22×C53#52511yescharacteristic
497C22×C53#52512yes—
498C22×C53#53411yescharacteristic
499C22×C53#53511yescharacteristic
500C22×C53#53812yes—
501C22×C53D4212yes—
502C22×C53D4212yes—
503C22×C53D4212yes—
504C22×C53#54612yes—
505C22×C53#54612yes—
506C22×C53#54612yes—
507C22×C53#54612yes—
508C22×C53#55112yes—
509C4×C53—24no—
510C4×C53—24no—
511C4×C53—44no—
512C4×C53—42no—
513C4×C53—42no—
514C4×C53—42no—
515C4×C53—44no—
516C4×C53—82no—
517C22×#120C2×C5311yescharacteristic
518C22×C4×D4C2×C5311yescharacteristic, complemented
519C23×C22⋊C4C2×C5311yescharacteristic, complemented
520C2×#386C2×C5312yescomplemented
521C2×#386C2×C5311yescharacteristic, complemented
522C2×#379C2×C5311yescharacteristic, complemented
523#1439C2×C5312yescomplemented
524#1438C2×C5312yescomplemented
525#1437C2×C5312yescomplemented
526C22⋊#95C2×C5311yescharacteristic, complemented
527C22⋊#95C2×C5311yescharacteristic, complemented
528C2×C53—28no—
529C2×C53—44no—
530C2×C53—48no—
531C2×C53C2×#38611yescharacteristic
532C2×C53C4×#12011yescharacteristic
533C2×C53#232111yescharacteristic
534C2×C53D4×C22⋊C412yes—
535C2×C53#235812yes—
536C2×C53#240311yescharacteristic
537C2×C53#240411yescharacteristic
538C2×C53#240811yescharacteristic
539C2×C53#241812yes—
540C2×C53#242412yes—
541C2×C53#253411yescharacteristic
542C26C22×C5311yescharacteristic
543C23×D4C22×C5312yes—
544C23×D4C22×C5311yescharacteristic
545C24×C4C22×C5311yescharacteristic
546C24×C4C22×C5311yescharacteristic
547C24×C4C22×C5311yescharacteristic, complemented
548C2×#120—24no—
549C2×#120—24no—
550C2×#120C4×C5318yescomplemented
551C2×C4×D4—24no—
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C22×C4⋊C4C22×C5311yescharacteristic, complemented
555C22×C22⋊C4—24no—
556C22×C22⋊C4—28no—
557C22×C22⋊C4C22×C5312yes—
558C22×C22⋊C4C22×C5311yescharacteristic
559C22×C22⋊C4C22×C5312yes—
560C22×C22⋊C4C22×C5312yes—
561C22×C22⋊C4C22×C5311yescharacteristic
562C22×C22⋊C4C22×C5312yes—
563C22×C22⋊C4C22×C5312yes—
564C22×C22⋊C4C22×C5311yescharacteristic
565C22×C22⋊C4C22×C5311yescharacteristic, complemented
566C22×C22⋊C4C22×C5312yescomplemented
567C22×C42C22×C5311yescharacteristic, complemented
568#386—24no—
569#386—28no—
570#379—24no—
571C2×#95C22×C5312yescomplemented
572C2×#95C22×C5312yescomplemented
573C2×#95C22×C5312yescomplemented
574C2×#95C22×C5312yescomplemented
575C2×#95C22×C5312yescomplemented
576C53#1396711yescharacteristic, direct product factor, Sylow
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C5314yescomplemented
588C25C23×C5311yescharacteristic
589C25C23×C5312yes—
590C25C23×C5311yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C5314yes—
602C22×D4C2×C4×C5318yescomplemented
603C22×D4D4×C5314yes—
604C22×D4D4×C5314yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C5314yescomplemented
620C23×C4C23×C5312yes—
621C23×C4C23×C5312yes—
622C23×C4C23×C5311yescharacteristic
623C23×C4C23×C5311yescharacteristic
624C23×C4C23×C5311yescharacteristic
625C23×C4C23×C5312yes—
626C23×C4C23×C5311yescharacteristic
627C23×C4C23×C5311yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C5314yescomplemented
661C2×C22⋊C4C2×C4×C5318yescomplemented
662C2×C22⋊C4D4×C5318yescomplemented
663C2×C22⋊C4D4×C5314yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C5312yes—
720C24C22×C4×C5314yes—
721C24C22×C4×C5312yes—
722C24C2×D4×C5312yes—
723C24C2×D4×C5312yes—
724C24C2×D4×C5314yes—
725C24C2×D4×C5312yes—
726C24C2×D4×C5312yes—
727C24C2×D4×C5312yes—
728C24C2×D4×C5312yes—
729C24#41×C5314yes—
730C24#41×C5312yes—
731C24#41×C5312yes—
732C24C24×C5311yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C53116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C5314yes—
801C22×C4C22×C4×C5312yes—
802C22×C4C2×D4×C5314yes—
803C22×C4C2×D4×C5312yes—
804C22×C4C2×D4×C5312yes—
805C22×C4C2×D4×C5312yes—
806C22×C4C2×D4×C5312yes—
807C22×C4C2×D4×C5312yes—
808C22×C4C2×D4×C5314yes—
809C22×C4C2×D4×C5312yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—432no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—416no—
877C23—432no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C5314yes—
906C23C2×C22⋊C4×C5314yescomplemented
907C23C4×D4×C5314yes—
908C23C4×D4×C5314yes—
909C23C4×D4×C5318yescomplemented
910C23#120×C5314yes—
911C23#121×C5314yes—
912C23#121×C5314yes—
913C23#123×C5314yes—
914C23C23×C4×C5311yescharacteristic
915C23C22×D4×C5311yescharacteristic
916C23C22×D4×C5311yescharacteristic
917C23C22×D4×C5311yescharacteristic
918C23C22×D4×C5311yescharacteristic
919C23C22×D4×C5312yes—
920C23C2×#41×C5311yescharacteristic
921C23C2×#41×C5311yescharacteristic
922C23C2×#41×C5312yes—
923C23H(5,𝔽2)×C5312yes—
924C23H(5,𝔽2)×C5312yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C5314yescomplemented
977C2×C4#120×C5314yescomplemented
978C22—28no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—28no—
983C22—28no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—42no—
999C22—44no—
1000C22—42no—
1001C22—44no—
1002C22—42no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22—44no—
1008C22—44no—
1009C22—42no—
1010C22—44no—
1011C22—42no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22C53×#38618yescomplemented
1016C22C22×C22⋊C4×C5311yescharacteristic
1017C22C2×C4×D4×C5311yescharacteristic
1018C22C2×C4×D4×C5311yescharacteristic
1019C22C2×C4×D4×C5312yes—
1020C22C53×#51812yes—
1021C22C2×#120×C5311yescharacteristic
1022C22C2×#120×C5311yescharacteristic
1023C22C2×#121×C5311yescharacteristic
1024C22C2×#121×C5311yescharacteristic
1025C22C2×#123×C5311yescharacteristic
1026C22C53×#52512yes—
1027C22C53×#52511yescharacteristic
1028C22C53×#53411yescharacteristic
1029C22C53×#53511yescharacteristic
1030C22C53×#53812yes—
1031C22D42×C5312yes—
1032C22D42×C5312yes—
1033C22D42×C5312yes—
1034C22C53×#54612yes—
1035C22C53×#54612yes—
1036C22C53×#54612yes—
1037C22C53×#54612yes—
1038C22C53×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C53×#38611yescharacteristic
1051C2C4×#120×C5311yescharacteristic
1052C2C53×#232111yescharacteristic
1053C2D4×C22⋊C4×C5312yes—
1054C2C53×#235812yes—
1055C2C53×#240311yescharacteristic
1056C2C53×#240411yescharacteristic
1057C2C53×#240811yescharacteristic
1058C2C53×#241812yes—
1059C2C53×#242412yes—
1060C2C53×#253411yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC22×#120×C53C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C53C2semidirect
3. C23×C22⋊C4×C53C2semidirect
4. C2×C53×#386C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#379C2semidirect
7. C53×#1439C2semidirect
8. C53×#1438C2semidirect
9. C53×#1437C2semidirect
10. C53×C22⋊#95C2semidirect
11. C53×C22⋊#95C2semidirect
17. C24×C4×C53C22semidirect
20. C2×#120×C53C4semidirect
24. C22×C4⋊C4×C53C22semidirect
35. C22×C22⋊C4×C53C22semidirect
36. C22×C22⋊C4×C53C22semidirect
37. C22×C42×C53C22semidirect
41. C2×#95×C53C22semidirect
42. C2×#95×C53C22semidirect
43. C2×#95×C53C22semidirect
44. C2×#95×C53C22semidirect
45. C2×#95×C53C22semidirect
56. C25×C53C2×C4semidirect
71. C22×D4×C53C2×C4semidirect
88. C23×C4×C53D4semidirect
129. C2×C22⋊C4×C53C2×C4semidirect
130. C2×C22⋊C4×C53C2×C4semidirect
131. C2×C22⋊C4×C53D4semidirect
132. C2×C22⋊C4×C53D4semidirect
215. C2×D4×C53C22⋊C4semidirect
375. C23×C53C2×C22⋊C4semidirect
378. C23×C53C4×D4semidirect
445. C2×C4×C53C2×C22⋊C4semidirect
446. C2×C4×C53#120semidirect
447. #13967C53direct (N × H)
485. C22×C53#386semidirect
518. C22×C4×D4C2×C53semidirect
519. C23×C22⋊C4C2×C53semidirect
520. C2×#386C2×C53semidirect
521. C2×#386C2×C53semidirect
522. C2×#379C2×C53semidirect
523. #1439C2×C53semidirect
524. #1438C2×C53semidirect
525. #1437C2×C53semidirect
526. C22⋊#95C2×C53semidirect
527. C22⋊#95C2×C53semidirect
547. C24×C4C22×C53semidirect
550. C2×#120C4×C53semidirect
554. C22×C4⋊C4C22×C53semidirect
565. C22×C22⋊C4C22×C53semidirect
566. C22×C22⋊C4C22×C53semidirect
567. C22×C42C22×C53semidirect
571. C2×#95C22×C53semidirect
572. C2×#95C22×C53semidirect
573. C2×#95C22×C53semidirect
574. C2×#95C22×C53semidirect
575. C2×#95C22×C53semidirect
576. C53#13967direct (N × H)
587. C25C2×C4×C53semidirect
602. C22×D4C2×C4×C53semidirect
619. C23×C4D4×C53semidirect
660. C2×C22⋊C4C2×C4×C53semidirect
661. C2×C22⋊C4C2×C4×C53semidirect
662. C2×C22⋊C4D4×C53semidirect
663. C2×C22⋊C4D4×C53semidirect
746. C2×D4C22⋊C4×C53semidirect
906. C23C2×C22⋊C4×C53semidirect
909. C23C4×D4×C53semidirect
976. C2×C4C2×C22⋊C4×C53semidirect
977. C2×C4#120×C53semidirect
1015. C22C53×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C532
C22×C4×D4×C532
C23×C22⋊C4×C532
C2×C53×#3862
C2×C53×#3792
C53×#14392
C53×#14382
C53×#14372
C53×C22⋊#952
#1396753