Finite Group Databasebeta

← C53×#13873 #27221385

Subgroups — C53×#13873 #27221385

Order 13568.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C53C211yesmaximal, characteristic
2C2×C53×#388C212yesmaximal, complemented
3C2×C53×#380C211yesmaximal, characteristic, complemented
4C2×C53×#379C211yesmaximal, characteristic
5C2×C53×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
7C53×#1440C212yesmaximal, complemented
8C53×#1439C212yesmaximal, complemented
9C53×#1437C212yesmaximal, complemented
10C53×C22⋊#95C211yesmaximal, characteristic, complemented
11C53×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C53C2211yescharacteristic
13C24×C4×C53C2211yescharacteristic
14C24×C4×C53C2211yescharacteristic
15C22×C4⋊C4×C53C2212yescomplemented
16C22×C22⋊C4×C53—28no—
17C22×C22⋊C4×C53C418yescomplemented
18C22×C22⋊C4×C53C2211yescharacteristic
19C22×C22⋊C4×C53C2211yescharacteristic
20C22×C22⋊C4×C53C2212yes—
21C22×C22⋊C4×C53C2212yes—
22C22×C22⋊C4×C53C2212yes—
23C22×C22⋊C4×C53C2212yes—
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×C42×C53C2212yescomplemented
31C53×#388—28no—
32C53×#380—24no—
33C53×#379—24no—
34C53×#379—24no—
35C4×C22⋊C4×C53—24no—
36C2×#95×C53C2212yescomplemented
37C2×#95×C53C2212yescomplemented
38C2×#95×C53C2212yescomplemented
39C2×#95×C53C2212yescomplemented
40C2×#95×C53C2212yescomplemented
41C2×#95×C53C2212yescomplemented
42C25×C53—24no—
43C25×C53—24no—
44C25×C53—22no—
45C25×C53—22no—
46C25×C53—22no—
47C25×C53—22no—
48C25×C53—22no—
49C25×C53—22no—
50C25×C53—42no—
51C25×C53—42no—
52C25×C53C2×C414yes—
53C25×C53C2311yescharacteristic
54C25×C53C2311yescharacteristic
55C25×C53C2311yescharacteristic
56C23×C4×C53—22no—
57C23×C4×C53—22no—
58C23×C4×C53—22no—
59C23×C4×C53—22no—
60C23×C4×C53—24no—
61C23×C4×C53—24no—
62C23×C4×C53—42no—
63C23×C4×C53—42no—
64C23×C4×C53C2×C414yes—
65C23×C4×C53C2×C414yes—
66C23×C4×C53C2312yes—
67C23×C4×C53C2312yes—
68C23×C4×C53C2311yescharacteristic
69C23×C4×C53C2311yescharacteristic
70C23×C4×C53C2312yes—
71C23×C4×C53C2312yes—
72C23×C4×C53C2311yescharacteristic
73C23×C4×C53C2311yescharacteristic
74C2×C4⋊C4×C53—24no—
75C2×C4⋊C4×C53—24no—
76C2×C4⋊C4×C53—42no—
77C2×C22⋊C4×C53—232no—
78C2×C22⋊C4×C53—24no—
79C2×C22⋊C4×C53—22no—
80C2×C22⋊C4×C53—22no—
81C2×C22⋊C4×C53—22no—
82C2×C22⋊C4×C53—22no—
83C2×C22⋊C4×C53—24no—
84C2×C22⋊C4×C53—24no—
85C2×C22⋊C4×C53—22no—
86C2×C22⋊C4×C53—22no—
87C2×C22⋊C4×C53—22no—
88C2×C22⋊C4×C53—24no—
89C2×C22⋊C4×C53—24no—
90C2×C22⋊C4×C53—22no—
91C2×C22⋊C4×C53—22no—
92C2×C22⋊C4×C53—22no—
93C2×C22⋊C4×C53—24no—
94C2×C22⋊C4×C53—24no—
95C2×C22⋊C4×C53—24no—
96C2×C22⋊C4×C53—24no—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—24no—
99C2×C22⋊C4×C53—42no—
100C2×C22⋊C4×C53—42no—
101C2×C22⋊C4×C53—42no—
102C2×C22⋊C4×C53—42no—
103C2×C22⋊C4×C53C2×C414yes—
104C2×C22⋊C4×C53C2×C414yes—
105C2×C22⋊C4×C53C2×C414yes—
106C2×C22⋊C4×C53C2×C414yes—
107C2×C22⋊C4×C53D414yes—
108C2×C22⋊C4×C53D414yes—
109C2×C22⋊C4×C53D418yes—
110C2×C42×C53—24no—
111C2×C42×C53—24no—
112C2×C42×C53—42no—
113#95×C53—24no—
114#95×C53—24no—
115#95×C53—24no—
116#95×C53—24no—
117#95×C53—42no—
118#95×C53—42no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—22no—
122C24×C53—22no—
123C24×C53—216no—
124C24×C53—216no—
125C24×C53—28no—
126C24×C53—28no—
127C24×C53—28no—
128C24×C53—22no—
129C24×C53—21no—
130C24×C53—21no—
131C24×C53—21no—
132C24×C53—21no—
133C24×C53—21no—
134C24×C53—21no—
135C24×C53—22no—
136C24×C53—21no—
137C24×C53—21no—
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—21no—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—28no—
147C24×C53—28no—
148C24×C53—44no—
149C24×C53—44no—
150C24×C53—48no—
151C24×C53—48no—
152C24×C53—48no—
153C24×C53—48no—
154C24×C53—48no—
155C24×C53—48no—
156C24×C53—48no—
157C24×C53—48no—
158C24×C53—48no—
159C24×C53—48no—
160C24×C53—44no—
161C24×C53—44no—
162C24×C53—44no—
163C24×C53—44no—
164C24×C53C22×C412yes—
165C24×C53C22×C412yes—
166C24×C53C22×C412yes—
167C24×C53C2×D414yes—
168C24×C53C2×D412yes—
169C24×C53C2×D412yes—
170C24×C53#4114yes—
171C24×C53#4112yes—
172C24×C53#4112yes—
173C24×C53#4112yes—
174C24×C53#4112yes—
175C24×C53C2411yescharacteristic
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—28no—
183C22×C4×C53—28no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—28no—
205C22×C4×C53—28no—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—22no—
213C22×C4×C53—22no—
214C22×C4×C53—22no—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—22no—
220C22×C4×C53—44no—
221C22×C4×C53—44no—
222C22×C4×C53—48no—
223C22×C4×C53—48no—
224C22×C4×C53—48no—
225C22×C4×C53—48no—
226C22×C4×C53C22×C412yes—
227C22×C4×C53C22×C412yes—
228C22×C4×C53C22×C412yes—
229C22×C4×C53C22×C412yes—
230C22×C4×C53C2×D414yes—
231C22×C4×C53C2×D414yes—
232C22×C4×C53C2×D414yes—
233C22×C4×C53C2×D414yes—
234C4⋊C4×C53—48no—
235C22⋊C4×C53—28no—
236C22⋊C4×C53—28no—
237C22⋊C4×C53—28no—
238C22⋊C4×C53—28no—
239C22⋊C4×C53—28no—
240C22⋊C4×C53—48no—
241C22⋊C4×C53—48no—
242C22⋊C4×C53—48no—
243C22⋊C4×C53—48no—
244C22⋊C4×C53—44no—
245C22⋊C4×C53—44no—
246C22⋊C4×C53C22⋊C4116yescomplemented
247C42×C53—48no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—24no—
253C23×C53—24no—
254C23×C53—24no—
255C23×C53—24no—
256C23×C53—24no—
257C23×C53—24no—
258C23×C53—24no—
259C23×C53—24no—
260C23×C53—24no—
261C23×C53—24no—
262C23×C53—24no—
263C23×C53—24no—
264C23×C53—232no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—24no—
278C23×C53—24no—
279C23×C53—24no—
280C23×C53—24no—
281C23×C53—24no—
282C23×C53—24no—
283C23×C53—24no—
284C23×C53—24no—
285C23×C53—24no—
286C23×C53—24no—
287C23×C53—24no—
288C23×C53—24no—
289C23×C53—416no—
290C23×C53—416no—
291C23×C53—416no—
292C23×C53—416no—
293C23×C53—416no—
294C23×C53—432no—
295C23×C53—432no—
296C23×C53—432no—
297C23×C53—432no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53—416no—
319C23×C53C2×C22⋊C414yes—
320C23×C53#11714yes—
321C23×C53#11714yes—
322C23×C53C4×D414yes—
323C23×C53C4×D414yes—
324C23×C53#12114yes—
325C23×C53#12314yes—
326C23×C53#12414yes—
327C23×C53#12614yes—
328C23×C53C23×C411yescharacteristic
329C23×C53C22×D412yes—
330C23×C53C22×D411yescharacteristic
331C23×C53C22×D411yescharacteristic
332C23×C53C2×#4111yescharacteristic
333C23×C53C2×#4111yescharacteristic
334C23×C53C2×#4112yes—
335C23×C53C2×#4111yescharacteristic
336C23×C53C2×#4111yescharacteristic
337C23×C53H(5,𝔽2)12yes—
338C23×C53H(5,𝔽2)12yes—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—24no—
344C2×C4×C53—24no—
345C2×C4×C53—24no—
346C2×C4×C53—24no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—24no—
354C2×C4×C53—24no—
355C2×C4×C53—24no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53—24no—
359C2×C4×C53—416no—
360C2×C4×C53—416no—
361C2×C4×C53—42no—
362C2×C4×C53—42no—
363C2×C4×C53—42no—
364C2×C4×C53—42no—
365C2×C4×C53—42no—
366C2×C4×C53—42no—
367C2×C4×C53—42no—
368C2×C4×C53—42no—
369C2×C4×C53—42no—
370C2×C4×C53—42no—
371C2×C4×C53—42no—
372C2×C4×C53—42no—
373C2×C4×C53—42no—
374C2×C4×C53—42no—
375C2×C4×C53—42no—
376C2×C4×C53—42no—
377C2×C4×C53—42no—
378C2×C4×C53—42no—
379C2×C4×C53—42no—
380C2×C4×C53—42no—
381C2×C4×C53—42no—
382C2×C4×C53—42no—
383C2×C4×C53—42no—
384C2×C4×C53—42no—
385C2×C4×C53—42no—
386C2×C4×C53—42no—
387C2×C4×C53C2×C22⋊C414yes—
388C2×C4×C53C2×C22⋊C414yes—
389#13873C5311yesmaximal, characteristic, direct product factor, Sylow
390C22×C53—24no—
391C22×C53—24no—
392C22×C53—24no—
393C22×C53—24no—
394C22×C53—24no—
395C22×C53—28no—
396C22×C53—28no—
397C22×C53—28no—
398C22×C53—28no—
399C22×C53—24no—
400C22×C53—24no—
401C22×C53—24no—
402C22×C53—24no—
403C22×C53—24no—
404C22×C53—24no—
405C22×C53—24no—
406C22×C53—464no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—42no—
412C22×C53—42no—
413C22×C53—44no—
414C22×C53—44no—
415C22×C53—44no—
416C22×C53—44no—
417C22×C53—44no—
418C22×C53—44no—
419C22×C53—44no—
420C22×C53—44no—
421C22×C53—42no—
422C22×C53—42no—
423C22×C53#38818yescomplemented
424C22×C53C22×C22⋊C411yescharacteristic
425C22×C53C2×#11711yescharacteristic
426C22×C53C2×#11711yescharacteristic
427C22×C53C2×C4×D411yescharacteristic
428C22×C53C2×C4×D411yescharacteristic
429C22×C53#51811yescharacteristic
430C22×C53#51811yescharacteristic
431C22×C53C2×#12111yescharacteristic
432C22×C53C2×#12311yescharacteristic
433C22×C53#52512yes—
434C22×C53#52512yes—
435C22×C53C2×#12411yescharacteristic
436C22×C53C2×#12611yescharacteristic
437C22×C53#53812yes—
438C22×C53#53812yes—
439C22×C53D4212yes—
440C22×C53D4212yes—
441C22×C53#54612yes—
442C22×C53#54612yes—
443C22×C53#54612yes—
444C22×C53#54612yes—
445C22×C53#55112yes—
446C22×C53#55112yes—
447C4×C53—24no—
448C4×C53—24no—
449C4×C53—42no—
450C4×C53—42no—
451C4×C53—44no—
452C4×C53—44no—
453C4×C53—82no—
454C4×C53—82no—
455C23×C22⋊C4C2×C5311yescharacteristic
456C2×#388C2×C5312yescomplemented
457C2×#380C2×C5311yescharacteristic, complemented
458C2×#379C2×C5311yescharacteristic
459C2×#379C2×C5311yescharacteristic
460C2×C4×C22⋊C4C2×C5311yescharacteristic, complemented
461#1440C2×C5312yescomplemented
462#1439C2×C5312yescomplemented
463#1437C2×C5312yescomplemented
464C22⋊#95C2×C5311yescharacteristic, complemented
465C22⋊#95C2×C5311yescharacteristic, complemented
466C2×C53—28no—
467C2×C53—44no—
468C2×C53—44no—
469C2×C53#228011yescharacteristic
470C2×C53C2×#38811yescharacteristic
471C2×C53#231211yescharacteristic
472C2×C53D4×C22⋊C411yescharacteristic
473C2×C53D4×C22⋊C411yescharacteristic
474C2×C53#234211yescharacteristic
475C2×C53#234211yescharacteristic
476C2×C53#241812yes—
477C2×C53#242412yes—
478C2×C53#247212yes—
479C2×C53#248012yes—
480C26C22×C5311yescharacteristic
481C24×C4C22×C5311yescharacteristic
482C24×C4C22×C5311yescharacteristic
483C22×C4⋊C4C22×C5312yescomplemented
484C22×C22⋊C4—28no—
485C22×C22⋊C4C4×C5318yescomplemented
486C22×C22⋊C4C22×C5311yescharacteristic
487C22×C22⋊C4C22×C5311yescharacteristic
488C22×C22⋊C4C22×C5312yes—
489C22×C22⋊C4C22×C5312yes—
490C22×C22⋊C4C22×C5312yes—
491C22×C22⋊C4C22×C5312yes—
492C22×C22⋊C4C22×C5311yescharacteristic
493C22×C22⋊C4C22×C5311yescharacteristic
494C22×C22⋊C4C22×C5311yescharacteristic
495C22×C22⋊C4C22×C5311yescharacteristic
496C22×C22⋊C4C22×C5311yescharacteristic
497C22×C22⋊C4C22×C5311yescharacteristic
498C22×C42C22×C5312yescomplemented
499#388—28no—
500#380—24no—
501#379—24no—
502#379—24no—
503C4×C22⋊C4—24no—
504C2×#95C22×C5312yescomplemented
505C2×#95C22×C5312yescomplemented
506C2×#95C22×C5312yescomplemented
507C2×#95C22×C5312yescomplemented
508C2×#95C22×C5312yescomplemented
509C2×#95C22×C5312yescomplemented
510C53#1387311yescharacteristic, direct product factor, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C5314yes—
522C25C23×C5311yescharacteristic
523C25C23×C5311yescharacteristic
524C25C23×C5311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C5314yes—
534C23×C4C2×C4×C5314yes—
535C23×C4C23×C5312yes—
536C23×C4C23×C5312yes—
537C23×C4C23×C5311yescharacteristic
538C23×C4C23×C5311yescharacteristic
539C23×C4C23×C5312yes—
540C23×C4C23×C5312yes—
541C23×C4C23×C5311yescharacteristic
542C23×C4C23×C5311yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C5314yes—
573C2×C22⋊C4C2×C4×C5314yes—
574C2×C22⋊C4C2×C4×C5314yes—
575C2×C22⋊C4C2×C4×C5314yes—
576C2×C22⋊C4D4×C5314yes—
577C2×C22⋊C4D4×C5314yes—
578C2×C22⋊C4D4×C5318yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C5312yes—
634C24C22×C4×C5312yes—
635C24C22×C4×C5312yes—
636C24C2×D4×C5314yes—
637C24C2×D4×C5312yes—
638C24C2×D4×C5312yes—
639C24#41×C5314yes—
640C24#41×C5312yes—
641C24#41×C5312yes—
642C24#41×C5312yes—
643C24#41×C5312yes—
644C24C24×C5311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C5312yes—
696C22×C4C22×C4×C5312yes—
697C22×C4C22×C4×C5312yes—
698C22×C4C22×C4×C5312yes—
699C22×C4C2×D4×C5314yes—
700C22×C4C2×D4×C5314yes—
701C22×C4C2×D4×C5314yes—
702C22×C4C2×D4×C5314yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C53116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—416no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C5314yes—
789C23#117×C5314yes—
790C23#117×C5314yes—
791C23C4×D4×C5314yes—
792C23C4×D4×C5314yes—
793C23#121×C5314yes—
794C23#123×C5314yes—
795C23#124×C5314yes—
796C23#126×C5314yes—
797C23C23×C4×C5311yescharacteristic
798C23C22×D4×C5312yes—
799C23C22×D4×C5311yescharacteristic
800C23C22×D4×C5311yescharacteristic
801C23C2×#41×C5311yescharacteristic
802C23C2×#41×C5311yescharacteristic
803C23C2×#41×C5312yes—
804C23C2×#41×C5311yescharacteristic
805C23C2×#41×C5311yescharacteristic
806C23H(5,𝔽2)×C5312yes—
807C23H(5,𝔽2)×C5312yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C5314yes—
857C2×C4C2×C22⋊C4×C5314yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—44no—
890C22—44no—
891C22C53×#38818yescomplemented
892C22C22×C22⋊C4×C5311yescharacteristic
893C22C2×#117×C5311yescharacteristic
894C22C2×#117×C5311yescharacteristic
895C22C2×C4×D4×C5311yescharacteristic
896C22C2×C4×D4×C5311yescharacteristic
897C22C53×#51811yescharacteristic
898C22C53×#51811yescharacteristic
899C22C2×#121×C5311yescharacteristic
900C22C2×#123×C5311yescharacteristic
901C22C53×#52512yes—
902C22C53×#52512yes—
903C22C2×#124×C5311yescharacteristic
904C22C2×#126×C5311yescharacteristic
905C22C53×#53812yes—
906C22C53×#53812yes—
907C22D42×C5312yes—
908C22D42×C5312yes—
909C22C53×#54612yes—
910C22C53×#54612yes—
911C22C53×#54612yes—
912C22C53×#54612yes—
913C22C53×#55112yes—
914C22C53×#55112yes—
915C4—24no—
916C4—24no—
917C4—44no—
918C4—42no—
919C4—42no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C53×#228011yescharacteristic
927C2C2×C53×#38811yescharacteristic
928C2C53×#231211yescharacteristic
929C2D4×C22⋊C4×C5311yescharacteristic
930C2D4×C22⋊C4×C5311yescharacteristic
931C2C53×#234211yescharacteristic
932C2C53×#234211yescharacteristic
933C2C53×#241812yes—
934C2C53×#242412yes—
935C2C53×#247212yes—
936C2C53×#248012yes—
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC26×C53C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C53×#388C2semidirect
3. C2×C53×#380C2semidirect
6. C2×C4×C22⋊C4×C53C2semidirect
7. C53×#1440C2semidirect
8. C53×#1439C2semidirect
9. C53×#1437C2semidirect
10. C53×C22⋊#95C2semidirect
11. C53×C22⋊#95C2semidirect
15. C22×C4⋊C4×C53C22semidirect
17. C22×C22⋊C4×C53C4semidirect
30. C22×C42×C53C22semidirect
36. C2×#95×C53C22semidirect
37. C2×#95×C53C22semidirect
38. C2×#95×C53C22semidirect
39. C2×#95×C53C22semidirect
40. C2×#95×C53C22semidirect
41. C2×#95×C53C22semidirect
246. C22⋊C4×C53C22⋊C4semidirect
389. #13873C53direct (N × H)
423. C22×C53#388semidirect
456. C2×#388C2×C53semidirect
457. C2×#380C2×C53semidirect
460. C2×C4×C22⋊C4C2×C53semidirect
461. #1440C2×C53semidirect
462. #1439C2×C53semidirect
463. #1437C2×C53semidirect
464. C22⋊#95C2×C53semidirect
465. C22⋊#95C2×C53semidirect
483. C22×C4⋊C4C22×C53semidirect
485. C22×C22⋊C4C4×C53semidirect
498. C22×C42C22×C53semidirect
504. C2×#95C22×C53semidirect
505. C2×#95C22×C53semidirect
506. C2×#95C22×C53semidirect
507. C2×#95C22×C53semidirect
508. C2×#95C22×C53semidirect
509. C2×#95C22×C53semidirect
510. C53#13873direct (N × H)
715. C22⋊C4C22⋊C4×C53semidirect
891. C22C53×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C532
C2×C53×#3882
C2×C53×#3802
C2×C53×#3792
C2×C4×C22⋊C4×C532
C53×#14402
C53×#14392
C53×#14372
C53×C22⋊#952
#1387353