Finite Group Databasebeta

← C53×#24440 #27231952

Subgroups — C53×#24440 #27231952

Order 13568.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C53C211yesmaximal, characteristic, complemented
2C2×C53×#469C211yesmaximal, characteristic, complemented
3C2×C53×#447C211yesmaximal, characteristic, complemented
4C2×C53×#447C211yesmaximal, characteristic, complemented
5C2×C53×#418C211yesmaximal, characteristic, complemented
6C53×#2414C211yesmaximal, characteristic, complemented
7C53×#2041C211yesmaximal, characteristic, complemented
8C53×#2034C211yesmaximal, characteristic, complemented
9C53×#2011C211yesmaximal, characteristic, complemented
10C53×#1999C211yesmaximal, characteristic, complemented
11C53×#1879C211yesmaximal, characteristic, complemented
12C53×#1875C211yesmaximal, characteristic, complemented
13C53×#1870C211yesmaximal, characteristic, complemented
14C53×#1864C211yesmaximal, characteristic, complemented
15C53×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C53—21no—
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C22×D8×C53C2211yescharacteristic
20C22×D8×C53C2211yescharacteristic, complemented
21C22×D8×C53C2211yescharacteristic, complemented
22C22×M16×C53C2211yescharacteristic, complemented
23D42×C53—24no—
24D42×C53—24no—
25C2×#127×C53C2211yescharacteristic
26C2×#121×C53—21no—
27C2×#121×C53C2211yescharacteristic
28C2×#121×C53C2211yescharacteristic
29C2×#121×C53C2211yescharacteristic, complemented
30C2×#121×C53C2211yescharacteristic, complemented
31C2×#120×C53—21no—
32C2×#120×C53—21no—
33C2×C4×D4×C53C2211yescharacteristic
34C2×C4×D4×C53C2211yescharacteristic
35C2×#117×C53C2211yescharacteristic, complemented
36C53×#469—24no—
37C53×#447—24no—
38C53×#447—24no—
39C2×#106×C53C2211yescharacteristic, complemented
40C53×#418—24no—
41C2×#102×C53C2211yescharacteristic
42C2×#102×C53C2211yescharacteristic
43C2×#102×C53C2211yescharacteristic
44C2×#102×C53C2211yescharacteristic, complemented
45C2×#102×C53C2211yescharacteristic, complemented
46C2×#102×C53C2211yescharacteristic, complemented
47C2×#102×C53C2211yescharacteristic, complemented
48C2×#102×C53C2211yescharacteristic, complemented
49C2×#102×C53C2211yescharacteristic, complemented
50C2×#102×C53C2211yescharacteristic, complemented
51C2×C22⋊C8×C53C2211yescharacteristic, complemented
52C2×C22⋊C8×C53C2211yescharacteristic, complemented
53C2×C22⋊C8×C53C2211yescharacteristic, complemented
54C53×#394—21no—
55C53×#392—21no—
56C53×#390—21no—
57C53×#390C2211yescharacteristic, complemented
58C53×#389C2211yescharacteristic, complemented
59C53×#388—21no—
60C53×#380C2211yescharacteristic, complemented
61C53×#340C2211yescharacteristic, complemented
62C53×#340C2211yescharacteristic, complemented
63C53×#336C2211yescharacteristic, complemented
64C53×#336C2211yescharacteristic, complemented
65C25×C53—21no—
66C25×C53—21no—
67C22×D4×C53—22no—
68C22×D4×C53—22no—
69C22×D4×C53—28no—
70C22×D4×C53—21no—
71C22×D4×C53—21no—
72C22×D4×C53—22no—
73C22×D4×C53—22no—
74C22×D4×C53—22no—
75C22×D4×C53—22no—
76C22×D4×C53—21no—
77C22×D4×C53—21no—
78C22×D4×C53—21no—
79C22×D4×C53—21no—
80C22×D4×C53—21no—
81C22×D4×C53—22no—
82C22×D4×C53—21no—
83C22×D4×C53—41no—
84C22×D4×C53—41no—
85C22×D4×C53—41no—
86C22×D4×C53—41no—
87C22×D4×C53—44no—
88C22×D4×C53—44no—
89C22×D4×C53D411yescharacteristic
90C22×D4×C53D414yescomplemented
91C22×D4×C53C2311yescharacteristic
92C22×D4×C53C2311yescharacteristic
93C22×D4×C53C2311yescharacteristic
94C22×D4×C53C2311yescharacteristic
95C23×C4×C53—21no—
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C2×D8×C53—22no—
99C2×D8×C53—22no—
100C2×D8×C53—22no—
101C2×D8×C53—22no—
102C2×D8×C53—22no—
103C2×D8×C53—22no—
104C2×D8×C53—41no—
105C2×D8×C53—41no—
106C2×D8×C53—41no—
107C2×M16×C53—22no—
108C2×M16×C53—22no—
109C2×M16×C53—41no—
110C22×C8×C53C2311yescharacteristic
111C22×C8×C53C2311yescharacteristic
112C22×C8×C53C2311yescharacteristic
113C22×C8×C53C2311yescharacteristic
114#127×C53—22no—
115#127×C53—22no—
116#121×C53—28no—
117#121×C53—22no—
118#121×C53—22no—
119#121×C53—22no—
120#121×C53—22no—
121#121×C53—22no—
122#121×C53—22no—
123#121×C53—41no—
124#121×C53D414yescomplemented
125#120×C53—28no—
126#120×C53—28no—
127C4×D4×C53—22no—
128C4×D4×C53—22no—
129C4×D4×C53—22no—
130C4×D4×C53—22no—
131#117×C53—22no—
132#117×C53—41no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53D411yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C22⋊C4×C53D411yescharacteristic
150C2×C42×C53—21no—
151C2×C42×C53C2311yescharacteristic
152#106×C53—22no—
153#102×C53—22no—
154#102×C53—22no—
155#102×C53—22no—
156#102×C53—22no—
157#102×C53—22no—
158#102×C53—22no—
159#102×C53—22no—
160#102×C53—22no—
161#102×C53—41no—
162#102×C53D414yescomplemented
163C22⋊C8×C53—22no—
164C22⋊C8×C53—22no—
165C22⋊C8×C53—41no—
166#95×C53—21no—
167#95×C53—21no—
168C24×C53—21no—
169C24×C53—24no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—24no—
173C24×C53—21no—
174C24×C53—42no—
175C24×C53—42no—
176C24×C53—42no—
177C24×C53—42no—
178C24×C53—42no—
179C24×C53—42no—
180C24×C53—42no—
181C24×C53—42no—
182C24×C53—81no—
183C24×C53—81no—
184C24×C53—81no—
185C24×C53—81no—
186C24×C53C2×D411yescharacteristic
187C24×C53C2×D411yescharacteristic
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—28no—
191C2×D4×C53—24no—
192C2×D4×C53—24no—
193C2×D4×C53—24no—
194C2×D4×C53—24no—
195C2×D4×C53—24no—
196C2×D4×C53—24no—
197C2×D4×C53—22no—
198C2×D4×C53—21no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—21no—
204C2×D4×C53—21no—
205C2×D4×C53—21no—
206C2×D4×C53—21no—
207C2×D4×C53—21no—
208C2×D4×C53—21no—
209C2×D4×C53—21no—
210C2×D4×C53—21no—
211C2×D4×C53—21no—
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53—21no—
216C2×D4×C53—21no—
217C2×D4×C53—44no—
218C2×D4×C53—44no—
219C2×D4×C53—44no—
220C2×D4×C53—42no—
221C2×D4×C53—42no—
222C2×D4×C53—42no—
223C2×D4×C53—42no—
224C2×D4×C53—42no—
225C2×D4×C53—42no—
226C2×D4×C53—44no—
227C2×D4×C53—44no—
228C2×D4×C53—432no—
229C2×D4×C53—44no—
230C2×D4×C53—42no—
231C2×D4×C53—42no—
232C2×D4×C53—42no—
233C2×D4×C53—42no—
234C2×D4×C53—44no—
235C2×D4×C53—42no—
236C2×D4×C53—42no—
237C2×D4×C53—42no—
238C2×D4×C53—81no—
239C2×D4×C53—81no—
240C2×D4×C53—81no—
241C2×D4×C53—81no—
242C2×D4×C53—81no—
243C2×D4×C53C2×D412yes—
244C2×D4×C53C2×D412yes—
245C2×D4×C53C2×D412yes—
246C2×D4×C53C2×D412yes—
247C2×D4×C53#4112yes—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—24no—
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—42no—
264C22×C4×C53—42no—
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2×D412yes—
269C22×C4×C53C2×D412yes—
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2411yescharacteristic
272D8×C53—44no—
273D8×C53—44no—
274D8×C53—44no—
275M16×C53—44no—
276C2×C8×C53—21no—
277C2×C8×C53—21no—
278C2×C8×C53—21no—
279C2×C8×C53—21no—
280C2×C8×C53—21no—
281C2×C8×C53—21no—
282C2×C8×C53—21no—
283C2×C8×C53—21no—
284C2×C8×C53—21no—
285C2×C8×C53—21no—
286C2×C8×C53—21no—
287C2×C8×C53C2×D412yescomplemented
288C4⋊C4×C53—22no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53—21no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53—21no—
293C4⋊C4×C53—21no—
294C4⋊C4×C53—21no—
295C4⋊C4×C53—81no—
296C4⋊C4×C53C2×D412yes—
297C4⋊C4×C53C2×D412yescomplemented
298C22⋊C4×C53—24no—
299C22⋊C4×C53—24no—
300C22⋊C4×C53—22no—
301C22⋊C4×C53—24no—
302C22⋊C4×C53—22no—
303C22⋊C4×C53—42no—
304C22⋊C4×C53—42no—
305C22⋊C4×C53—42no—
306C22⋊C4×C53—42no—
307C22⋊C4×C53—81no—
308C22⋊C4×C53—81no—
309C42×C53—21no—
310C42×C53—21no—
311C42×C53—42no—
312C23×C53—21no—
313C23×C53—22no—
314C23×C53—21no—
315C23×C53—21no—
316C23×C53—22no—
317C23×C53—21no—
318C23×C53—21no—
319C23×C53—22no—
320C23×C53—21no—
321C23×C53—21no—
322C23×C53—21no—
323C23×C53—21no—
324C23×C53—21no—
325C23×C53—21no—
326C23×C53—21no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—48no—
330C23×C53—48no—
331C23×C53—48no—
332C23×C53—48no—
333C23×C53—41no—
334C23×C53—41no—
335C23×C53—41no—
336C23×C53—41no—
337C23×C53—41no—
338C23×C53—41no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—84no—
357C23×C53—84no—
358C23×C53—84no—
359C23×C53—84no—
360C23×C53—84no—
361C23×C53—84no—
362C23×C53—84no—
363C23×C53—84no—
364C23×C53—84no—
365C23×C53—84no—
366C23×C53#12012yes—
367C23×C53AGL(1,ℤ/8)12yes—
368C23×C53C22×D411yescharacteristic
369D4×C53—28no—
370D4×C53—22no—
371D4×C53—22no—
372D4×C53—22no—
373D4×C53—22no—
374D4×C53—22no—
375D4×C53—22no—
376D4×C53—22no—
377D4×C53—48no—
378D4×C53—48no—
379D4×C53—48no—
380D4×C53—48no—
381D4×C53—48no—
382D4×C53—41no—
383D4×C53—41no—
384D4×C53—41no—
385D4×C53—41no—
386D4×C53—41no—
387D4×C53—41no—
388D4×C53—41no—
389D4×C53—41no—
390D4×C53—84no—
391D4×C53—84no—
392D4×C53—84no—
393D4×C53#12114yes—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—21no—
397C2×C4×C53—21no—
398C2×C4×C53—22no—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—21no—
406C2×C4×C53—22no—
407C2×C4×C53—21no—
408C2×C4×C53—21no—
409C2×C4×C53—21no—
410C2×C4×C53—48no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53#12012yes—
426C2×C4×C53AGL(1,ℤ/8)12yes—
427C2×C4×C53C22×D411yescharacteristic
428C2×C4×C53C22×D411yescharacteristic
429C2×C4×C53C22×D411yescharacteristic
430C2×C4×C53C2×#4111yescharacteristic
431C2×C4×C53H(5,𝔽2)11yescharacteristic
432C2×C4×C53H(5,𝔽2)11yescharacteristic
433C8×C53—22no—
434C8×C53—41no—
435C8×C53—41no—
436C8×C53—41no—
437#24440C5311yesmaximal, characteristic, direct product factor, Sylow
438C22×C53—22no—
439C22×C53—24no—
440C22×C53—22no—
441C22×C53—22no—
442C22×C53—22no—
443C22×C53—22no—
444C22×C53—22no—
445C22×C53—41no—
446C22×C53—42no—
447C22×C53—41no—
448C22×C53—42no—
449C22×C53—41no—
450C22×C53—42no—
451C22×C53—41no—
452C22×C53—41no—
453C22×C53—42no—
454C22×C53—41no—
455C22×C53—42no—
456C22×C53—41no—
457C22×C53—41no—
458C22×C53—42no—
459C22×C53—42no—
460C22×C53—42no—
461C22×C53—42no—
462C22×C53—42no—
463C22×C53—42no—
464C22×C53—42no—
465C22×C53—816no—
466C22×C53—816no—
467C22×C53—81no—
468C22×C53—81no—
469C22×C53—81no—
470C22×C53—81no—
471C22×C53—81no—
472C22×C53—81no—
473C22×C53—81no—
474C22×C53—81no—
475C22×C53—81no—
476C22×C53—81no—
477C22×C53—81no—
478C22×C53—81no—
479C22×C53—81no—
480C22×C53—81no—
481C22×C53—81no—
482C22×C53C2×#12011yescharacteristic
483C22×C53D4211yescharacteristic
484C22×C53#54611yescharacteristic
485C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C53#57611yescharacteristic
488C22×C53#57611yescharacteristic
489C4×C53—22no—
490C4×C53—22no—
491C4×C53—41no—
492C4×C53—42no—
493C4×C53—41no—
494C4×C53—42no—
495C4×C53—81no—
496C4×C53—81no—
497C4×C53C2×#12111yescharacteristic
498C4×C53#53411yescharacteristic
499C4×C53D4211yescharacteristic
500C4×C53#54611yescharacteristic
501C2×D42C2×C5311yescharacteristic, complemented
502C2×#469C2×C5311yescharacteristic, complemented
503C2×#447C2×C5311yescharacteristic, complemented
504C2×#447C2×C5311yescharacteristic, complemented
505C2×#418C2×C5311yescharacteristic, complemented
506#2414C2×C5311yescharacteristic, complemented
507#2041C2×C5311yescharacteristic, complemented
508#2034C2×C5311yescharacteristic, complemented
509#2011C2×C5311yescharacteristic, complemented
510#1999C2×C5311yescharacteristic, complemented
511#1879C2×C5311yescharacteristic, complemented
512#1875C2×C5311yescharacteristic, complemented
513#1870C2×C5311yescharacteristic, complemented
514#1864C2×C5311yescharacteristic, complemented
515#1786C2×C5311yescharacteristic, complemented
516C2×C53—42no—
517C2×C53—42no—
518C2×C53—44no—
519C2×C53—82no—
520C2×C53—82no—
521C2×C53—161no—
522C2×C53#241011yescharacteristic
523C2×C53#300311yescharacteristic
524C2×C53#300811yescharacteristic
525C2×C53#326411yescharacteristic
526C2×C53#327411yescharacteristic
527C2×C53#331811yescharacteristic
528C2×C53#332511yescharacteristic
529C23×D4—21no—
530C23×D4C22×C5311yescharacteristic
531C23×D4C22×C5311yescharacteristic
532C22×D8C22×C5311yescharacteristic
533C22×D8C22×C5311yescharacteristic, complemented
534C22×D8C22×C5311yescharacteristic, complemented
535C22×M16C22×C5311yescharacteristic, complemented
536D42—24no—
537D42—24no—
538C2×#127C22×C5311yescharacteristic
539C2×#121—21no—
540C2×#121C22×C5311yescharacteristic
541C2×#121C22×C5311yescharacteristic
542C2×#121C22×C5311yescharacteristic, complemented
543C2×#121C22×C5311yescharacteristic, complemented
544C2×#120—21no—
545C2×#120—21no—
546C2×C4×D4C22×C5311yescharacteristic
547C2×C4×D4C22×C5311yescharacteristic
548C2×#117C22×C5311yescharacteristic, complemented
549#469—24no—
550#447—24no—
551#447—24no—
552C2×#106C22×C5311yescharacteristic, complemented
553#418—24no—
554C2×#102C22×C5311yescharacteristic
555C2×#102C22×C5311yescharacteristic
556C2×#102C22×C5311yescharacteristic
557C2×#102C22×C5311yescharacteristic, complemented
558C2×#102C22×C5311yescharacteristic, complemented
559C2×#102C22×C5311yescharacteristic, complemented
560C2×#102C22×C5311yescharacteristic, complemented
561C2×#102C22×C5311yescharacteristic, complemented
562C2×#102C22×C5311yescharacteristic, complemented
563C2×#102C22×C5311yescharacteristic, complemented
564C2×C22⋊C8C22×C5311yescharacteristic, complemented
565C2×C22⋊C8C22×C5311yescharacteristic, complemented
566C2×C22⋊C8C22×C5311yescharacteristic, complemented
567#394—21no—
568#392—21no—
569#390—21no—
570#390C22×C5311yescharacteristic, complemented
571#389C22×C5311yescharacteristic, complemented
572#388—21no—
573#380C22×C5311yescharacteristic, complemented
574#340C22×C5311yescharacteristic, complemented
575#340C22×C5311yescharacteristic, complemented
576#336C22×C5311yescharacteristic, complemented
577#336C22×C5311yescharacteristic, complemented
578C53#2444011yescharacteristic, direct product factor, Sylow
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C5311yescharacteristic
604C22×D4D4×C5314yescomplemented
605C22×D4C23×C5311yescharacteristic
606C22×D4C23×C5311yescharacteristic
607C22×D4C23×C5311yescharacteristic
608C22×D4C23×C5311yescharacteristic
609C23×C4—21no—
610C23×C4C23×C5311yescharacteristic
611C23×C4C23×C5311yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C5311yescharacteristic
625C22×C8C23×C5311yescharacteristic
626C22×C8C23×C5311yescharacteristic
627C22×C8C23×C5311yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C5314yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C5311yescharacteristic
649C2×C4⋊C4C23×C5311yescharacteristic
650C2×C4⋊C4C23×C5311yescharacteristic
651C2×C4⋊C4C23×C5311yescharacteristic
652C2×C4⋊C4C23×C5311yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C5311yescharacteristic
663C2×C22⋊C4D4×C5311yescharacteristic
664C2×C42—21no—
665C2×C42C23×C5311yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C5314yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C5311yescharacteristic
701C24C2×D4×C5311yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C5312yes—
758C2×D4C2×D4×C5312yes—
759C2×D4C2×D4×C5312yes—
760C2×D4C2×D4×C5312yes—
761C2×D4#41×C5312yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C5311yescharacteristic
780C22×C4C2×D4×C5311yescharacteristic
781C22×C4C2×D4×C5311yescharacteristic
782C22×C4C2×D4×C5312yes—
783C22×C4C2×D4×C5312yes—
784C22×C4C2×D4×C5311yescharacteristic
785C22×C4C24×C5311yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C5312yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C5312yes—
811C4⋊C4C2×D4×C5312yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C5312yes—
881C23AGL(1,ℤ/8)×C5312yes—
882C23C22×D4×C5311yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C5314yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C5312yes—
940C2×C4AGL(1,ℤ/8)×C5312yes—
941C2×C4C22×D4×C5311yescharacteristic
942C2×C4C22×D4×C5311yescharacteristic
943C2×C4C22×D4×C5311yescharacteristic
944C2×C4C2×#41×C5311yescharacteristic
945C2×C4H(5,𝔽2)×C5311yescharacteristic
946C2×C4H(5,𝔽2)×C5311yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C5311yescharacteristic
996C22D42×C5311yescharacteristic
997C22C53×#54611yescharacteristic
998C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
999C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
1000C22C53×#57611yescharacteristic
1001C22C53×#57611yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—42no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C5311yescharacteristic
1011C4C53×#53411yescharacteristic
1012C4D42×C5311yescharacteristic
1013C4C53×#54611yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C53×#241011yescharacteristic
1021C2C53×#300311yescharacteristic
1022C2C53×#300811yescharacteristic
1023C2C53×#326411yescharacteristic
1024C2C53×#327411yescharacteristic
1025C2C53×#331811yescharacteristic
1026C2C53×#332511yescharacteristic
subgroupG/H
center, socleC23×C53C22×D4
commutator, Frattini, cosocleC22×C4C24×C53
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×C4×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D42×C53C2semidirect
2. C2×C53×#469C2semidirect
3. C2×C53×#447C2semidirect
4. C2×C53×#447C2semidirect
5. C2×C53×#418C2semidirect
6. C53×#2414C2semidirect
7. C53×#2041C2semidirect
8. C53×#2034C2semidirect
9. C53×#2011C2semidirect
10. C53×#1999C2semidirect
11. C53×#1879C2semidirect
12. C53×#1875C2semidirect
13. C53×#1870C2semidirect
14. C53×#1864C2semidirect
15. C53×#1786C2semidirect
20. C22×D8×C53C22semidirect
21. C22×D8×C53C22semidirect
22. C22×M16×C53C22semidirect
29. C2×#121×C53C22semidirect
30. C2×#121×C53C22semidirect
35. C2×#117×C53C22semidirect
39. C2×#106×C53C22semidirect
44. C2×#102×C53C22semidirect
45. C2×#102×C53C22semidirect
46. C2×#102×C53C22semidirect
47. C2×#102×C53C22semidirect
48. C2×#102×C53C22semidirect
49. C2×#102×C53C22semidirect
50. C2×#102×C53C22semidirect
51. C2×C22⋊C8×C53C22semidirect
52. C2×C22⋊C8×C53C22semidirect
53. C2×C22⋊C8×C53C22semidirect
57. C53×#390C22semidirect
58. C53×#389C22semidirect
60. C53×#380C22semidirect
61. C53×#340C22semidirect
62. C53×#340C22semidirect
63. C53×#336C22semidirect
64. C53×#336C22semidirect
90. C22×D4×C53D4semidirect
124. #121×C53D4semidirect
162. #102×C53D4semidirect
287. C2×C8×C53C2×D4semidirect
297. C4⋊C4×C53C2×D4semidirect
437. #24440C53direct (N × H)
501. C2×D42C2×C53semidirect
502. C2×#469C2×C53semidirect
503. C2×#447C2×C53semidirect
504. C2×#447C2×C53semidirect
505. C2×#418C2×C53semidirect
506. #2414C2×C53semidirect
507. #2041C2×C53semidirect
508. #2034C2×C53semidirect
509. #2011C2×C53semidirect
510. #1999C2×C53semidirect
511. #1879C2×C53semidirect
512. #1875C2×C53semidirect
513. #1870C2×C53semidirect
514. #1864C2×C53semidirect
515. #1786C2×C53semidirect
533. C22×D8C22×C53semidirect
534. C22×D8C22×C53semidirect
535. C22×M16C22×C53semidirect
542. C2×#121C22×C53semidirect
543. C2×#121C22×C53semidirect
548. C2×#117C22×C53semidirect
552. C2×#106C22×C53semidirect
557. C2×#102C22×C53semidirect
558. C2×#102C22×C53semidirect
559. C2×#102C22×C53semidirect
560. C2×#102C22×C53semidirect
561. C2×#102C22×C53semidirect
562. C2×#102C22×C53semidirect
563. C2×#102C22×C53semidirect
564. C2×C22⋊C8C22×C53semidirect
565. C2×C22⋊C8C22×C53semidirect
566. C2×C22⋊C8C22×C53semidirect
570. #390C22×C53semidirect
571. #389C22×C53semidirect
573. #380C22×C53semidirect
574. #340C22×C53semidirect
575. #340C22×C53semidirect
576. #336C22×C53semidirect
577. #336C22×C53semidirect
578. C53#24440direct (N × H)
604. C22×D4D4×C53semidirect
638. #121D4×C53semidirect
676. #102D4×C53semidirect
801. C2×C8C2×D4×C53semidirect
811. C4⋊C4C2×D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C532
C2×C53×#4692
C2×C53×#4472
C2×C53×#4182
C53×#24142
C53×#20412
C53×#20342
C53×#20112
C53×#19992
C53×#18792
C53×#18752
C53×#18702
C53×#18642
C53×#17862
#2444053