Finite Group Databasebeta

← C53×#24432 #27231944

Subgroups — C53×#24432 #27231944

Order 13568.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C53C211yesmaximal, characteristic
2C2×C53×#465C211yesmaximal, characteristic, complemented
3C2×C53×#450C211yesmaximal, characteristic, complemented
4C2×C53×#450C211yesmaximal, characteristic, complemented
5C22×#102×C53C211yesmaximal, characteristic, complemented
6C53×#2417C211yesmaximal, characteristic, complemented
7C53×#2041C211yesmaximal, characteristic, complemented
8C53×#2034C211yesmaximal, characteristic, complemented
9C53×#2014C211yesmaximal, characteristic, complemented
10C53×#2000C211yesmaximal, characteristic, complemented
11C53×#1877C211yesmaximal, characteristic, complemented
12C53×#1874C211yesmaximal, characteristic, complemented
13C53×#1869C211yesmaximal, characteristic, complemented
14C53×#1864C211yesmaximal, characteristic, complemented
15C53×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C53—21no—
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C22×SD16×C53C2211yescharacteristic
20C22×SD16×C53C2211yescharacteristic, complemented
21C22×SD16×C53C2211yescharacteristic, complemented
22C23×C8×C53C2211yescharacteristic, complemented
23D42×C53—24no—
24D42×C53—24no—
25C2×#127×C53C2211yescharacteristic
26C2×C22⋊Q8×C53C2211yescharacteristic, complemented
27C2×C22⋊Q8×C53C2211yescharacteristic, complemented
28C2×#121×C53—21no—
29C2×#121×C53C2211yescharacteristic
30C2×#121×C53C2211yescharacteristic
31C2×#120×C53—21no—
32C2×#120×C53—21no—
33C2×C4×D4×C53C2211yescharacteristic
34C2×C4×D4×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic, complemented
36C53×#465—24no—
37C53×#450—24no—
38C53×#450—24no—
39C2×#106×C53C2211yescharacteristic, complemented
40C2×#103×C53C2211yescharacteristic, complemented
41C2×#102×C53—24no—
42C2×#102×C53C2211yescharacteristic
43C2×#102×C53C2211yescharacteristic
44C2×#102×C53C2211yescharacteristic
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×#398—21no—
55C53×#396—21no—
56C53×#391C2211yescharacteristic, complemented
57C53×#389C2211yescharacteristic, complemented
58C53×#386—21no—
59C53×#380—21no—
60C53×#380C2211yescharacteristic, complemented
61C53×#340C2211yescharacteristic, complemented
62C53×#340C2211yescharacteristic, complemented
63C53×#336C2211yescharacteristic, complemented
64C53×#336C2211yescharacteristic, complemented
65C25×C53—21no—
66C25×C53—21no—
67C22×Q8×C53C2311yescharacteristic
68C22×D4×C53—22no—
69C22×D4×C53—22no—
70C22×D4×C53—28no—
71C22×D4×C53—21no—
72C22×D4×C53—21no—
73C22×D4×C53—22no—
74C22×D4×C53—22no—
75C22×D4×C53—22no—
76C22×D4×C53—22no—
77C22×D4×C53—21no—
78C22×D4×C53—21no—
79C22×D4×C53—21no—
80C22×D4×C53—22no—
81C22×D4×C53—21no—
82C22×D4×C53—41no—
83C22×D4×C53—41no—
84C22×D4×C53—41no—
85C22×D4×C53—41no—
86C22×D4×C53—44no—
87C22×D4×C53—44no—
88C22×D4×C53D411yescharacteristic
89C22×D4×C53D414yes—
90C22×D4×C53C2311yescharacteristic
91C22×D4×C53C2311yescharacteristic
92C22×D4×C53C2311yescharacteristic
93C23×C4×C53—21no—
94C23×C4×C53—21no—
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C2×SD16×C53—22no—
98C2×SD16×C53—22no—
99C2×SD16×C53—22no—
100C2×SD16×C53—22no—
101C2×SD16×C53—22no—
102C2×SD16×C53—22no—
103C2×SD16×C53—41no—
104C2×SD16×C53—41no—
105C2×SD16×C53—41no—
106C22×C8×C53—22no—
107C22×C8×C53—22no—
108C22×C8×C53—41no—
109C22×C8×C53C2311yescharacteristic
110C22×C8×C53C2311yescharacteristic
111C22×C8×C53C2311yescharacteristic
112C22×C8×C53C2311yescharacteristic
113#127×C53—22no—
114#127×C53—22no—
115C22⋊Q8×C53—22no—
116C22⋊Q8×C53—22no—
117C22⋊Q8×C53—22no—
118C22⋊Q8×C53—41no—
119#121×C53—28no—
120#121×C53—22no—
121#121×C53—22no—
122#121×C53—22no—
123#121×C53D414yes—
124#120×C53—28no—
125#120×C53—28no—
126C4×D4×C53—22no—
127C4×D4×C53—22no—
128C4×D4×C53—22no—
129C4×D4×C53—22no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—22no—
135C2×C4⋊C4×C53—41no—
136C2×C4⋊C4×C53D411yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
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×C53D411yescharacteristic
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C42×C53C2311yescharacteristic
150#106×C53—22no—
151#103×C53—22no—
152#102×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—41no—
160#102×C53D414yescomplemented
161C22⋊C8×C53—22no—
162C22⋊C8×C53—22no—
163C22⋊C8×C53—41no—
164#95×C53—21no—
165#95×C53—21no—
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—42no—
174C24×C53—42no—
175C24×C53—42no—
176C24×C53—42no—
177C24×C53—42no—
178C24×C53—42no—
179C24×C53—42no—
180C24×C53—42no—
181C24×C53—81no—
182C24×C53—81no—
183C24×C53—81no—
184C24×C53—81no—
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—21no—
192C2×Q8×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—28no—
196C2×D4×C53—24no—
197C2×D4×C53—24no—
198C2×D4×C53—24no—
199C2×D4×C53—24no—
200C2×D4×C53—24no—
201C2×D4×C53—24no—
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—44no—
216C2×D4×C53—44no—
217C2×D4×C53—44no—
218C2×D4×C53—42no—
219C2×D4×C53—42no—
220C2×D4×C53—42no—
221C2×D4×C53—42no—
222C2×D4×C53—42no—
223C2×D4×C53—44no—
224C2×D4×C53—44no—
225C2×D4×C53—432no—
226C2×D4×C53—44no—
227C2×D4×C53—42no—
228C2×D4×C53—42no—
229C2×D4×C53—42no—
230C2×D4×C53—42no—
231C2×D4×C53—44no—
232C2×D4×C53—42no—
233C2×D4×C53—81no—
234C2×D4×C53—81no—
235C2×D4×C53SD1614yescomplemented
236C2×D4×C53C2×D412yes—
237C2×D4×C53C2×D412yes—
238C2×D4×C53C2×D412yes—
239C2×D4×C53C2×D412yes—
240C2×D4×C53#4112yes—
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—24no—
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—21no—
256C22×C4×C53—21no—
257C22×C4×C53—42no—
258C22×C4×C53—42no—
259C22×C4×C53—42no—
260C22×C4×C53—42no—
261C22×C4×C53—81no—
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D412yes—
266C22×C4×C53C2×D412yes—
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2411yescharacteristic
269SD16×C53—44no—
270SD16×C53—44no—
271SD16×C53—44no—
272C2×C8×C53—21no—
273C2×C8×C53—21no—
274C2×C8×C53—21no—
275C2×C8×C53—21no—
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—44no—
284C2×C8×C53C2×D412yescomplemented
285C4⋊C4×C53—22no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53—21no—
288C4⋊C4×C53—21no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53—21no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53—42no—
293C4⋊C4×C53—42no—
294C4⋊C4×C53—42no—
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—81no—
306C42×C53—21no—
307C42×C53—21no—
308C23×C53—21no—
309C23×C53—21no—
310C23×C53—21no—
311C23×C53—21no—
312C23×C53—21no—
313C23×C53—22no—
314C23×C53—21no—
315C23×C53—22no—
316C23×C53—21no—
317C23×C53—22no—
318C23×C53—21no—
319C23×C53—21no—
320C23×C53—21no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—48no—
324C23×C53—48no—
325C23×C53—48no—
326C23×C53—41no—
327C23×C53—41no—
328C23×C53—41no—
329C23×C53—41no—
330C23×C53—41no—
331C23×C53—41no—
332C23×C53—41no—
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—48no—
343C23×C53—84no—
344C23×C53—84no—
345C23×C53—84no—
346C23×C53—84no—
347C23×C53—84no—
348C23×C53—84no—
349C23×C53—84no—
350C23×C53—84no—
351C23×C53—84no—
352C23×C53—84no—
353C23×C53#12012yes—
354C23×C53C2×SD1612yes—
355C23×C53C2×SD1612yes—
356C23×C53AGL(1,ℤ/8)12yes—
357C23×C53C22×D411yescharacteristic
358Q8×C53—41no—
359Q8×C53—41no—
360Q8×C53—41no—
361Q8×C53—41no—
362D4×C53—28no—
363D4×C53—22no—
364D4×C53—22no—
365D4×C53—22no—
366D4×C53—22no—
367D4×C53—22no—
368D4×C53—22no—
369D4×C53—22no—
370D4×C53—48no—
371D4×C53—48no—
372D4×C53—48no—
373D4×C53—48no—
374D4×C53—48no—
375D4×C53—41no—
376D4×C53—41no—
377D4×C53—41no—
378D4×C53—41no—
379D4×C53—84no—
380D4×C53#12114yes—
381C2×C4×C53—21no—
382C2×C4×C53—21no—
383C2×C4×C53—21no—
384C2×C4×C53—21no—
385C2×C4×C53—22no—
386C2×C4×C53—22no—
387C2×C4×C53—22no—
388C2×C4×C53—22no—
389C2×C4×C53—22no—
390C2×C4×C53—21no—
391C2×C4×C53—21no—
392C2×C4×C53—21no—
393C2×C4×C53—22no—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—21no—
397C2×C4×C53—48no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—41no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—84no—
416C2×C4×C53#12012yes—
417C2×C4×C53C2×SD1612yes—
418C2×C4×C53C22×D411yescharacteristic
419C2×C4×C53C22×D411yescharacteristic
420C2×C4×C53C22×D411yescharacteristic
421C2×C4×C53C2×#4111yescharacteristic
422C2×C4×C53H(5,𝔽2)11yescharacteristic
423C2×C4×C53H(5,𝔽2)11yescharacteristic
424C8×C53—22no—
425C8×C53—41no—
426C8×C53—41no—
427C8×C53—41no—
428#24432C5311yesmaximal, characteristic, direct product factor, Sylow
429C22×C53—22no—
430C22×C53—22no—
431C22×C53—22no—
432C22×C53—22no—
433C22×C53—22no—
434C22×C53—22no—
435C22×C53—24no—
436C22×C53—22no—
437C22×C53—22no—
438C22×C53—22no—
439C22×C53—41no—
440C22×C53—42no—
441C22×C53—41no—
442C22×C53—42no—
443C22×C53—41no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—41no—
448C22×C53—42no—
449C22×C53—42no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—42no—
453C22×C53—42no—
454C22×C53—42no—
455C22×C53—816no—
456C22×C53—816no—
457C22×C53—81no—
458C22×C53—81no—
459C22×C53—81no—
460C22×C53—81no—
461C22×C53—81no—
462C22×C53—81no—
463C22×C53—81no—
464C22×C53—81no—
465C22×C53#45014yescomplemented
466C22×C53C2×#12011yescharacteristic
467C22×C53D4211yescharacteristic
468C22×C53#54611yescharacteristic
469C22×C53C22×SD1611yescharacteristic
470C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C53#57611yescharacteristic
472C22×C53#57711yescharacteristic
473C4×C53—22no—
474C4×C53—22no—
475C4×C53—41no—
476C4×C53—42no—
477C4×C53—42no—
478C4×C53—41no—
479C4×C53—81no—
480C4×C53—81no—
481C4×C53—81no—
482C4×C53C2×#12111yescharacteristic
483C4×C53#53411yescharacteristic
484C4×C53D4211yescharacteristic
485C4×C53#54611yescharacteristic
486C2×D42C2×C5311yescharacteristic
487C2×#465C2×C5311yescharacteristic, complemented
488C2×#450C2×C5311yescharacteristic, complemented
489C2×#450C2×C5311yescharacteristic, complemented
490C22×#102C2×C5311yescharacteristic, complemented
491#2417C2×C5311yescharacteristic, complemented
492#2041C2×C5311yescharacteristic, complemented
493#2034C2×C5311yescharacteristic, complemented
494#2014C2×C5311yescharacteristic, complemented
495#2000C2×C5311yescharacteristic, complemented
496#1877C2×C5311yescharacteristic, complemented
497#1874C2×C5311yescharacteristic, complemented
498#1869C2×C5311yescharacteristic, complemented
499#1864C2×C5311yescharacteristic, complemented
500#1786C2×C5311yescharacteristic, complemented
501C2×C53—24no—
502C2×C53—42no—
503C2×C53—44no—
504C2×C53—82no—
505C2×C53—82no—
506C2×C53#241011yescharacteristic
507C2×C53C2×#45011yescharacteristic
508C2×C53#301211yescharacteristic
509C2×C53#326411yescharacteristic
510C2×C53D4×SD1611yescharacteristic
511C2×C53#329511yescharacteristic
512C2×C53#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C5311yescharacteristic
515C23×D4C22×C5311yescharacteristic
516C22×SD16C22×C5311yescharacteristic
517C22×SD16C22×C5311yescharacteristic, complemented
518C22×SD16C22×C5311yescharacteristic, complemented
519C23×C8C22×C5311yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C5311yescharacteristic
523C2×C22⋊Q8C22×C5311yescharacteristic, complemented
524C2×C22⋊Q8C22×C5311yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C5311yescharacteristic
527C2×#121C22×C5311yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C5311yescharacteristic
531C2×C4×D4C22×C5311yescharacteristic
532C22×C4⋊C4C22×C5311yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C5311yescharacteristic, complemented
537C2×#103C22×C5311yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C5311yescharacteristic
540C2×#102C22×C5311yescharacteristic
541C2×#102C22×C5311yescharacteristic
542C2×#102C22×C5311yescharacteristic, complemented
543C2×#102C22×C5311yescharacteristic, complemented
544C2×#102C22×C5311yescharacteristic, complemented
545C2×#102C22×C5311yescharacteristic, complemented
546C2×#102C22×C5311yescharacteristic, complemented
547C2×#102C22×C5311yescharacteristic, complemented
548C2×C22⋊C8C22×C5311yescharacteristic, complemented
549C2×C22⋊C8C22×C5311yescharacteristic, complemented
550C2×C22⋊C8C22×C5311yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C5311yescharacteristic, complemented
554#389C22×C5311yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C5311yescharacteristic, complemented
558#340C22×C5311yescharacteristic, complemented
559#340C22×C5311yescharacteristic, complemented
560#336C22×C5311yescharacteristic, complemented
561#336C22×C5311yescharacteristic, complemented
562C53#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C5311yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C5311yescharacteristic
587C22×D4D4×C5314yes—
588C22×D4C23×C5311yescharacteristic
589C22×D4C23×C5311yescharacteristic
590C22×D4C23×C5311yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C5311yescharacteristic
594C23×C4C23×C5311yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C5311yescharacteristic
608C22×C8C23×C5311yescharacteristic
609C22×C8C23×C5311yescharacteristic
610C22×C8C23×C5311yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C5314yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C5311yescharacteristic
635C2×C4⋊C4C23×C5311yescharacteristic
636C2×C4⋊C4C23×C5311yescharacteristic
637C2×C4⋊C4C23×C5311yescharacteristic
638C2×C4⋊C4C23×C5311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C5311yescharacteristic
646C2×C22⋊C4D4×C5311yescharacteristic
647C2×C42C23×C5311yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C5314yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C5311yescharacteristic
684C24C2×D4×C5311yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C5314yescomplemented
734C2×D4C2×D4×C5312yes—
735C2×D4C2×D4×C5312yes—
736C2×D4C2×D4×C5312yes—
737C2×D4C2×D4×C5312yes—
738C2×D4#41×C5312yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C5311yescharacteristic
761C22×C4C2×D4×C5311yescharacteristic
762C22×C4C2×D4×C5311yescharacteristic
763C22×C4C2×D4×C5312yes—
764C22×C4C2×D4×C5312yes—
765C22×C4C2×D4×C5311yescharacteristic
766C22×C4C24×C5311yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C5312yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C5312yes—
795C4⋊C4C2×D4×C5312yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C5312yes—
852C23C2×SD16×C5312yes—
853C23C2×SD16×C5312yes—
854C23AGL(1,ℤ/8)×C5312yes—
855C23C22×D4×C5311yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C5314yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C5312yes—
915C2×C4C2×SD16×C5312yes—
916C2×C4C22×D4×C5311yescharacteristic
917C2×C4C22×D4×C5311yescharacteristic
918C2×C4C22×D4×C5311yescharacteristic
919C2×C4C2×#41×C5311yescharacteristic
920C2×C4H(5,𝔽2)×C5311yescharacteristic
921C2×C4H(5,𝔽2)×C5311yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—24no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—41no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C53×#45014yescomplemented
963C22C2×#120×C5311yescharacteristic
964C22D42×C5311yescharacteristic
965C22C53×#54611yescharacteristic
966C22C22×SD16×C5311yescharacteristic
967C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
968C22C53×#57611yescharacteristic
969C22C53×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—42no—
973C4—42no—
974C4—41no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C5311yescharacteristic
980C4C53×#53411yescharacteristic
981C4D42×C5311yescharacteristic
982C4C53×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C53×#241011yescharacteristic
989C2C2×C53×#45011yescharacteristic
990C2C53×#301211yescharacteristic
991C2C53×#326411yescharacteristic
992C2D4×SD16×C5311yescharacteristic
993C2C53×#329511yescharacteristic
994C2C53×#331011yescharacteristic
subgroupG/H
center, socleC23×C53C22×D4
commutator, Frattini, cosocleC22×C4C24×C53
prime radicalC2×D42×C53C2
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
2. C2×C53×#465C2semidirect
3. C2×C53×#450C2semidirect
4. C2×C53×#450C2semidirect
5. C22×#102×C53C2semidirect
6. C53×#2417C2semidirect
7. C53×#2041C2semidirect
8. C53×#2034C2semidirect
9. C53×#2014C2semidirect
10. C53×#2000C2semidirect
11. C53×#1877C2semidirect
12. C53×#1874C2semidirect
13. C53×#1869C2semidirect
14. C53×#1864C2semidirect
15. C53×#1786C2semidirect
20. C22×SD16×C53C22semidirect
21. C22×SD16×C53C22semidirect
22. C23×C8×C53C22semidirect
26. C2×C22⋊Q8×C53C22semidirect
27. C2×C22⋊Q8×C53C22semidirect
35. C22×C4⋊C4×C53C22semidirect
39. C2×#106×C53C22semidirect
40. C2×#103×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
56. C53×#391C22semidirect
57. C53×#389C22semidirect
60. C53×#380C22semidirect
61. C53×#340C22semidirect
62. C53×#340C22semidirect
63. C53×#336C22semidirect
64. C53×#336C22semidirect
160. #102×C53D4semidirect
235. C2×D4×C53SD16semidirect
284. C2×C8×C53C2×D4semidirect
297. C4⋊C4×C53C2×D4semidirect
428. #24432C53direct (N × H)
465. C22×C53#450semidirect
487. C2×#465C2×C53semidirect
488. C2×#450C2×C53semidirect
489. C2×#450C2×C53semidirect
490. C22×#102C2×C53semidirect
491. #2417C2×C53semidirect
492. #2041C2×C53semidirect
493. #2034C2×C53semidirect
494. #2014C2×C53semidirect
495. #2000C2×C53semidirect
496. #1877C2×C53semidirect
497. #1874C2×C53semidirect
498. #1869C2×C53semidirect
499. #1864C2×C53semidirect
500. #1786C2×C53semidirect
517. C22×SD16C22×C53semidirect
518. C22×SD16C22×C53semidirect
519. C23×C8C22×C53semidirect
523. C2×C22⋊Q8C22×C53semidirect
524. C2×C22⋊Q8C22×C53semidirect
532. C22×C4⋊C4C22×C53semidirect
536. C2×#106C22×C53semidirect
537. C2×#103C22×C53semidirect
542. C2×#102C22×C53semidirect
543. C2×#102C22×C53semidirect
544. C2×#102C22×C53semidirect
545. C2×#102C22×C53semidirect
546. C2×#102C22×C53semidirect
547. C2×#102C22×C53semidirect
548. C2×C22⋊C8C22×C53semidirect
549. C2×C22⋊C8C22×C53semidirect
550. C2×C22⋊C8C22×C53semidirect
553. #391C22×C53semidirect
554. #389C22×C53semidirect
557. #380C22×C53semidirect
558. #340C22×C53semidirect
559. #340C22×C53semidirect
560. #336C22×C53semidirect
561. #336C22×C53semidirect
562. C53#24432direct (N × H)
658. #102D4×C53semidirect
733. C2×D4SD16×C53semidirect
782. C2×C8C2×D4×C53semidirect
795. C4⋊C4C2×D4×C53semidirect
962. C22C53×#450semidirect

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×#4652
C2×C53×#4502
C22×#102×C532
C53×#24172
C53×#20412
C53×#20342
C53×#20142
C53×#20002
C53×#18772
C53×#18742
C53×#18692
C53×#18642
C53×#17862
#2443253