Finite Group Databasebeta

← C53×#24388 #27231900

Subgroups — C53×#24388 #27231900

Order 13568.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#525C211yesmaximal, characteristic, complemented
2C2×C53×#469C211yesmaximal, characteristic, complemented
3C2×C53×#468C211yesmaximal, characteristic, complemented
4C2×C53×#449C211yesmaximal, characteristic, complemented
5C2×C53×#407C211yesmaximal, characteristic, complemented
6C53×#2847C211yesmaximal, characteristic, complemented
7C53×#2035C211yesmaximal, characteristic, complemented
8C53×#2033C211yesmaximal, characteristic, complemented
9C53×#2000C211yesmaximal, characteristic, complemented
10C53×#1999C211yesmaximal, characteristic, complemented
11C53×#1895C211yesmaximal, characteristic, complemented
12C53×#1894C211yesmaximal, characteristic, complemented
13C53×#1875C211yesmaximal, characteristic, complemented
14C53×#1854C211yesmaximal, characteristic, complemented
15C53×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C53C2211yescharacteristic
17C24×C4×C53C2211yescharacteristic
18C22×SD16×C53C2211yescharacteristic, complemented
19C22×D8×C53C2211yescharacteristic, complemented
20C22×M16×C53C2211yescharacteristic
21C22×M16×C53C2211yescharacteristic
22C53×#525—24no—
23C53×#525—24no—
24C2×#123×C53—21no—
25C2×C22⋊Q8×C53C2211yescharacteristic
26C2×C22⋊Q8×C53C2211yescharacteristic
27C2×#121×C53C2211yescharacteristic
28C2×#121×C53C2211yescharacteristic
29C2×#121×C53C2211yescharacteristic
30C2×#121×C53C2211yescharacteristic
31C2×#121×C53C2211yescharacteristic
32C2×#120×C53—21no—
33C2×#120×C53—21no—
34C2×C4×D4×C53—21no—
35C2×C4×D4×C53—21no—
36C2×#117×C53C2211yescharacteristic
37C53×#469—24no—
38C53×#468—24no—
39C53×#449—24no—
40C2×#107×C53C2211yescharacteristic, complemented
41C2×#106×C53C2211yescharacteristic, complemented
42C2×#103×C53C2211yescharacteristic, complemented
43C2×#103×C53C2211yescharacteristic, complemented
44C2×#103×C53C2211yescharacteristic, complemented
45C2×#102×C53C2211yescharacteristic, complemented
46C2×#102×C53C2211yescharacteristic, complemented
47C2×#102×C53C2211yescharacteristic, complemented
48C2×#102×C53C2211yescharacteristic, complemented
49C2×#102×C53C2211yescharacteristic, complemented
50C53×#407—24no—
51C2×C22⋊C8×C53C2211yescharacteristic
52C2×C22⋊C8×C53C2211yescharacteristic
53C2×C22⋊C8×C53C2211yescharacteristic
54C2×C22⋊C8×C53C2211yescharacteristic
55C53×#386—21no—
56C53×#386—21no—
57C53×#386—21no—
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C53×#340C2211yescharacteristic, complemented
62C53×#340C2211yescharacteristic, complemented
63C53×#340C2211yescharacteristic, complemented
64C53×#340C2211yescharacteristic, complemented
65C25×C53D411yescharacteristic
66C2×#41×C53—22no—
67C2×#41×C53—22no—
68C2×#41×C53—22no—
69C2×#41×C53—22no—
70C2×#41×C53—41no—
71C2×#41×C53—41no—
72C22×Q8×C53C2311yescharacteristic
73C22×D4×C53—21no—
74C22×D4×C53—21no—
75C22×D4×C53—21no—
76C22×D4×C53—21no—
77C22×D4×C53—21no—
78C22×D4×C53—21no—
79C22×D4×C53C2311yescharacteristic
80C22×D4×C53C2311yescharacteristic
81C23×C4×C53—21no—
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53—22no—
85C23×C4×C53—22no—
86C23×C4×C53—41no—
87C23×C4×C53—41no—
88C23×C4×C53D411yescharacteristic
89C23×C4×C53D411yescharacteristic
90C23×C4×C53D411yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C2×SD16×C53—22no—
95C2×SD16×C53—22no—
96C2×SD16×C53—41no—
97C2×D8×C53—22no—
98C2×D8×C53—22no—
99C2×D8×C53—41no—
100C2×M16×C53—22no—
101C2×M16×C53—22no—
102C2×M16×C53—22no—
103C2×M16×C53—22no—
104C2×M16×C53—41no—
105C2×M16×C53—41no—
106C22×C8×C53C2311yescharacteristic
107C22×C8×C53C2311yescharacteristic
108C22×C8×C53C2311yescharacteristic
109C22×C8×C53C2311yescharacteristic
110#123×C53—28no—
111C22⋊Q8×C53—22no—
112C22⋊Q8×C53—22no—
113C22⋊Q8×C53—22no—
114C22⋊Q8×C53D414yescomplemented
115#121×C53—22no—
116#121×C53—22no—
117#121×C53—22no—
118#121×C53—22no—
119#121×C53—22no—
120#121×C53—22no—
121#121×C53—22no—
122#121×C53—41no—
123#121×C53—41no—
124#121×C53D414yescomplemented
125#120×C53—28no—
126#120×C53—44no—
127C4×D4×C53—28no—
128C4×D4×C53—28no—
129#117×C53—22no—
130#117×C53—22no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C22⋊C4×C53—21no—
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×C53—21no—
149C2×C42×C53—21no—
150#107×C53—22no—
151#106×C53—22no—
152#103×C53—22no—
153#103×C53—22no—
154#103×C53—41no—
155#102×C53—22no—
156#102×C53—22no—
157#102×C53—22no—
158#102×C53—22no—
159#102×C53—41no—
160C22⋊C8×C53—22no—
161C22⋊C8×C53—22no—
162C22⋊C8×C53—22no—
163C22⋊C8×C53D414yescomplemented
164#95×C53—21no—
165#95×C53—21no—
166#95×C53—21no—
167C24×C53—22no—
168C24×C53—22no—
169C24×C53—22no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—41no—
173C24×C53—41no—
174C24×C53—41no—
175C24×C53—41no—
176C24×C53C2×D411yescharacteristic
177C24×C53C2×D411yescharacteristic
178C24×C53C2×D411yescharacteristic
179#41×C53—44no—
180#41×C53—44no—
181#41×C53—44no—
182#41×C53—44no—
183C2×Q8×C53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53C2×D412yes—
189C2×D4×C53—24no—
190C2×D4×C53—24no—
191C2×D4×C53—24no—
192C2×D4×C53—21no—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—21no—
196C2×D4×C53—21no—
197C2×D4×C53—21no—
198C2×D4×C53—21no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—42no—
204C2×D4×C53—42no—
205C2×D4×C53—42no—
206C2×D4×C53—42no—
207C2×D4×C53—42no—
208C2×D4×C53—42no—
209C2×D4×C53—42no—
210C2×D4×C53—42no—
211C2×D4×C53—42no—
212C2×D4×C53—42no—
213C2×D4×C53—42no—
214C2×D4×C53—42no—
215C2×D4×C53—42no—
216C2×D4×C53—42no—
217C2×D4×C53—42no—
218C2×D4×C53C2×D412yes—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—24no—
228C22×C4×C53—22no—
229C22×C4×C53—22no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—22no—
234C22×C4×C53—22no—
235C22×C4×C53—22no—
236C22×C4×C53—22no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—21no—
246C22×C4×C53—41no—
247C22×C4×C53—41no—
248C22×C4×C53—41no—
249C22×C4×C53—44no—
250C22×C4×C53—44no—
251C22×C4×C53—44no—
252C22×C4×C53—44no—
253C22×C4×C53—42no—
254C22×C4×C53—42no—
255C22×C4×C53C2×D411yescharacteristic
256C22×C4×C53C2×D411yescharacteristic
257C22×C4×C53C2×D412yes—
258C22×C4×C53C2×D412yes—
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D412yes—
261C22×C4×C53#4112yes—
262C22×C4×C53C2411yescharacteristic
263SD16×C53—44no—
264D8×C53—44no—
265M16×C53—44no—
266M16×C53—44no—
267C2×C8×C53—21no—
268C2×C8×C53—21no—
269C2×C8×C53—21no—
270C2×C8×C53—21no—
271C2×C8×C53—21no—
272C2×C8×C53—21no—
273C2×C8×C53—21no—
274C2×C8×C53—21no—
275C2×C8×C53—21no—
276C2×C8×C53—21no—
277C2×C8×C53C2×D412yes—
278C2×C8×C53C2×D412yes—
279C4⋊C4×C53—24no—
280C4⋊C4×C53—24no—
281C4⋊C4×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53—21no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53—21no—
288C4⋊C4×C53—21no—
289C4⋊C4×C53C2×D412yes—
290C4⋊C4×C53C2×D412yes—
291C22⋊C4×C53—24no—
292C22⋊C4×C53—24no—
293C22⋊C4×C53—24no—
294C22⋊C4×C53—24no—
295C22⋊C4×C53—24no—
296C22⋊C4×C53—42no—
297C22⋊C4×C53—42no—
298C22⋊C4×C53—42no—
299C22⋊C4×C53—42no—
300C22⋊C4×C53—42no—
301C22⋊C4×C53—42no—
302C42×C53—24no—
303C23×C53—21no—
304C23×C53—21no—
305C23×C53—21no—
306C23×C53—21no—
307C23×C53—21no—
308C23×C53—21no—
309C23×C53—21no—
310C23×C53—21no—
311C23×C53—21no—
312C23×C53—21no—
313C23×C53—21no—
314C23×C53—21no—
315C23×C53—21no—
316C23×C53—21no—
317C23×C53—21no—
318C23×C53—21no—
319C23×C53—21no—
320C23×C53—21no—
321C23×C53—22no—
322C23×C53—44no—
323C23×C53—44no—
324C23×C53—44no—
325C23×C53—44no—
326C23×C53—44no—
327C23×C53—44no—
328C23×C53—44no—
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#12012yes—
343C23×C53#12112yes—
344C23×C53AGL(1,ℤ/8)12yes—
345C23×C53C22×D411yescharacteristic
346Q8×C53—22no—
347Q8×C53—22no—
348Q8×C53—41no—
349Q8×C53—41no—
350D4×C53—22no—
351D4×C53—22no—
352D4×C53—48no—
353D4×C53—48no—
354D4×C53—48no—
355D4×C53—41no—
356D4×C53—41no—
357D4×C53—41no—
358D4×C53—41no—
359D4×C53—41no—
360D4×C53—41no—
361D4×C53—84no—
362D4×C53—84no—
363D4×C53—84no—
364C2×C4×C53—21no—
365C2×C4×C53—21no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
368C2×C4×C53—22no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—21no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—21no—
381C2×C4×C53—21no—
382C2×C4×C53—44no—
383C2×C4×C53—44no—
384C2×C4×C53—44no—
385C2×C4×C53—48no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—41no—
393C2×C4×C53—41no—
394C2×C4×C53—41no—
395C2×C4×C53—41no—
396C2×C4×C53—41no—
397C2×C4×C53—41no—
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#12012yes—
406C2×C4×C53#12112yes—
407C2×C4×C53C22×D411yescharacteristic
408C2×C4×C53C22×D411yescharacteristic
409C2×C4×C53C22×D411yescharacteristic
410C2×C4×C53C2×#4111yescharacteristic
411C2×C4×C53H(5,𝔽2)11yescharacteristic
412C2×C4×C53H(5,𝔽2)11yescharacteristic
413C8×C53—22no—
414C8×C53—22no—
415C8×C53—41no—
416C8×C53—41no—
417#24388C5311yesmaximal, characteristic, direct product factor, Sylow
418C22×C53—22no—
419C22×C53—22no—
420C22×C53—22no—
421C22×C53—22no—
422C22×C53—22no—
423C22×C53—22no—
424C22×C53—22no—
425C22×C53—22no—
426C22×C53—22no—
427C22×C53—416no—
428C22×C53—41no—
429C22×C53—41no—
430C22×C53—41no—
431C22×C53—41no—
432C22×C53—41no—
433C22×C53—41no—
434C22×C53—41no—
435C22×C53—41no—
436C22×C53—41no—
437C22×C53—41no—
438C22×C53—41no—
439C22×C53—41no—
440C22×C53—42no—
441C22×C53—42no—
442C22×C53—42no—
443C22×C53—81no—
444C22×C53—81no—
445C22×C53—81no—
446C22×C53—81no—
447C22×C53—81no—
448C22×C53—81no—
449C22×C53—81no—
450C22×C53—81no—
451C22×C53—81no—
452C22×C53—81no—
453C22×C53—81no—
454C22×C53C2×#12011yescharacteristic
455C22×C53C2×#12111yescharacteristic
456C22×C53#53411yescharacteristic
457C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
458C22×C53#57511yescharacteristic
459C22×C53#57511yescharacteristic
460C22×C53#57511yescharacteristic
461C4×C53—22no—
462C4×C53—22no—
463C4×C53—41no—
464C4×C53—42no—
465C4×C53—42no—
466C4×C53—42no—
467C4×C53—81no—
468C4×C53—81no—
469C4×C53—81no—
470C4×C53D4211yescharacteristic
471C4×C53D4211yescharacteristic
472C4×C53#54611yescharacteristic
473C4×C53#54611yescharacteristic
474C2×#525C2×C5311yescharacteristic, complemented
475C2×#469C2×C5311yescharacteristic, complemented
476C2×#468C2×C5311yescharacteristic, complemented
477C2×#449C2×C5311yescharacteristic, complemented
478C2×#407C2×C5311yescharacteristic, complemented
479#2847C2×C5311yescharacteristic, complemented
480#2035C2×C5311yescharacteristic, complemented
481#2033C2×C5311yescharacteristic, complemented
482#2000C2×C5311yescharacteristic, complemented
483#1999C2×C5311yescharacteristic, complemented
484#1895C2×C5311yescharacteristic, complemented
485#1894C2×C5311yescharacteristic, complemented
486#1875C2×C5311yescharacteristic, complemented
487#1854C2×C5311yescharacteristic, complemented
488#1788C2×C5311yescharacteristic, complemented
489C2×C53—42no—
490C2×C53—42no—
491C2×C53—42no—
492C2×C53—82no—
493C2×C53—161no—
494C2×C53#241011yescharacteristic
495C2×C53#300511yescharacteristic
496C2×C53#300611yescharacteristic
497C2×C53#305411yescharacteristic
498C2×C53#305511yescharacteristic
499C2×C53#319411yescharacteristic
500C2×C53#319711yescharacteristic
501C22×#41C22×C5311yescharacteristic
502C24×C4C22×C5311yescharacteristic
503C22×SD16C22×C5311yescharacteristic, complemented
504C22×D8C22×C5311yescharacteristic, complemented
505C22×M16C22×C5311yescharacteristic
506C22×M16C22×C5311yescharacteristic
507#525—24no—
508#525—24no—
509C2×#123—21no—
510C2×C22⋊Q8C22×C5311yescharacteristic
511C2×C22⋊Q8C22×C5311yescharacteristic
512C2×#121C22×C5311yescharacteristic
513C2×#121C22×C5311yescharacteristic
514C2×#121C22×C5311yescharacteristic
515C2×#121C22×C5311yescharacteristic
516C2×#121C22×C5311yescharacteristic
517C2×#120—21no—
518C2×#120—21no—
519C2×C4×D4—21no—
520C2×C4×D4—21no—
521C2×#117C22×C5311yescharacteristic
522#469—24no—
523#468—24no—
524#449—24no—
525C2×#107C22×C5311yescharacteristic, complemented
526C2×#106C22×C5311yescharacteristic, complemented
527C2×#103C22×C5311yescharacteristic, complemented
528C2×#103C22×C5311yescharacteristic, complemented
529C2×#103C22×C5311yescharacteristic, complemented
530C2×#102C22×C5311yescharacteristic, complemented
531C2×#102C22×C5311yescharacteristic, complemented
532C2×#102C22×C5311yescharacteristic, complemented
533C2×#102C22×C5311yescharacteristic, complemented
534C2×#102C22×C5311yescharacteristic, complemented
535#407—24no—
536C2×C22⋊C8C22×C5311yescharacteristic
537C2×C22⋊C8C22×C5311yescharacteristic
538C2×C22⋊C8C22×C5311yescharacteristic
539C2×C22⋊C8C22×C5311yescharacteristic
540#386—21no—
541#386—21no—
542#386—21no—
543#380C22×C5311yescharacteristic
544#380C22×C5311yescharacteristic
545#380C22×C5311yescharacteristic
546#340C22×C5311yescharacteristic, complemented
547#340C22×C5311yescharacteristic, complemented
548#340C22×C5311yescharacteristic, complemented
549#340C22×C5311yescharacteristic, complemented
550C53#2438811yescharacteristic, direct product factor, Sylow
551C25D4×C5311yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C5311yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C5311yescharacteristic
566C22×D4C23×C5311yescharacteristic
567C23×C4—21no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C5311yescharacteristic
575C23×C4D4×C5311yescharacteristic
576C23×C4D4×C5311yescharacteristic
577C23×C4C23×C5311yescharacteristic
578C23×C4C23×C5311yescharacteristic
579C23×C4C23×C5311yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—22no—
590C2×M16—41no—
591C2×M16—41no—
592C22×C8C23×C5311yescharacteristic
593C22×C8C23×C5311yescharacteristic
594C22×C8C23×C5311yescharacteristic
595C22×C8C23×C5311yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C5314yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C5314yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C5311yescharacteristic
620C2×C4⋊C4C23×C5311yescharacteristic
621C2×C4⋊C4C23×C5311yescharacteristic
622C2×C4⋊C4C23×C5311yescharacteristic
623C2×C4⋊C4C23×C5311yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C5314yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C5311yescharacteristic
663C24C2×D4×C5311yescharacteristic
664C24C2×D4×C5311yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C5312yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C5312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C5311yescharacteristic
742C22×C4C2×D4×C5311yescharacteristic
743C22×C4C2×D4×C5312yes—
744C22×C4C2×D4×C5312yes—
745C22×C4C2×D4×C5311yescharacteristic
746C22×C4C2×D4×C5312yes—
747C22×C4#41×C5312yes—
748C22×C4C24×C5311yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C5312yes—
764C2×C8C2×D4×C5312yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C5312yes—
776C4⋊C4C2×D4×C5312yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23#120×C5312yes—
829C23#121×C5312yes—
830C23AGL(1,ℤ/8)×C5312yes—
831C23C22×D4×C5311yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4#120×C5312yes—
892C2×C4#121×C5312yes—
893C2×C4C22×D4×C5311yescharacteristic
894C2×C4C22×D4×C5311yescharacteristic
895C2×C4C22×D4×C5311yescharacteristic
896C2×C4C2×#41×C5311yescharacteristic
897C2×C4H(5,𝔽2)×C5311yescharacteristic
898C2×C4H(5,𝔽2)×C5311yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×#120×C5311yescharacteristic
940C22C2×#121×C5311yescharacteristic
941C22C53×#53411yescharacteristic
942C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
943C22C53×#57511yescharacteristic
944C22C53×#57511yescharacteristic
945C22C53×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—42no—
949C4—42no—
950C4—41no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C5311yescharacteristic
956C4D42×C5311yescharacteristic
957C4C53×#54611yescharacteristic
958C4C53×#54611yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C53×#241011yescharacteristic
965C2C53×#300511yescharacteristic
966C2C53×#300611yescharacteristic
967C2C53×#305411yescharacteristic
968C2C53×#305511yescharacteristic
969C2C53×#319411yescharacteristic
970C2C53×#319711yescharacteristic
subgroupG/H
center, socleC23×C53C22×D4
commutator, Frattini, cosocleC22×C4C24×C53
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C24×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#525C2semidirect
2. C2×C53×#469C2semidirect
3. C2×C53×#468C2semidirect
4. C2×C53×#449C2semidirect
5. C2×C53×#407C2semidirect
6. C53×#2847C2semidirect
7. C53×#2035C2semidirect
8. C53×#2033C2semidirect
9. C53×#2000C2semidirect
10. C53×#1999C2semidirect
11. C53×#1895C2semidirect
12. C53×#1894C2semidirect
13. C53×#1875C2semidirect
14. C53×#1854C2semidirect
15. C53×#1788C2semidirect
18. C22×SD16×C53C22semidirect
19. C22×D8×C53C22semidirect
40. C2×#107×C53C22semidirect
41. C2×#106×C53C22semidirect
42. C2×#103×C53C22semidirect
43. C2×#103×C53C22semidirect
44. C2×#103×C53C22semidirect
45. C2×#102×C53C22semidirect
46. C2×#102×C53C22semidirect
47. C2×#102×C53C22semidirect
48. C2×#102×C53C22semidirect
49. C2×#102×C53C22semidirect
61. C53×#340C22semidirect
62. C53×#340C22semidirect
63. C53×#340C22semidirect
64. C53×#340C22semidirect
114. C22⋊Q8×C53D4semidirect
124. #121×C53D4semidirect
163. C22⋊C8×C53D4semidirect
417. #24388C53direct (N × H)
474. C2×#525C2×C53semidirect
475. C2×#469C2×C53semidirect
476. C2×#468C2×C53semidirect
477. C2×#449C2×C53semidirect
478. C2×#407C2×C53semidirect
479. #2847C2×C53semidirect
480. #2035C2×C53semidirect
481. #2033C2×C53semidirect
482. #2000C2×C53semidirect
483. #1999C2×C53semidirect
484. #1895C2×C53semidirect
485. #1894C2×C53semidirect
486. #1875C2×C53semidirect
487. #1854C2×C53semidirect
488. #1788C2×C53semidirect
503. C22×SD16C22×C53semidirect
504. C22×D8C22×C53semidirect
525. C2×#107C22×C53semidirect
526. C2×#106C22×C53semidirect
527. C2×#103C22×C53semidirect
528. C2×#103C22×C53semidirect
529. C2×#103C22×C53semidirect
530. C2×#102C22×C53semidirect
531. C2×#102C22×C53semidirect
532. C2×#102C22×C53semidirect
533. C2×#102C22×C53semidirect
534. C2×#102C22×C53semidirect
546. #340C22×C53semidirect
547. #340C22×C53semidirect
548. #340C22×C53semidirect
549. #340C22×C53semidirect
550. C53#24388direct (N × H)
600. C22⋊Q8D4×C53semidirect
610. #121D4×C53semidirect
649. C22⋊C8D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#5252
C2×C53×#4692
C2×C53×#4682
C2×C53×#4492
C2×C53×#4072
C53×#28472
C53×#20352
C53×#20332
C53×#20002
C53×#19992
C53×#18952
C53×#18942
C53×#18752
C53×#18542
C53×#17882
#2438853