Finite Group Databasebeta

← C53×#14098 #27221610

Subgroups — C53×#14098 #27221610

Order 13568.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C53C211yesmaximal, characteristic
2C2×C53×#391C211yesmaximal, characteristic, complemented
3C2×C53×#388C211yesmaximal, characteristic, complemented
4C2×C53×#386C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
6C53×#1446C211yesmaximal, characteristic, complemented
7C53×#1440C211yesmaximal, characteristic, complemented
8C53×#1439C211yesmaximal, characteristic, complemented
9C53×#1438C211yesmaximal, characteristic
10C53×#1437C211yesmaximal, characteristic, complemented
11C53×#1437C211yesmaximal, characteristic, complemented
12C53×#1437C211yesmaximal, characteristic, complemented
13C53×#1434C211yesmaximal, characteristic, complemented
14C53×C22⋊#95C211yesmaximal, characteristic, complemented
15C4×#95×C53C211yesmaximal, characteristic, complemented
16C23×Q8×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C24×C4×C53C2211yescharacteristic
19C2×#124×C53—24no—
20C2×#124×C53—24no—
21C2×#124×C53C418yescomplemented
22C22×C4⋊C4×C53C2211yescharacteristic
23C22×C22⋊C4×C53C2211yescharacteristic
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×C22⋊C4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2211yescharacteristic
33C22×C22⋊C4×C53C2211yescharacteristic
34C22×C42×C53C2211yescharacteristic
35C22×C42×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C53×#391—24no—
39C53×#388—24no—
40C53×#386—24no—
41C4×C22⋊C4×C53—24no—
42C2×#95×C53C2211yescharacteristic
43C2×#95×C53C2211yescharacteristic
44C2×#95×C53C2211yescharacteristic
45C2×#95×C53C2211yescharacteristic
46C2×#95×C53C2211yescharacteristic
47C2×#95×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C25×C53C2311yescharacteristic
59C25×C53C2311yescharacteristic
60C22×Q8×C53—22no—
61C22×Q8×C53—22no—
62C22×Q8×C53—22no—
63C22×Q8×C53—22no—
64C22×Q8×C53—41no—
65C22×Q8×C53—41no—
66C22×Q8×C53C2×C414yescomplemented
67C22×D4×C53—22no—
68C22×D4×C53—22no—
69C22×D4×C53—22no—
70C22×D4×C53—22no—
71C22×D4×C53—41no—
72C22×D4×C53—41no—
73C22×D4×C53C2×C414yes—
74C23×C4×C53—22no—
75C23×C4×C53—22no—
76C23×C4×C53—22no—
77C23×C4×C53—22no—
78C23×C4×C53—22no—
79C23×C4×C53—41no—
80C23×C4×C53—41no—
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94#124×C53—232no—
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—41no—
98C2×C22⋊C4×C53—22no—
99C2×C22⋊C4×C53—22no—
100C2×C22⋊C4×C53—22no—
101C2×C22⋊C4×C53—22no—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—22no—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53—22no—
115C2×C22⋊C4×C53—22no—
116C2×C22⋊C4×C53—22no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—41no—
120C2×C22⋊C4×C53—41no—
121C2×C22⋊C4×C53—41no—
122C2×C22⋊C4×C53—41no—
123C2×C22⋊C4×C53—41no—
124C2×C22⋊C4×C53—41no—
125C2×C22⋊C4×C53C2×C414yes—
126C2×C22⋊C4×C53C2×C414yes—
127C2×C22⋊C4×C53C2×C414yescomplemented
128C2×C22⋊C4×C53C2×C414yescomplemented
129C2×C22⋊C4×C53D414yes—
130C2×C22⋊C4×C53D414yes—
131C2×C42×C53—22no—
132C2×C42×C53—22no—
133C2×C42×C53—22no—
134C2×C42×C53—22no—
135C2×C42×C53—22no—
136C2×C42×C53—22no—
137C2×C42×C53—22no—
138C2×C42×C53—22no—
139C2×C42×C53—41no—
140C2×C42×C53—41no—
141C2×C42×C53—41no—
142C2×C42×C53C2×C414yescomplemented
143#95×C53—22no—
144#95×C53—22no—
145#95×C53—22no—
146#95×C53—22no—
147#95×C53—22no—
148#95×C53—22no—
149#95×C53—22no—
150#95×C53—22no—
151#95×C53—22no—
152#95×C53—22no—
153#95×C53—22no—
154#95×C53—22no—
155#95×C53—22no—
156#95×C53—41no—
157#95×C53—41no—
158#95×C53D414yes—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53C22×C412yes—
186C24×C53C22×C412yes—
187C24×C53C2×D412yes—
188C24×C53C2×D412yes—
189C24×C53C2411yescharacteristic
190C2×Q8×C53—28no—
191C2×Q8×C53—28no—
192C2×Q8×C53—44no—
193C2×Q8×C53—44no—
194C2×Q8×C53—44no—
195C2×Q8×C53—44no—
196C2×Q8×C53—44no—
197C2×D4×C53—28no—
198C2×D4×C53—28no—
199C2×D4×C53—44no—
200C2×D4×C53—44no—
201C2×D4×C53—44no—
202C2×D4×C53—44no—
203C2×D4×C53—44no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—28no—
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—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53—21no—
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—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—21no—
258C22×C4×C53—21no—
259C22×C4×C53—21no—
260C22×C4×C53—21no—
261C22×C4×C53—21no—
262C22×C4×C53—21no—
263C22×C4×C53—21no—
264C22×C4×C53—21no—
265C22×C4×C53—21no—
266C22×C4×C53—21no—
267C22×C4×C53—21no—
268C22×C4×C53—21no—
269C22×C4×C53—21no—
270C22×C4×C53—21no—
271C22×C4×C53—21no—
272C22×C4×C53—21no—
273C22×C4×C53—21no—
274C22×C4×C53—21no—
275C22×C4×C53—21no—
276C22×C4×C53—21no—
277C22×C4×C53—44no—
278C22×C4×C53—44no—
279C22×C4×C53—44no—
280C22×C4×C53—44no—
281C22×C4×C53—44no—
282C22×C4×C53—44no—
283C22×C4×C53C22×C412yes—
284C22×C4×C53C22×C412yes—
285C22×C4×C53C22×C412yes—
286C22×C4×C53C22×C412yes—
287C22×C4×C53C22×C412yes—
288C22×C4×C53C2×D412yes—
289C22×C4×C53C2×D412yes—
290C22×C4×C53C2×D412yes—
291C22×C4×C53C2×D412yes—
292C22×C4×C53C2×D412yes—
293C22×C4×C53C2×D412yes—
294C22×C4×C53C2×D412yes—
295C22×C4×C53#4112yes—
296C22×C4×C53#4112yes—
297C22×C4×C53#4112yes—
298C22×C4×C53#4112yes—
299C22×C4×C53#4112yes—
300C22×C4×C53#4112yes—
301C22×C4×C53#4112yes—
302C4⋊C4×C53—44no—
303C22⋊C4×C53—28no—
304C22⋊C4×C53—28no—
305C22⋊C4×C53—28no—
306C22⋊C4×C53—28no—
307C22⋊C4×C53—44no—
308C22⋊C4×C53—44no—
309C22⋊C4×C53—44no—
310C22⋊C4×C53—44no—
311C22⋊C4×C53—44no—
312C22⋊C4×C53—44no—
313C22⋊C4×C53C22⋊C4116yescomplemented
314C42×C53—28no—
315C42×C53—44no—
316C42×C53—44no—
317C42×C53—44no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
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—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53—41no—
384C23×C53—41no—
385C23×C53—41no—
386C23×C53—41no—
387C23×C53C2×C22⋊C414yes—
388C23×C53C23×C411yescharacteristic
389C23×C53C22×D411yescharacteristic
390C23×C53C22×D411yescharacteristic
391C23×C53C22×D411yescharacteristic
392C23×C53C2×#4111yescharacteristic
393C23×C53C2×#4111yescharacteristic
394C23×C53C2×#4111yescharacteristic
395C23×C53C2×#4111yescharacteristic
396C23×C53C2×#4111yescharacteristic
397C23×C53C2×#4111yescharacteristic
398C23×C53C2×#4111yescharacteristic
399C23×C53H(5,𝔽2)11yescharacteristic
400C23×C53H(5,𝔽2)11yescharacteristic
401C23×C53H(5,𝔽2)11yescharacteristic
402C23×C532−1+411yescharacteristic
403Q8×C53—416no—
404D4×C53—416no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—22no—
435C2×C4×C53—22no—
436C2×C4×C53—22no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53—22no—
447C2×C4×C53—22no—
448C2×C4×C53—22no—
449C2×C4×C53—22no—
450C2×C4×C53—416no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53—41no—
461C2×C4×C53—41no—
462C2×C4×C53—41no—
463C2×C4×C53—41no—
464C2×C4×C53—41no—
465C2×C4×C53—41no—
466C2×C4×C53—41no—
467C2×C4×C53—41no—
468C2×C4×C53—41no—
469C2×C4×C53—41no—
470C2×C4×C53—41no—
471C2×C4×C53—41no—
472C2×C4×C53—41no—
473C2×C4×C53—41no—
474C2×C4×C53—41no—
475C2×C4×C53—41no—
476C2×C4×C53—41no—
477C2×C4×C53—41no—
478C2×C4×C53—41no—
479C2×C4×C53—41no—
480C2×C4×C53—41no—
481C2×C4×C53—41no—
482C2×C4×C53—41no—
483C2×C4×C53—41no—
484C2×C4×C53—41no—
485C2×C4×C53—41no—
486C2×C4×C53—41no—
487C2×C4×C53—41no—
488C2×C4×C53—41no—
489C2×C4×C53—41no—
490C2×C4×C53—41no—
491C2×C4×C53—41no—
492C2×C4×C53—41no—
493C2×C4×C53C2×C22⋊C414yes—
494C2×C4×C53C2×C22⋊C414yes—
495C2×C4×C53C4×D414yes—
496C2×C4×C53#12414yescomplemented
497#14098C5311yesmaximal, characteristic, direct product factor, Sylow
498C22×C53—24no—
499C22×C53—24no—
500C22×C53—24no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—42no—
516C22×C53—42no—
517C22×C53—42no—
518C22×C53—42no—
519C22×C53—42no—
520C22×C53—81no—
521C22×C53—81no—
522C22×C53—81no—
523C22×C53—81no—
524C22×C53—81no—
525C22×C53—81no—
526C22×C53—81no—
527C22×C53—81no—
528C22×C53C22×C22⋊C411yescharacteristic
529C22×C53C2×C4×D411yescharacteristic
530C22×C53C4×#4111yescharacteristic
531C22×C53C4×#4111yescharacteristic
532C22×C53C4×#4111yescharacteristic
533C22×C53#51811yescharacteristic
534C22×C53#52011yescharacteristic
535C22×C53#52511yescharacteristic
536C22×C53#52511yescharacteristic
537C22×C53C2×#12411yescharacteristic
538C22×C53#52911yescharacteristic
539C22×C53#52911yescharacteristic
540C22×C53#53211yescharacteristic
541C22×C53#53211yescharacteristic
542C22×C53#53211yescharacteristic
543C22×C53#53811yescharacteristic
544C22×C53#53811yescharacteristic
545C22×C53#54211yescharacteristic
546C22×C53#54211yescharacteristic
547C22×C53D4211yescharacteristic
548C22×C53D4211yescharacteristic
549C22×C53#54611yescharacteristic
550C22×C53#54611yescharacteristic
551C22×C53#54611yescharacteristic
552C22×C53#54611yescharacteristic
553C22×C53#54611yescharacteristic
554C22×C53#54711yescharacteristic
555C22×C53#54711yescharacteristic
556C22×C53#54811yescharacteristic
557C22×C53#55111yescharacteristic
558C22×C53#55111yescharacteristic
559C22×C53#55511yescharacteristic
560C22×C53#55511yescharacteristic
561C22×C53#55611yescharacteristic
562C22×C53#55911yescharacteristic
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—24no—
566C4×C53—24no—
567C4×C53—42no—
568C4×C53—42no—
569C4×C53—42no—
570C4×C53—42no—
571C4×C53—42no—
572C4×C53—42no—
573C4×C53—42no—
574C4×C53—81no—
575C4×C53—81no—
576C22×#124C2×C5311yescharacteristic
577C2×#391C2×C5311yescharacteristic, complemented
578C2×#388C2×C5311yescharacteristic, complemented
579C2×#386C2×C5311yescharacteristic
580C2×C4×C22⋊C4C2×C5311yescharacteristic, complemented
581#1446C2×C5311yescharacteristic, complemented
582#1440C2×C5311yescharacteristic, complemented
583#1439C2×C5311yescharacteristic, complemented
584#1438C2×C5311yescharacteristic
585#1437C2×C5311yescharacteristic, complemented
586#1437C2×C5311yescharacteristic, complemented
587#1437C2×C5311yescharacteristic, complemented
588#1434C2×C5311yescharacteristic, complemented
589C22⋊#95C2×C5311yescharacteristic, complemented
590C4×#95C2×C5311yescharacteristic, complemented
591C2×C53—44no—
592C2×C53—82no—
593C2×C53#229711yescharacteristic
594C2×C53C4×#12411yescharacteristic
595C2×C53#233711yescharacteristic
596C2×C53D4×C22⋊C411yescharacteristic
597C2×C53#233911yescharacteristic
598C2×C53#236711yescharacteristic
599C2×C53#237211yescharacteristic
600C2×C53#245911yescharacteristic
601C2×C53#246111yescharacteristic
602C2×C53#247211yescharacteristic
603C2×C53#247411yescharacteristic
604C2×C53#249111yescharacteristic
605C2×C53#252111yescharacteristic
606C2×C53#255511yescharacteristic
607C2×C53#255711yescharacteristic
608C23×Q8C22×C5311yescharacteristic
609C23×D4C22×C5311yescharacteristic
610C24×C4C22×C5311yescharacteristic
611C2×#124—24no—
612C2×#124—24no—
613C2×#124C4×C5318yescomplemented
614C22×C4⋊C4C22×C5311yescharacteristic
615C22×C22⋊C4C22×C5311yescharacteristic
616C22×C22⋊C4C22×C5311yescharacteristic
617C22×C22⋊C4C22×C5311yescharacteristic
618C22×C22⋊C4C22×C5311yescharacteristic
619C22×C22⋊C4C22×C5311yescharacteristic
620C22×C22⋊C4C22×C5311yescharacteristic
621C22×C22⋊C4C22×C5311yescharacteristic
622C22×C22⋊C4C22×C5311yescharacteristic
623C22×C22⋊C4C22×C5311yescharacteristic
624C22×C22⋊C4C22×C5311yescharacteristic
625C22×C22⋊C4C22×C5311yescharacteristic
626C22×C42C22×C5311yescharacteristic
627C22×C42C22×C5311yescharacteristic
628C22×C42C22×C5311yescharacteristic
629C22×C42C22×C5311yescharacteristic
630#391—24no—
631#388—24no—
632#386—24no—
633C4×C22⋊C4—24no—
634C2×#95C22×C5311yescharacteristic
635C2×#95C22×C5311yescharacteristic
636C2×#95C22×C5311yescharacteristic
637C2×#95C22×C5311yescharacteristic
638C2×#95C22×C5311yescharacteristic
639C2×#95C22×C5311yescharacteristic
640C2×#95C22×C5311yescharacteristic
641C2×#95C22×C5311yescharacteristic
642C2×#95C22×C5311yescharacteristic
643C2×#95C22×C5311yescharacteristic
644C2×#95C22×C5311yescharacteristic
645C2×#95C22×C5311yescharacteristic
646C2×#95C22×C5311yescharacteristic
647C2×#95C22×C5311yescharacteristic
648C2×#95C22×C5311yescharacteristic
649C2×#95C22×C5311yescharacteristic
650C53#1409811yescharacteristic, direct product factor, Sylow
651C25C23×C5311yescharacteristic
652C25C23×C5311yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×C4×C5314yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×C4×C5314yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C5311yescharacteristic
675C23×C4C23×C5311yescharacteristic
676C23×C4C23×C5311yescharacteristic
677C23×C4C23×C5311yescharacteristic
678C23×C4C23×C5311yescharacteristic
679C23×C4C23×C5311yescharacteristic
680C23×C4C23×C5311yescharacteristic
681C23×C4C23×C5311yescharacteristic
682C23×C4C23×C5311yescharacteristic
683C23×C4C23×C5311yescharacteristic
684C23×C4C23×C5311yescharacteristic
685C23×C4C23×C5311yescharacteristic
686C23×C4C23×C5311yescharacteristic
687#124—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4C2×C4×C5314yes—
719C2×C22⋊C4C2×C4×C5314yes—
720C2×C22⋊C4C2×C4×C5314yescomplemented
721C2×C22⋊C4C2×C4×C5314yescomplemented
722C2×C22⋊C4D4×C5314yes—
723C2×C22⋊C4D4×C5314yes—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—41no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42C2×C4×C5314yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—41no—
750#95—41no—
751#95D4×C5314yes—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×C4×C5312yes—
779C24C22×C4×C5312yes—
780C24C2×D4×C5312yes—
781C24C2×D4×C5312yes—
782C24C24×C5311yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—28no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4C22×C4×C5312yes—
877C22×C4C22×C4×C5312yes—
878C22×C4C22×C4×C5312yes—
879C22×C4C22×C4×C5312yes—
880C22×C4C22×C4×C5312yes—
881C22×C4C2×D4×C5312yes—
882C22×C4C2×D4×C5312yes—
883C22×C4C2×D4×C5312yes—
884C22×C4C2×D4×C5312yes—
885C22×C4C2×D4×C5312yes—
886C22×C4C2×D4×C5312yes—
887C22×C4C2×D4×C5312yes—
888C22×C4#41×C5312yes—
889C22×C4#41×C5312yes—
890C22×C4#41×C5312yes—
891C22×C4#41×C5312yes—
892C22×C4#41×C5312yes—
893C22×C4#41×C5312yes—
894C22×C4#41×C5312yes—
895C4⋊C4—44no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4C22⋊C4×C53116yescomplemented
907C42—28no—
908C42—44no—
909C42—44no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊C4×C5314yes—
981C23C23×C4×C5311yescharacteristic
982C23C22×D4×C5311yescharacteristic
983C23C22×D4×C5311yescharacteristic
984C23C22×D4×C5311yescharacteristic
985C23C2×#41×C5311yescharacteristic
986C23C2×#41×C5311yescharacteristic
987C23C2×#41×C5311yescharacteristic
988C23C2×#41×C5311yescharacteristic
989C23C2×#41×C5311yescharacteristic
990C23C2×#41×C5311yescharacteristic
991C23C2×#41×C5311yescharacteristic
992C23H(5,𝔽2)×C5311yescharacteristic
993C23H(5,𝔽2)×C5311yescharacteristic
994C23H(5,𝔽2)×C5311yescharacteristic
995C232−1+4×C5311yescharacteristic
996Q8—416no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4C2×C22⋊C4×C5314yes—
1087C2×C4C2×C22⋊C4×C5314yes—
1088C2×C4C4×D4×C5314yes—
1089C2×C4#124×C5314yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊C4×C5311yescharacteristic
1121C22C2×C4×D4×C5311yescharacteristic
1122C22C4×#41×C5311yescharacteristic
1123C22C4×#41×C5311yescharacteristic
1124C22C4×#41×C5311yescharacteristic
1125C22C53×#51811yescharacteristic
1126C22C53×#52011yescharacteristic
1127C22C53×#52511yescharacteristic
1128C22C53×#52511yescharacteristic
1129C22C2×#124×C5311yescharacteristic
1130C22C53×#52911yescharacteristic
1131C22C53×#52911yescharacteristic
1132C22C53×#53211yescharacteristic
1133C22C53×#53211yescharacteristic
1134C22C53×#53211yescharacteristic
1135C22C53×#53811yescharacteristic
1136C22C53×#53811yescharacteristic
1137C22C53×#54211yescharacteristic
1138C22C53×#54211yescharacteristic
1139C22D42×C5311yescharacteristic
1140C22D42×C5311yescharacteristic
1141C22C53×#54611yescharacteristic
1142C22C53×#54611yescharacteristic
1143C22C53×#54611yescharacteristic
1144C22C53×#54611yescharacteristic
1145C22C53×#54611yescharacteristic
1146C22C53×#54711yescharacteristic
1147C22C53×#54711yescharacteristic
1148C22C53×#54811yescharacteristic
1149C22C53×#55111yescharacteristic
1150C22C53×#55111yescharacteristic
1151C22C53×#55511yescharacteristic
1152C22C53×#55511yescharacteristic
1153C22C53×#55611yescharacteristic
1154C22C53×#55911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C53×#229711yescharacteristic
1171C2C4×#124×C5311yescharacteristic
1172C2C53×#233711yescharacteristic
1173C2D4×C22⋊C4×C5311yescharacteristic
1174C2C53×#233911yescharacteristic
1175C2C53×#236711yescharacteristic
1176C2C53×#237211yescharacteristic
1177C2C53×#245911yescharacteristic
1178C2C53×#246111yescharacteristic
1179C2C53×#247211yescharacteristic
1180C2C53×#247411yescharacteristic
1181C2C53×#249111yescharacteristic
1182C2C53×#252111yescharacteristic
1183C2C53×#255511yescharacteristic
1184C2C53×#255711yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC23×D4×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×#391C2semidirect
3. C2×C53×#388C2semidirect
5. C2×C4×C22⋊C4×C53C2semidirect
6. C53×#1446C2semidirect
7. C53×#1440C2semidirect
8. C53×#1439C2semidirect
10. C53×#1437C2semidirect
11. C53×#1437C2semidirect
12. C53×#1437C2semidirect
13. C53×#1434C2semidirect
14. C53×C22⋊#95C2semidirect
15. C4×#95×C53C2semidirect
21. C2×#124×C53C4semidirect
66. C22×Q8×C53C2×C4semidirect
127. C2×C22⋊C4×C53C2×C4semidirect
128. C2×C22⋊C4×C53C2×C4semidirect
142. C2×C42×C53C2×C4semidirect
313. C22⋊C4×C53C22⋊C4semidirect
496. C2×C4×C53#124semidirect
497. #14098C53direct (N × H)
577. C2×#391C2×C53semidirect
578. C2×#388C2×C53semidirect
580. C2×C4×C22⋊C4C2×C53semidirect
581. #1446C2×C53semidirect
582. #1440C2×C53semidirect
583. #1439C2×C53semidirect
585. #1437C2×C53semidirect
586. #1437C2×C53semidirect
587. #1437C2×C53semidirect
588. #1434C2×C53semidirect
589. C22⋊#95C2×C53semidirect
590. C4×#95C2×C53semidirect
613. C2×#124C4×C53semidirect
650. C53#14098direct (N × H)
659. C22×Q8C2×C4×C53semidirect
720. C2×C22⋊C4C2×C4×C53semidirect
721. C2×C22⋊C4C2×C4×C53semidirect
735. C2×C42C2×C4×C53semidirect
906. C22⋊C4C22⋊C4×C53semidirect
1089. C2×C4#124×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C532
C2×C53×#3912
C2×C53×#3882
C2×C53×#3862
C2×C4×C22⋊C4×C532
C53×#14462
C53×#14402
C53×#14392
C53×#14382
C53×#14372
C53×#14342
C53×C22⋊#952
C4×#95×C532
#1409853