Finite Group Databasebeta

← C53×#15475 #27222987

Subgroups — C53×#15475 #27222987

Order 13568.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#395C211yesmaximal, characteristic, complemented
2C2×C53×#393C211yesmaximal, characteristic
3C2×C53×#385C211yesmaximal, characteristic
4C2×C53×#380C211yesmaximal, characteristic
5C53×#1446C211yesmaximal, characteristic, complemented
6C53×#1442C211yesmaximal, characteristic, complemented
7C53×#1442C211yesmaximal, characteristic, complemented
8C53×#1441C211yesmaximal, characteristic, complemented
9C53×#1441C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic
11C53×#1439C211yesmaximal, characteristic
12C53×#1437C211yesmaximal, characteristic
13C53×#1436C211yesmaximal, characteristic, complemented
14C53×C4⋊#95C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C53C2211yescharacteristic
17C24×C4×C53C2211yescharacteristic
18C22×C4⋊C4×C53C2211yescharacteristic
19C22×C4⋊C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C4⋊C4×C53C2211yescharacteristic
22C22×C4⋊C4×C53C2211yescharacteristic
23C22×C4⋊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×C42×C53C2211yescharacteristic
31C53×#395—24no—
32C53×#393—24no—
33C53×#385—24no—
34C53×#380—24no—
35C2×#95×C53C2211yescharacteristic
36C2×#95×C53C2211yescharacteristic
37C2×#95×C53C2211yescharacteristic
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2211yescharacteristic
41C2×#95×C53C2211yescharacteristic
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
55C25×C53C2311yescharacteristic
56C22×Q8×C53—22no—
57C22×Q8×C53—22no—
58C22×Q8×C53—22no—
59C22×Q8×C53—41no—
60C22×Q8×C53—41no—
61C22×Q8×C53—41no—
62C22×Q8×C53—41no—
63C23×C4×C53—22no—
64C23×C4×C53—22no—
65C23×C4×C53—22no—
66C23×C4×C53—22no—
67C23×C4×C53—22no—
68C23×C4×C53—41no—
69C23×C4×C53—41no—
70C23×C4×C53C2311yescharacteristic
71C23×C4×C53C2311yescharacteristic
72C23×C4×C53C2311yescharacteristic
73C23×C4×C53C2311yescharacteristic
74C23×C4×C53C2311yescharacteristic
75C23×C4×C53C2311yescharacteristic
76C23×C4×C53C2311yescharacteristic
77C23×C4×C53C2311yescharacteristic
78C23×C4×C53C2311yescharacteristic
79C23×C4×C53C2311yescharacteristic
80C23×C4×C53C2311yescharacteristic
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C2×C4⋊C4×C53—22no—
85C2×C4⋊C4×C53—22no—
86C2×C4⋊C4×C53—22no—
87C2×C4⋊C4×C53—22no—
88C2×C4⋊C4×C53—22no—
89C2×C4⋊C4×C53—22no—
90C2×C4⋊C4×C53—22no—
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—41no—
97C2×C4⋊C4×C53—41no—
98C2×C4⋊C4×C53—41no—
99C2×C4⋊C4×C53—41no—
100C2×C4⋊C4×C53—41no—
101C2×C4⋊C4×C53—41no—
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—41no—
110C2×C22⋊C4×C53—41no—
111C2×C22⋊C4×C53—41no—
112C2×C22⋊C4×C53—41no—
113C2×C22⋊C4×C53—41no—
114C2×C22⋊C4×C53—41no—
115C2×C22⋊C4×C53—41no—
116C2×C22⋊C4×C53—41no—
117C2×C22⋊C4×C53D414yes—
118C2×C22⋊C4×C53Q814yescomplemented
119C2×C22⋊C4×C53Q814yescomplemented
120C2×C42×C53—22no—
121C2×C42×C53—41no—
122C2×C42×C53—41no—
123#95×C53—22no—
124#95×C53—22no—
125#95×C53—22no—
126#95×C53—22no—
127#95×C53—22no—
128#95×C53—22no—
129#95×C53—22no—
130#95×C53—22no—
131#95×C53—22no—
132#95×C53—22no—
133#95×C53—22no—
134#95×C53—41no—
135#95×C53—41no—
136#95×C53—41no—
137#95×C53—41no—
138#95×C53—41no—
139#95×C53—41no—
140#95×C53—41no—
141#95×C53—41no—
142#95×C53D414yes—
143C24×C53—21no—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53C2×D412yes—
156C24×C53C2×Q812yes—
157C24×C53C2×Q812yes—
158C24×C53C2411yescharacteristic
159C2×Q8×C53—44no—
160C2×Q8×C53—44no—
161C2×Q8×C53—44no—
162C2×Q8×C53—44no—
163C2×Q8×C53—44no—
164C2×Q8×C53—44no—
165C2×Q8×C53—44no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—28no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
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—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—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—44no—
252C22×C4×C53—44no—
253C22×C4×C53—44no—
254C22×C4×C53—44no—
255C22×C4×C53—44no—
256C22×C4×C53—44no—
257C22×C4×C53C2×D412yes—
258C22×C4×C53C2×D412yes—
259C22×C4×C53C2×D412yes—
260C22×C4×C53C2×D412yes—
261C22×C4×C53C2×D412yes—
262C22×C4×C53C2×Q812yes—
263C22×C4×C53C2×Q812yes—
264C22×C4×C53C2×Q812yes—
265C22×C4×C53C2×Q812yes—
266C22×C4×C53#4112yes—
267C22×C4×C53#4112yes—
268C22×C4×C53#4112yes—
269C22×C4×C53#4112yes—
270C22×C4×C53#4112yes—
271C4⋊C4×C53—44no—
272C4⋊C4×C53—44no—
273C4⋊C4×C53—44no—
274C4⋊C4×C53—44no—
275C4⋊C4×C53—44no—
276C4⋊C4×C53—44no—
277C22⋊C4×C53—28no—
278C22⋊C4×C53—44no—
279C22⋊C4×C53—44no—
280C22⋊C4×C53—44no—
281C22⋊C4×C53—44no—
282C22⋊C4×C53—44no—
283C42×C53—44no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53C4⋊Q814yes—
319C23×C53C22×D411yescharacteristic
320C23×C53C22×D411yescharacteristic
321C23×C53C22×Q811yescharacteristic
322C23×C53C22×Q811yescharacteristic
323C23×C53C2×#4111yescharacteristic
324C23×C53C2×#4111yescharacteristic
325C23×C53C2×#4111yescharacteristic
326C23×C53C2×#4111yescharacteristic
327C23×C53C2×#4111yescharacteristic
328C23×C53H(5,𝔽2)11yescharacteristic
329C23×C53H(5,𝔽2)11yescharacteristic
330C23×C53H(5,𝔽2)11yescharacteristic
331C23×C53H(5,𝔽2)11yescharacteristic
332C23×C53H(5,𝔽2)11yescharacteristic
333C23×C532−1+411yescharacteristic
334Q8×C53—416no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—416no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
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—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—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—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53C22⋊Q814yes—
433C2×C4×C53#12414yes—
434#15475C5311yesmaximal, characteristic, direct product factor, Sylow
435C22×C53—24no—
436C22×C53—24no—
437C22×C53—24no—
438C22×C53—42no—
439C22×C53—42no—
440C22×C53—42no—
441C22×C53—42no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—42no—
448C22×C53—42no—
449C22×C53—42no—
450C22×C53C2×C22⋊Q811yescharacteristic
451C22×C53#52511yescharacteristic
452C22×C53C2×#12411yescharacteristic
453C22×C53#52911yescharacteristic
454C22×C53C2×C4⋊Q811yescharacteristic
455C22×C53#53311yescharacteristic
456C22×C53#53411yescharacteristic
457C22×C53#53511yescharacteristic
458C22×C53#53811yescharacteristic
459C22×C53#53811yescharacteristic
460C22×C53#53811yescharacteristic
461C22×C53#54211yescharacteristic
462C22×C53#54211yescharacteristic
463C22×C53#54311yescharacteristic
464C22×C53#54411yescharacteristic
465C22×C53D4211yescharacteristic
466C22×C53#54611yescharacteristic
467C22×C53#54611yescharacteristic
468C22×C53#54611yescharacteristic
469C22×C53#54611yescharacteristic
470C22×C53#54711yescharacteristic
471C22×C53D4×Q811yescharacteristic
472C22×C53#55111yescharacteristic
473C22×C53#55411yescharacteristic
474C22×C53#55411yescharacteristic
475C22×C53#55411yescharacteristic
476C22×C53#55411yescharacteristic
477C22×C53#55411yescharacteristic
478C22×C53#55411yescharacteristic
479C22×C53#55411yescharacteristic
480C22×C53#55511yescharacteristic
481C22×C53#55511yescharacteristic
482C22×C53#55611yescharacteristic
483C22×C53#56011yescharacteristic
484C22×C53#56211yescharacteristic
485C4×C53—24no—
486C4×C53—24no—
487C4×C53—42no—
488C4×C53—42no—
489C4×C53—42no—
490C4×C53—42no—
491C4×C53—42no—
492C4×C53—42no—
493C4×C53—42no—
494C4×C53—42no—
495C4×C53—81no—
496C4×C53—81no—
497C4×C53—81no—
498C4×C53—81no—
499C2×#395C2×C5311yescharacteristic, complemented
500C2×#393C2×C5311yescharacteristic
501C2×#385C2×C5311yescharacteristic
502C2×#380C2×C5311yescharacteristic
503#1446C2×C5311yescharacteristic, complemented
504#1442C2×C5311yescharacteristic, complemented
505#1442C2×C5311yescharacteristic, complemented
506#1441C2×C5311yescharacteristic, complemented
507#1441C2×C5311yescharacteristic, complemented
508#1439C2×C5311yescharacteristic
509#1439C2×C5311yescharacteristic
510#1437C2×C5311yescharacteristic
511#1436C2×C5311yescharacteristic, complemented
512C4⋊#95C2×C5311yescharacteristic, complemented
513C22⋊#95C2×C5311yescharacteristic
514C2×C53—44no—
515C2×C53#244011yescharacteristic
516C2×C53#245011yescharacteristic
517C2×C53#247211yescharacteristic
518C2×C53#247411yescharacteristic
519C2×C53#249211yescharacteristic
520C2×C53#254911yescharacteristic
521C2×C53#256311yescharacteristic
522C2×C53#257411yescharacteristic
523C2×C53#258311yescharacteristic
524C2×C53#267811yescharacteristic
525C2×C53#268611yescharacteristic
526C2×C53#269211yescharacteristic
527C2×C53#274211yescharacteristic
528C2×C53#278411yescharacteristic
529C2×C53#278811yescharacteristic
530C23×Q8C22×C5311yescharacteristic
531C24×C4C22×C5311yescharacteristic
532C22×C4⋊C4C22×C5311yescharacteristic
533C22×C4⋊C4C22×C5311yescharacteristic
534C22×C4⋊C4C22×C5311yescharacteristic
535C22×C4⋊C4C22×C5311yescharacteristic
536C22×C4⋊C4C22×C5311yescharacteristic
537C22×C4⋊C4C22×C5311yescharacteristic
538C22×C22⋊C4C22×C5311yescharacteristic
539C22×C22⋊C4C22×C5311yescharacteristic
540C22×C22⋊C4C22×C5311yescharacteristic
541C22×C22⋊C4C22×C5311yescharacteristic
542C22×C22⋊C4C22×C5311yescharacteristic
543C22×C22⋊C4C22×C5311yescharacteristic
544C22×C42C22×C5311yescharacteristic
545#395—24no—
546#393—24no—
547#385—24no—
548#380—24no—
549C2×#95C22×C5311yescharacteristic
550C2×#95C22×C5311yescharacteristic
551C2×#95C22×C5311yescharacteristic
552C2×#95C22×C5311yescharacteristic
553C2×#95C22×C5311yescharacteristic
554C2×#95C22×C5311yescharacteristic
555C2×#95C22×C5311yescharacteristic
556C2×#95C22×C5311yescharacteristic
557C2×#95C22×C5311yescharacteristic
558C2×#95C22×C5311yescharacteristic
559C2×#95C22×C5311yescharacteristic
560C2×#95C22×C5311yescharacteristic
561C2×#95C22×C5311yescharacteristic
562C2×#95C22×C5311yescharacteristic
563C2×#95C22×C5311yescharacteristic
564C2×#95C22×C5311yescharacteristic
565C2×#95C22×C5311yescharacteristic
566C2×#95C22×C5311yescharacteristic
567C2×#95C22×C5311yescharacteristic
568C2×#95C22×C5311yescharacteristic
569C53#1547511yescharacteristic, direct product factor, Sylow
570C25C23×C5311yescharacteristic
571C22×Q8—22no—
572C22×Q8—22no—
573C22×Q8—22no—
574C22×Q8—41no—
575C22×Q8—41no—
576C22×Q8—41no—
577C22×Q8—41no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C5311yescharacteristic
586C23×C4C23×C5311yescharacteristic
587C23×C4C23×C5311yescharacteristic
588C23×C4C23×C5311yescharacteristic
589C23×C4C23×C5311yescharacteristic
590C23×C4C23×C5311yescharacteristic
591C23×C4C23×C5311yescharacteristic
592C23×C4C23×C5311yescharacteristic
593C23×C4C23×C5311yescharacteristic
594C23×C4C23×C5311yescharacteristic
595C23×C4C23×C5311yescharacteristic
596C23×C4C23×C5311yescharacteristic
597C23×C4C23×C5311yescharacteristic
598C23×C4C23×C5311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—41no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4—41no—
632C2×C22⋊C4D4×C5314yes—
633C2×C22⋊C4Q8×C5314yescomplemented
634C2×C22⋊C4Q8×C5314yescomplemented
635C2×C42—22no—
636C2×C42—41no—
637C2×C42—41no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95—41no—
654#95—41no—
655#95—41no—
656#95—41no—
657#95D4×C5314yes—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24C2×D4×C5312yes—
671C24C2×Q8×C5312yes—
672C24C2×Q8×C5312yes—
673C24C24×C5311yescharacteristic
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—28no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
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—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
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—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C2×D4×C5312yes—
773C22×C4C2×D4×C5312yes—
774C22×C4C2×D4×C5312yes—
775C22×C4C2×D4×C5312yes—
776C22×C4C2×D4×C5312yes—
777C22×C4C2×Q8×C5312yes—
778C22×C4C2×Q8×C5312yes—
779C22×C4C2×Q8×C5312yes—
780C22×C4C2×Q8×C5312yes—
781C22×C4#41×C5312yes—
782C22×C4#41×C5312yes—
783C22×C4#41×C5312yes—
784C22×C4#41×C5312yes—
785C22×C4#41×C5312yes—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C42—44no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23C4⋊Q8×C5314yes—
834C23C22×D4×C5311yescharacteristic
835C23C22×D4×C5311yescharacteristic
836C23C22×Q8×C5311yescharacteristic
837C23C22×Q8×C5311yescharacteristic
838C23C2×#41×C5311yescharacteristic
839C23C2×#41×C5311yescharacteristic
840C23C2×#41×C5311yescharacteristic
841C23C2×#41×C5311yescharacteristic
842C23C2×#41×C5311yescharacteristic
843C23H(5,𝔽2)×C5311yescharacteristic
844C23H(5,𝔽2)×C5311yescharacteristic
845C23H(5,𝔽2)×C5311yescharacteristic
846C23H(5,𝔽2)×C5311yescharacteristic
847C23H(5,𝔽2)×C5311yescharacteristic
848C232−1+4×C5311yescharacteristic
849Q8—416no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
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—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—416no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
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—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
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—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4C22⋊Q8×C5314yes—
948C2×C4#124×C5314yes—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22C2×C22⋊Q8×C5311yescharacteristic
965C22C53×#52511yescharacteristic
966C22C2×#124×C5311yescharacteristic
967C22C53×#52911yescharacteristic
968C22C2×C4⋊Q8×C5311yescharacteristic
969C22C53×#53311yescharacteristic
970C22C53×#53411yescharacteristic
971C22C53×#53511yescharacteristic
972C22C53×#53811yescharacteristic
973C22C53×#53811yescharacteristic
974C22C53×#53811yescharacteristic
975C22C53×#54211yescharacteristic
976C22C53×#54211yescharacteristic
977C22C53×#54311yescharacteristic
978C22C53×#54411yescharacteristic
979C22D42×C5311yescharacteristic
980C22C53×#54611yescharacteristic
981C22C53×#54611yescharacteristic
982C22C53×#54611yescharacteristic
983C22C53×#54611yescharacteristic
984C22C53×#54711yescharacteristic
985C22D4×Q8×C5311yescharacteristic
986C22C53×#55111yescharacteristic
987C22C53×#55411yescharacteristic
988C22C53×#55411yescharacteristic
989C22C53×#55411yescharacteristic
990C22C53×#55411yescharacteristic
991C22C53×#55411yescharacteristic
992C22C53×#55411yescharacteristic
993C22C53×#55411yescharacteristic
994C22C53×#55511yescharacteristic
995C22C53×#55511yescharacteristic
996C22C53×#55611yescharacteristic
997C22C53×#56011yescharacteristic
998C22C53×#56211yescharacteristic
999C4—24no—
1000C4—24no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C2—44no—
1014C2C53×#244011yescharacteristic
1015C2C53×#245011yescharacteristic
1016C2C53×#247211yescharacteristic
1017C2C53×#247411yescharacteristic
1018C2C53×#249211yescharacteristic
1019C2C53×#254911yescharacteristic
1020C2C53×#256311yescharacteristic
1021C2C53×#257411yescharacteristic
1022C2C53×#258311yescharacteristic
1023C2C53×#267811yescharacteristic
1024C2C53×#268611yescharacteristic
1025C2C53×#269211yescharacteristic
1026C2C53×#274211yescharacteristic
1027C2C53×#278411yescharacteristic
1028C2C53×#278811yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
prime radicalC25×C53C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#395C2semidirect
5. C53×#1446C2semidirect
6. C53×#1442C2semidirect
7. C53×#1442C2semidirect
8. C53×#1441C2semidirect
9. C53×#1441C2semidirect
13. C53×#1436C2semidirect
14. C53×C4⋊#95C2semidirect
118. C2×C22⋊C4×C53Q8semidirect
119. C2×C22⋊C4×C53Q8semidirect
434. #15475C53direct (N × H)
499. C2×#395C2×C53semidirect
503. #1446C2×C53semidirect
504. #1442C2×C53semidirect
505. #1442C2×C53semidirect
506. #1441C2×C53semidirect
507. #1441C2×C53semidirect
511. #1436C2×C53semidirect
512. C4⋊#95C2×C53semidirect
569. C53#15475direct (N × H)
633. C2×C22⋊C4Q8×C53semidirect
634. C2×C22⋊C4Q8×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3952
C2×C53×#3932
C2×C53×#3852
C2×C53×#3802
C53×#14462
C53×#14422
C53×#14412
C53×#14392
C53×#14372
C53×#14362
C53×C4⋊#952
C53×C22⋊#952
#1547553