Finite Group Databasebeta

← C53×#13789 #27221301

Subgroups — C53×#13789 #27221301

Order 13568.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#388C211yesmaximal, characteristic
2C2×C53×#388C211yesmaximal, characteristic
3C2×C53×#385C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
6C53×#1437C211yesmaximal, characteristic
7C53×#1437C211yesmaximal, characteristic
8C53×#1436C211yesmaximal, characteristic, complemented
9C53×#1436C211yesmaximal, characteristic, complemented
10C53×#1436C211yesmaximal, characteristic, complemented
11C53×#1436C211yesmaximal, characteristic, complemented
12C53×C4⋊#95C211yesmaximal, characteristic, complemented
13C53×#1434C211yesmaximal, characteristic, complemented
14C53×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C53C211yesmaximal, characteristic, complemented
16C24×C4×C53C2211yescharacteristic
17C22×C4⋊C4×C53C2211yescharacteristic
18C22×C4⋊C4×C53C2211yescharacteristic
19C22×C4⋊C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C22⋊C4×C53C2211yescharacteristic
22C22×C22⋊C4×C53C2211yescharacteristic
23C22×C22⋊C4×C53C2211yescharacteristic
24C22×C22⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C42×C53C2211yescharacteristic
28C22×C42×C53C2211yescharacteristic
29C22×C42×C53C2211yescharacteristic
30C22×C42×C53C2211yescharacteristic
31C22×C42×C53C2211yescharacteristic
32C22×C42×C53C2211yescharacteristic
33C53×#388C418yescomplemented
34C53×#388C418yescomplemented
35C53×#385C418yescomplemented
36C4×C4⋊C4×C53—24no—
37C4×C22⋊C4×C53—24no—
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
55C2×#95×C53C2211yescharacteristic
56C25×C53C2311yescharacteristic
57C23×C4×C53—22no—
58C23×C4×C53—22no—
59C23×C4×C53—41no—
60C23×C4×C53—41no—
61C23×C4×C53—41no—
62C23×C4×C53—41no—
63C23×C4×C53C2×C414yes—
64C23×C4×C53C2311yescharacteristic
65C23×C4×C53C2311yescharacteristic
66C23×C4×C53C2311yescharacteristic
67C23×C4×C53C2311yescharacteristic
68C23×C4×C53C2311yescharacteristic
69C23×C4×C53C2311yescharacteristic
70C23×C4×C53C2311yescharacteristic
71C23×C4×C53C2311yescharacteristic
72C23×C4×C53C2311yescharacteristic
73C23×C4×C53C2311yescharacteristic
74C23×C4×C53C2311yescharacteristic
75C23×C4×C53C2311yescharacteristic
76C23×C4×C53C2311yescharacteristic
77C23×C4×C53C2311yescharacteristic
78C2×C4⋊C4×C53—22no—
79C2×C4⋊C4×C53—22no—
80C2×C4⋊C4×C53—22no—
81C2×C4⋊C4×C53—22no—
82C2×C4⋊C4×C53—41no—
83C2×C4⋊C4×C53—41no—
84C2×C4⋊C4×C53—41no—
85C2×C4⋊C4×C53—41no—
86C2×C4⋊C4×C53C2×C414yes—
87C2×C4⋊C4×C53C2×C414yes—
88C2×C4⋊C4×C53C2×C414yescomplemented
89C2×C4⋊C4×C53C2×C414yescomplemented
90C2×C22⋊C4×C53—22no—
91C2×C22⋊C4×C53—22no—
92C2×C22⋊C4×C53—22no—
93C2×C22⋊C4×C53—22no—
94C2×C22⋊C4×C53—41no—
95C2×C22⋊C4×C53—41no—
96C2×C22⋊C4×C53—41no—
97C2×C22⋊C4×C53—41no—
98C2×C22⋊C4×C53—41no—
99C2×C22⋊C4×C53—41no—
100C2×C22⋊C4×C53C2×C414yes—
101C2×C22⋊C4×C53C2×C414yes—
102C2×C22⋊C4×C53C2×C414yes—
103C2×C22⋊C4×C53C2×C414yes—
104C2×C22⋊C4×C53C2×C414yes—
105C2×C22⋊C4×C53C2×C414yes—
106C2×C22⋊C4×C53C2×C414yes—
107C2×C22⋊C4×C53C2×C414yes—
108C2×C42×C53—22no—
109C2×C42×C53—22no—
110C2×C42×C53—22no—
111C2×C42×C53—22no—
112C2×C42×C53—22no—
113C2×C42×C53—41no—
114C2×C42×C53—41no—
115C2×C42×C53—41no—
116C2×C42×C53—41no—
117C2×C42×C53—41no—
118C2×C42×C53—41no—
119C2×C42×C53—41no—
120C2×C42×C53—41no—
121C2×C42×C53—41no—
122C2×C42×C53—41no—
123C2×C42×C53C2×C414yescomplemented
124C2×C42×C53C2×C414yescomplemented
125C2×C42×C53D414yes—
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—41no—
133#95×C53—41no—
134#95×C53—41no—
135#95×C53—41no—
136#95×C53—41no—
137#95×C53—41no—
138#95×C53C2×C414yes—
139#95×C53C2×C414yes—
140#95×C53C2×C414yescomplemented
141#95×C53C2×C414yescomplemented
142#95×C53C2×C414yescomplemented
143#95×C53C2×C414yescomplemented
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×C53—21no—
156C24×C53C22×C412yes—
157C24×C53C22×C412yes—
158C24×C53C22×C412yes—
159C24×C53C2411yescharacteristic
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
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—21no—
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—28no—
235C22×C4×C53—44no—
236C22×C4×C53—44no—
237C22×C4×C53—44no—
238C22×C4×C53—44no—
239C22×C4×C53—44no—
240C22×C4×C53—44no—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C22×C412yes—
243C22×C4×C53C22×C412yes—
244C22×C4×C53C22×C412yes—
245C22×C4×C53C22×C412yes—
246C22×C4×C53C22×C412yes—
247C22×C4×C53C22×C412yes—
248C22×C4×C53C22×C412yes—
249C22×C4×C53C22×C412yes—
250C22×C4×C53C22×C412yes—
251C22×C4×C53C22×C412yes—
252C22×C4×C53C22×C412yes—
253C22×C4×C53C22×C412yes—
254C22×C4×C53C22×C412yes—
255C22×C4×C53C22×C412yes—
256C22×C4×C53C22×C412yes—
257C22×C4×C53C22×C412yes—
258C22×C4×C53C22×C412yes—
259C22×C4×C53C2×D412yes—
260C22×C4×C53C2×D412yes—
261C22×C4×C53C2×D412yes—
262C22×C4×C53#4112yes—
263C22×C4×C53#4112yes—
264C22×C4×C53#4112yes—
265C4⋊C4×C53—28no—
266C4⋊C4×C53—28no—
267C4⋊C4×C53—44no—
268C4⋊C4×C53—44no—
269C22⋊C4×C53—28no—
270C22⋊C4×C53—28no—
271C22⋊C4×C53—44no—
272C22⋊C4×C53—44no—
273C22⋊C4×C53—44no—
274C22⋊C4×C53C42116yescomplemented
275C42×C53—28no—
276C42×C53—44no—
277C42×C53—44no—
278C42×C53—44no—
279C42×C53—44no—
280C42×C53—44no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
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—41no—
300C23×C53—41no—
301C23×C53—41no—
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×C53C2×C4214yes—
316C23×C53C23×C411yescharacteristic
317C23×C53C23×C411yescharacteristic
318C23×C53C23×C411yescharacteristic
319C23×C53C22×D411yescharacteristic
320C23×C53C2×#4111yescharacteristic
321C23×C53C2×#4111yescharacteristic
322C23×C53C2×#4111yescharacteristic
323C23×C53H(5,𝔽2)11yescharacteristic
324C23×C53H(5,𝔽2)11yescharacteristic
325C23×C53H(5,𝔽2)11yescharacteristic
326C23×C53H(5,𝔽2)11yescharacteristic
327C23×C53H(5,𝔽2)11yescharacteristic
328C23×C532−1+411yescharacteristic
329C23×C532−1+411yescharacteristic
330C23×C532−1+411yescharacteristic
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
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—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—22no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53—22no—
386C2×C4×C53—22no—
387C2×C4×C53—22no—
388C2×C4×C53—416no—
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×C53C2×C4214yes—
426C2×C4×C53C2×C4214yes—
427C2×C4×C53C4×D414yes—
428C2×C4×C53C4×D414yes—
429C2×C4×C53C4×D414yes—
430#13789C5311yesmaximal, characteristic, direct product factor, Sylow
431C22×C53—24no—
432C22×C53—24no—
433C22×C53—24no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—42no—
437C22×C53—42no—
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×C53C22×C4211yescharacteristic
447C22×C53C2×C4×D411yescharacteristic
448C22×C53C2×C4×D411yescharacteristic
449C22×C53C2×C4×D411yescharacteristic
450C22×C53C4×#4111yescharacteristic
451C22×C53C4×#4111yescharacteristic
452C22×C53C4×#4111yescharacteristic
453C22×C53#51811yescharacteristic
454C22×C53#51811yescharacteristic
455C22×C53#51811yescharacteristic
456C22×C53#51811yescharacteristic
457C22×C53#51911yescharacteristic
458C22×C53#52011yescharacteristic
459C22×C53#52011yescharacteristic
460C22×C53#52011yescharacteristic
461C22×C53#52011yescharacteristic
462C22×C53#52011yescharacteristic
463C22×C53#52011yescharacteristic
464C22×C53#52011yescharacteristic
465C22×C53#53411yescharacteristic
466C22×C53#53511yescharacteristic
467C22×C53#53611yescharacteristic
468C22×C53#53711yescharacteristic
469C22×C53#53811yescharacteristic
470C22×C53#53811yescharacteristic
471C22×C53#53811yescharacteristic
472C22×C53#53911yescharacteristic
473C22×C53#53911yescharacteristic
474C22×C53#53911yescharacteristic
475C22×C53#54011yescharacteristic
476C22×C53#54111yescharacteristic
477C22×C53#54211yescharacteristic
478C22×C53#54211yescharacteristic
479C22×C53#54211yescharacteristic
480C22×C53#54211yescharacteristic
481C4×C53—24no—
482C4×C53—24no—
483C4×C53—24no—
484C4×C53—24no—
485C4×C53—24no—
486C4×C53—42no—
487C4×C53—42no—
488C4×C53—42no—
489C4×C53—42no—
490C4×C53—42no—
491C4×C53—42no—
492C4×C53—42no—
493C4×C53—42no—
494C4×C53—42no—
495C2×#388C2×C5311yescharacteristic
496C2×#388C2×C5311yescharacteristic
497C2×#385C2×C5311yescharacteristic
498C2×C4×C4⋊C4C2×C5311yescharacteristic, complemented
499C2×C4×C22⋊C4C2×C5311yescharacteristic
500#1437C2×C5311yescharacteristic
501#1437C2×C5311yescharacteristic
502#1436C2×C5311yescharacteristic, complemented
503#1436C2×C5311yescharacteristic, complemented
504#1436C2×C5311yescharacteristic, complemented
505#1436C2×C5311yescharacteristic, complemented
506C4⋊#95C2×C5311yescharacteristic, complemented
507#1434C2×C5311yescharacteristic, complemented
508C22⋊#95C2×C5311yescharacteristic
509C4×#95C2×C5311yescharacteristic, complemented
510C2×C53—44no—
511C2×C53C42×D411yescharacteristic
512C2×C53#227411yescharacteristic
513C2×C53#227511yescharacteristic
514C2×C53#232111yescharacteristic
515C2×C53#232211yescharacteristic
516C2×C53#232311yescharacteristic
517C2×C53#232411yescharacteristic
518C2×C53#232511yescharacteristic
519C2×C53#232611yescharacteristic
520C2×C53#233211yescharacteristic
521C2×C53#233411yescharacteristic
522C2×C53#233411yescharacteristic
523C2×C53#233511yescharacteristic
524C2×C53#233511yescharacteristic
525C2×C53#233711yescharacteristic
526C24×C4C22×C5311yescharacteristic
527C22×C4⋊C4C22×C5311yescharacteristic
528C22×C4⋊C4C22×C5311yescharacteristic
529C22×C4⋊C4C22×C5311yescharacteristic
530C22×C4⋊C4C22×C5311yescharacteristic
531C22×C22⋊C4C22×C5311yescharacteristic
532C22×C22⋊C4C22×C5311yescharacteristic
533C22×C22⋊C4C22×C5311yescharacteristic
534C22×C22⋊C4C22×C5311yescharacteristic
535C22×C22⋊C4C22×C5311yescharacteristic
536C22×C22⋊C4C22×C5311yescharacteristic
537C22×C42C22×C5311yescharacteristic
538C22×C42C22×C5311yescharacteristic
539C22×C42C22×C5311yescharacteristic
540C22×C42C22×C5311yescharacteristic
541C22×C42C22×C5311yescharacteristic
542C22×C42C22×C5311yescharacteristic
543#388C4×C5318yescomplemented
544#388C4×C5318yescomplemented
545#385C4×C5318yescomplemented
546C4×C4⋊C4—24no—
547C4×C22⋊C4—24no—
548C2×#95C22×C5311yescharacteristic
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
566C53#1378911yescharacteristic, direct product factor, Sylow
567C25C23×C5311yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C5314yes—
575C23×C4C23×C5311yescharacteristic
576C23×C4C23×C5311yescharacteristic
577C23×C4C23×C5311yescharacteristic
578C23×C4C23×C5311yescharacteristic
579C23×C4C23×C5311yescharacteristic
580C23×C4C23×C5311yescharacteristic
581C23×C4C23×C5311yescharacteristic
582C23×C4C23×C5311yescharacteristic
583C23×C4C23×C5311yescharacteristic
584C23×C4C23×C5311yescharacteristic
585C23×C4C23×C5311yescharacteristic
586C23×C4C23×C5311yescharacteristic
587C23×C4C23×C5311yescharacteristic
588C23×C4C23×C5311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×C4×C5314yes—
598C2×C4⋊C4C2×C4×C5314yes—
599C2×C4⋊C4C2×C4×C5314yescomplemented
600C2×C4⋊C4C2×C4×C5314yescomplemented
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4C2×C4×C5314yes—
612C2×C22⋊C4C2×C4×C5314yes—
613C2×C22⋊C4C2×C4×C5314yes—
614C2×C22⋊C4C2×C4×C5314yes—
615C2×C22⋊C4C2×C4×C5314yes—
616C2×C22⋊C4C2×C4×C5314yes—
617C2×C22⋊C4C2×C4×C5314yes—
618C2×C22⋊C4C2×C4×C5314yes—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42C2×C4×C5314yescomplemented
635C2×C42C2×C4×C5314yescomplemented
636C2×C42D4×C5314yes—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95C2×C4×C5314yes—
650#95C2×C4×C5314yes—
651#95C2×C4×C5314yescomplemented
652#95C2×C4×C5314yescomplemented
653#95C2×C4×C5314yescomplemented
654#95C2×C4×C5314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C5312yes—
668C24C22×C4×C5312yes—
669C24C22×C4×C5312yes—
670C24C24×C5311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
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—21no—
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—28no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4C22×C4×C5312yes—
753C22×C4C22×C4×C5312yes—
754C22×C4C22×C4×C5312yes—
755C22×C4C22×C4×C5312yes—
756C22×C4C22×C4×C5312yes—
757C22×C4C22×C4×C5312yes—
758C22×C4C22×C4×C5312yes—
759C22×C4C22×C4×C5312yes—
760C22×C4C22×C4×C5312yes—
761C22×C4C22×C4×C5312yes—
762C22×C4C22×C4×C5312yes—
763C22×C4C22×C4×C5312yes—
764C22×C4C22×C4×C5312yes—
765C22×C4C22×C4×C5312yes—
766C22×C4C22×C4×C5312yes—
767C22×C4C22×C4×C5312yes—
768C22×C4C22×C4×C5312yes—
769C22×C4C22×C4×C5312yes—
770C22×C4C2×D4×C5312yes—
771C22×C4C2×D4×C5312yes—
772C22×C4C2×D4×C5312yes—
773C22×C4#41×C5312yes—
774C22×C4#41×C5312yes—
775C22×C4#41×C5312yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4C42×C53116yescomplemented
786C42—28no—
787C42—44no—
788C42—44no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C42×C5314yes—
827C23C23×C4×C5311yescharacteristic
828C23C23×C4×C5311yescharacteristic
829C23C23×C4×C5311yescharacteristic
830C23C22×D4×C5311yescharacteristic
831C23C2×#41×C5311yescharacteristic
832C23C2×#41×C5311yescharacteristic
833C23C2×#41×C5311yescharacteristic
834C23H(5,𝔽2)×C5311yescharacteristic
835C23H(5,𝔽2)×C5311yescharacteristic
836C23H(5,𝔽2)×C5311yescharacteristic
837C23H(5,𝔽2)×C5311yescharacteristic
838C23H(5,𝔽2)×C5311yescharacteristic
839C232−1+4×C5311yescharacteristic
840C232−1+4×C5311yescharacteristic
841C232−1+4×C5311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
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—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—416no—
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×C4C2×C42×C5314yes—
937C2×C4C2×C42×C5314yes—
938C2×C4C4×D4×C5314yes—
939C2×C4C4×D4×C5314yes—
940C2×C4C4×D4×C5314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C42×C5311yescharacteristic
957C22C2×C4×D4×C5311yescharacteristic
958C22C2×C4×D4×C5311yescharacteristic
959C22C2×C4×D4×C5311yescharacteristic
960C22C4×#41×C5311yescharacteristic
961C22C4×#41×C5311yescharacteristic
962C22C4×#41×C5311yescharacteristic
963C22C53×#51811yescharacteristic
964C22C53×#51811yescharacteristic
965C22C53×#51811yescharacteristic
966C22C53×#51811yescharacteristic
967C22C53×#51911yescharacteristic
968C22C53×#52011yescharacteristic
969C22C53×#52011yescharacteristic
970C22C53×#52011yescharacteristic
971C22C53×#52011yescharacteristic
972C22C53×#52011yescharacteristic
973C22C53×#52011yescharacteristic
974C22C53×#52011yescharacteristic
975C22C53×#53411yescharacteristic
976C22C53×#53511yescharacteristic
977C22C53×#53611yescharacteristic
978C22C53×#53711yescharacteristic
979C22C53×#53811yescharacteristic
980C22C53×#53811yescharacteristic
981C22C53×#53811yescharacteristic
982C22C53×#53911yescharacteristic
983C22C53×#53911yescharacteristic
984C22C53×#53911yescharacteristic
985C22C53×#54011yescharacteristic
986C22C53×#54111yescharacteristic
987C22C53×#54211yescharacteristic
988C22C53×#54211yescharacteristic
989C22C53×#54211yescharacteristic
990C22C53×#54211yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C2—44no—
1006C2C42×D4×C5311yescharacteristic
1007C2C53×#227411yescharacteristic
1008C2C53×#227511yescharacteristic
1009C2C53×#232111yescharacteristic
1010C2C53×#232211yescharacteristic
1011C2C53×#232311yescharacteristic
1012C2C53×#232411yescharacteristic
1013C2C53×#232511yescharacteristic
1014C2C53×#232611yescharacteristic
1015C2C53×#233211yescharacteristic
1016C2C53×#233411yescharacteristic
1017C2C53×#233411yescharacteristic
1018C2C53×#233511yescharacteristic
1019C2C53×#233511yescharacteristic
1020C2C53×#233711yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC22C22×C42×C53
Frattini, cosocleC24C24×C53
prime radicalC25×C53C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊C4×C53C2semidirect
8. C53×#1436C2semidirect
9. C53×#1436C2semidirect
10. C53×#1436C2semidirect
11. C53×#1436C2semidirect
12. C53×C4⋊#95C2semidirect
13. C53×#1434C2semidirect
15. C4×#95×C53C2semidirect
33. C53×#388C4semidirect
34. C53×#388C4semidirect
35. C53×#385C4semidirect
88. C2×C4⋊C4×C53C2×C4semidirect
89. C2×C4⋊C4×C53C2×C4semidirect
123. C2×C42×C53C2×C4semidirect
124. C2×C42×C53C2×C4semidirect
140. #95×C53C2×C4semidirect
141. #95×C53C2×C4semidirect
142. #95×C53C2×C4semidirect
143. #95×C53C2×C4semidirect
274. C22⋊C4×C53C42semidirect
430. #13789C53direct (N × H)
498. C2×C4×C4⋊C4C2×C53semidirect
502. #1436C2×C53semidirect
503. #1436C2×C53semidirect
504. #1436C2×C53semidirect
505. #1436C2×C53semidirect
506. C4⋊#95C2×C53semidirect
507. #1434C2×C53semidirect
509. C4×#95C2×C53semidirect
543. #388C4×C53semidirect
544. #388C4×C53semidirect
545. #385C4×C53semidirect
566. C53#13789direct (N × H)
599. C2×C4⋊C4C2×C4×C53semidirect
600. C2×C4⋊C4C2×C4×C53semidirect
634. C2×C42C2×C4×C53semidirect
635. C2×C42C2×C4×C53semidirect
651. #95C2×C4×C53semidirect
652. #95C2×C4×C53semidirect
653. #95C2×C4×C53semidirect
654. #95C2×C4×C53semidirect
785. C22⋊C4C42×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3882
C2×C53×#3852
C2×C4×C4⋊C4×C532
C2×C4×C22⋊C4×C532
C53×#14372
C53×#14362
C53×C4⋊#952
C53×#14342
C53×C22⋊#952
C4×#95×C532
#1378953