Finite Group Databasebeta

← C53×#13080 #27220592

Subgroups — C53×#13080 #27220592

Order 13568.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C53C211yesmaximal, characteristic
2C53×#2405C211yesmaximal, characteristic
3C2×C53×#352C212yesmaximal, complemented
4C53×#1781C211yesmaximal, characteristic
5C53×#1390C212yesmaximal, complemented
6C23×D4×C53C2211yescharacteristic
7C22×M16×C53—21no—
8C2×#123×C53C411yescharacteristic, complemented
9C2×#123×C53C2211yescharacteristic
10C22×C22⋊C4×C53C411yescharacteristic, complemented
11C2×#100×C53—21no—
12C2×#100×C53—24no—
13C2×#100×C53C2212yes—
14C2×#99×C53—21no—
15C2×#99×C53C2212yes—
16C53×#394—21no—
17C53×#394—21no—
18C53×#386C411yescharacteristic, complemented
19C53×#386C2211yescharacteristic
20C53×#385—21no—
21C53×#379—21no—
22C53×#379—21no—
23C53×#379C411yescharacteristic, complemented
24C53×#352—24no—
25C25×C53C2×C411yescharacteristic
26C25×C53D411yescharacteristic
27C22×D4×C53—22no—
28C22×D4×C53—22no—
29C22×D4×C53—42no—
30C22×D4×C53—41no—
31C22×D4×C53—41no—
32C22×D4×C53C2×C411yescharacteristic
33C22×D4×C53D411yescharacteristic
34C22×D4×C53D411yescharacteristic
35C22×D4×C53C2311yescharacteristic
36C23×C4×C53C2×C411yescharacteristic
37C23×C4×C53C2×C411yescharacteristic
38C23×C4×C53D411yescharacteristic
39C2×M16×C53—24no—
40C2×M16×C53—22no—
41C2×M16×C53—41no—
42C2×M16×C53—42no—
43C22×C8×C53—41no—
44#123×C53—22no—
45#123×C53—22no—
46#123×C53—42no—
47C2×C4⋊C4×C53—21no—
48C2×C4⋊C4×C53—21no—
49C2×C22⋊C4×C53—21no—
50C2×C22⋊C4×C53—21no—
51C2×C22⋊C4×C53—21no—
52C2×C22⋊C4×C53—21no—
53C2×C22⋊C4×C53—21no—
54C2×C22⋊C4×C53—21no—
55C2×C22⋊C4×C53—21no—
56C2×C22⋊C4×C53—21no—
57C2×C22⋊C4×C53—22no—
58C2×C22⋊C4×C53—41no—
59C2×C22⋊C4×C53—41no—
60C2×C22⋊C4×C53—41no—
61C2×C22⋊C4×C53—41no—
62C2×C22⋊C4×C53C2×C411yescharacteristic
63C2×C22⋊C4×C53C2×C411yescharacteristic
64#100×C53—24no—
65#100×C53—22no—
66#100×C53D414yes—
67#99×C53—22no—
68#99×C53—22no—
69#99×C53—42no—
70#95×C53—21no—
71#95×C53—21no—
72C24×C53—21no—
73C24×C53—21no—
74C24×C53—21no—
75C24×C53—21no—
76C24×C53—22no—
77C24×C53—22no—
78C24×C53—41no—
79C24×C53—41no—
80C24×C53—42no—
81C24×C53—42no—
82C24×C53—81no—
83C24×C53—81no—
84C24×C53C22⋊C411yescharacteristic
85C24×C53C22⋊C411yescharacteristic
86C24×C53C22⋊C411yescharacteristic
87C24×C53C22×C411yescharacteristic
88C24×C53C2×D411yescharacteristic
89C2×D4×C53—22no—
90C2×D4×C53—22no—
91C2×D4×C53—22no—
92C2×D4×C53—22no—
93C2×D4×C53—21no—
94C2×D4×C53—21no—
95C2×D4×C53—41no—
96C2×D4×C53—41no—
97C2×D4×C53—41no—
98C2×D4×C53—41no—
99C2×D4×C53—41no—
100C2×D4×C53—41no—
101C2×D4×C53—44no—
102C2×D4×C53—44no—
103C2×D4×C53—44no—
104C2×D4×C53—44no—
105C2×D4×C53C2×D412yes—
106C2×D4×C53#4112yes—
107C22×C4×C53—21no—
108C22×C4×C53—21no—
109C22×C4×C53—22no—
110C22×C4×C53—21no—
111C22×C4×C53—21no—
112C22×C4×C53—21no—
113C22×C4×C53—21no—
114C22×C4×C53—21no—
115C22×C4×C53—21no—
116C22×C4×C53—22no—
117C22×C4×C53—41no—
118C22×C4×C53—41no—
119C22×C4×C53—41no—
120C22×C4×C53—42no—
121C22×C4×C53—81no—
122C22×C4×C53C22⋊C411yescharacteristic
123C22×C4×C53C2×D411yescharacteristic
124M16×C53—24no—
125M16×C53—44no—
126M16×C53—42no—
127C2×C8×C53—44no—
128C2×C8×C53—42no—
129C4⋊C4×C53—42no—
130C4⋊C4×C53—41no—
131C4⋊C4×C53—41no—
132C22⋊C4×C53—22no—
133C22⋊C4×C53—42no—
134C22⋊C4×C53—42no—
135C22⋊C4×C53—42no—
136C22⋊C4×C53—41no—
137C22⋊C4×C53—41no—
138C22⋊C4×C53—42no—
139C22⋊C4×C53—41no—
140C22⋊C4×C53—42no—
141C22⋊C4×C53—42no—
142C22⋊C4×C53—81no—
143C22⋊C4×C53—81no—
144C22⋊C4×C53—81no—
145C22⋊C4×C53—82no—
146C22⋊C4×C53—82no—
147C23×C53—22no—
148C23×C53—21no—
149C23×C53—21no—
150C23×C53—21no—
151C23×C53—21no—
152C23×C53—21no—
153C23×C53—21no—
154C23×C53—21no—
155C23×C53—21no—
156C23×C53—21no—
157C23×C53—21no—
158C23×C53—21no—
159C23×C53—21no—
160C23×C53—41no—
161C23×C53—42no—
162C23×C53—42no—
163C23×C53—42no—
164C23×C53—42no—
165C23×C53—41no—
166C23×C53—41no—
167C23×C53—41no—
168C23×C53—41no—
169C23×C53—41no—
170C23×C53—41no—
171C23×C53—42no—
172C23×C53—42no—
173C23×C53—41no—
174C23×C53—41no—
175C23×C53—42no—
176C23×C53—42no—
177C23×C53—81no—
178C23×C53—81no—
179C23×C53—81no—
180C23×C53—81no—
181C23×C53—84no—
182C23×C53—84no—
183C23×C53—84no—
184C23×C53—84no—
185C23×C53#9911yescharacteristic
186C23×C53#9911yescharacteristic
187C23×C53C2×C22⋊C411yescharacteristic
188C23×C53C4×D412yes—
189C23×C53#12112yes—
190D4×C53—42no—
191D4×C53—42no—
192D4×C53—44no—
193D4×C53—44no—
194D4×C53—42no—
195D4×C53—42no—
196C2×C4×C53—22no—
197C2×C4×C53—22no—
198C2×C4×C53—22no—
199C2×C4×C53—22no—
200C2×C4×C53—21no—
201C2×C4×C53—21no—
202C2×C4×C53—21no—
203C2×C4×C53—21no—
204C2×C4×C53—41no—
205C2×C4×C53—41no—
206C2×C4×C53—41no—
207C2×C4×C53—41no—
208C2×C4×C53—41no—
209C2×C4×C53—41no—
210C2×C4×C53—41no—
211C2×C4×C53—41no—
212C2×C4×C53—41no—
213C2×C4×C53—41no—
214C2×C4×C53—41no—
215C2×C4×C53—41no—
216C2×C4×C53—82no—
217C2×C4×C53—82no—
218C2×C4×C53—82no—
219C2×C4×C53—82no—
220C2×C4×C53—82no—
221C2×C4×C53#9912yes—
222C2×C4×C53#12011yescharacteristic
223C2×C4×C53#12311yescharacteristic
224C8×C53—44no—
225#13080C5311yesmaximal, characteristic, direct product factor, Sylow
226C22×C53—21no—
227C22×C53—21no—
228C22×C53—21no—
229C22×C53—21no—
230C22×C53—21no—
231C22×C53—21no—
232C22×C53—21no—
233C22×C53—22no—
234C22×C53—22no—
235C22×C53—42no—
236C22×C53—42no—
237C22×C53—42no—
238C22×C53—42no—
239C22×C53—42no—
240C22×C53—42no—
241C22×C53—41no—
242C22×C53—41no—
243C22×C53—41no—
244C22×C53—41no—
245C22×C53—41no—
246C22×C53—41no—
247C22×C53—41no—
248C22×C53—41no—
249C22×C53—41no—
250C22×C53—41no—
251C22×C53—81no—
252C22×C53—84no—
253C22×C53—84no—
254C22×C53—81no—
255C22×C53—81no—
256C22×C53—81no—
257C22×C53—84no—
258C22×C53—84no—
259C22×C53#35212yescomplemented
260C22×C53#38611yescharacteristic
261C22×C53C2×#9911yescharacteristic
262C22×C53C2×#9911yescharacteristic
263C4×C53—21no—
264C4×C53—22no—
265C4×C53—21no—
266C4×C53—81no—
267C4×C53—81no—
268C4×C53—81no—
269C4×C53—81no—
270C4×C53—162no—
271C22×#100C2×C5311yescharacteristic
272#2405C2×C5311yescharacteristic
273C2×#352C2×C5312yescomplemented
274#1781C2×C5311yescharacteristic
275#1390C2×C5312yescomplemented
276C2×C53—21no—
277C2×C53—21no—
278C2×C53—22no—
279C2×C53—42no—
280C2×C53—41no—
281C2×C53—42no—
282C2×C53—81no—
283C2×C53—81no—
284C2×C53#189811yescharacteristic
285C2×C53C2×#35211yescharacteristic
286C2×C53#212111yescharacteristic
287C23×D4C22×C5311yescharacteristic
288C22×M16—21no—
289C2×#123C4×C5311yescharacteristic, complemented
290C2×#123C22×C5311yescharacteristic
291C22×C22⋊C4C4×C5311yescharacteristic, complemented
292C2×#100—21no—
293C2×#100—24no—
294C2×#100C22×C5312yes—
295C2×#99—21no—
296C2×#99C22×C5312yes—
297#394—21no—
298#394—21no—
299#386C4×C5311yescharacteristic, complemented
300#386C22×C5311yescharacteristic
301#385—21no—
302#379—21no—
303#379—21no—
304#379C4×C5311yescharacteristic, complemented
305#352—24no—
306C53#1308011yescharacteristic, direct product factor, Sylow
307C25C2×C4×C5311yescharacteristic
308C25D4×C5311yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C5311yescharacteristic
315C22×D4D4×C5311yescharacteristic
316C22×D4D4×C5311yescharacteristic
317C22×D4C23×C5311yescharacteristic
318C23×C4C2×C4×C5311yescharacteristic
319C23×C4C2×C4×C5311yescharacteristic
320C23×C4D4×C5311yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C5311yescharacteristic
345C2×C22⋊C4C2×C4×C5311yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C5314yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C5311yescharacteristic
367C24C22⋊C4×C5311yescharacteristic
368C24C22⋊C4×C5311yescharacteristic
369C24C22×C4×C5311yescharacteristic
370C24C2×D4×C5311yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C5312yes—
388C2×D4#41×C5312yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C5311yescharacteristic
405C22×C4C2×D4×C5311yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C5311yescharacteristic
468C23#99×C5311yescharacteristic
469C23C2×C22⋊C4×C5311yescharacteristic
470C23C4×D4×C5312yes—
471C23#121×C5312yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C5312yes—
504C2×C4#120×C5311yescharacteristic
505C2×C4#123×C5311yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22C53×#35212yescomplemented
541C22C53×#38611yescharacteristic
542C22C2×#99×C5311yescharacteristic
543C22C2×#99×C5311yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C53×#189811yescharacteristic
561C2C2×C53×#35211yescharacteristic
562C2C53×#212111yescharacteristic
subgroupG/H
center, socleC22×C53C2×#99
commutatorC24C22×C4×C53
Frattini, cosocleC22×D4C23×C53
prime radicalC23×D4×C53C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C24×C53 ◁ C23×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C53×#352C2semidirect
5. C53×#1390C2semidirect
8. C2×#123×C53C4semidirect
10. C22×C22⋊C4×C53C4semidirect
18. C53×#386C4semidirect
23. C53×#379C4semidirect
225. #13080C53direct (N × H)
259. C22×C53#352semidirect
273. C2×#352C2×C53semidirect
275. #1390C2×C53semidirect
289. C2×#123C4×C53semidirect
291. C22×C22⋊C4C4×C53semidirect
299. #386C4×C53semidirect
304. #379C4×C53semidirect
306. C53#13080direct (N × H)
540. C22C53×#352semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C532
C53×#24052
C2×C53×#3522
C53×#17812
C53×#13902
#1308053