Finite Group Databasebeta

← C53×#10433 #27217945

Subgroups — C53×#10433 #27217945

Order 13568.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#2538C211yesmaximal, characteristic
2C53×#1834C211yesmaximal, characteristic, complemented
3C53×#1803C211yesmaximal, characteristic, complemented
4C53×#1802C211yesmaximal, characteristic
5C2×C53×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C53×D4⋊C8C211yesmaximal, characteristic
7C53×#1296C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C53—21no—
9C2×C4×Q8×C53C2211yescharacteristic
10C2×C4×D4×C53C2211yescharacteristic
11C2×C4⋊C8×C53C2211yescharacteristic
12C2×C4⋊C8×C53C2211yescharacteristic
13C2×#103×C53—21no—
14C2×#102×C53—21no—
15C2×C4×C8×C53C2211yescharacteristic
16C53×#396—22no—
17C53×#390—21no—
18C53×#389—21no—
19C53×#384C2211yescharacteristic
20C53×#384C2211yescharacteristic
21C53×#380—21no—
22C53×#340—21no—
23C53×#340—21no—
24C53×#340—22no—
25C53×Q8⋊C8—22no—
26C53×D4⋊C8—22no—
27C22×Q8×C53D411yescharacteristic
28C22×D4×C53D411yescharacteristic
29C23×C4×C53—21no—
30C22×C8×C53—21no—
31C22×C8×C53—21no—
32C22×C8×C53—21no—
33C22⋊Q8×C53—42no—
34C22⋊Q8×C53—42no—
35C4×Q8×C53—21no—
36C4×Q8×C53—21no—
37C4×Q8×C53—21no—
38C4×Q8×C53—21no—
39C4×D4×C53—21no—
40C4×D4×C53—21no—
41C4×D4×C53—21no—
42C4×D4×C53—21no—
43C2×C4⋊C4×C53—22no—
44C2×C4⋊C4×C53—21no—
45C2×C4⋊C4×C53—21no—
46C2×C4⋊C4×C53—21no—
47C2×C4⋊C4×C53—21no—
48C2×C4⋊C4×C53—21no—
49C2×C4⋊C4×C53—21no—
50C2×C4⋊C4×C53D411yescharacteristic
51C2×C4⋊C4×C53D411yescharacteristic
52C2×C4⋊C4×C53D412yes—
53C2×C22⋊C4×C53—22no—
54C2×C22⋊C4×C53—22no—
55C2×C22⋊C4×C53—21no—
56C2×C42×C53—21no—
57C2×C42×C53C2311yescharacteristic
58C4⋊C8×C53—21no—
59C4⋊C8×C53—21no—
60C4⋊C8×C53—21no—
61C4⋊C8×C53—21no—
62#103×C53—42no—
63#102×C53—42no—
64C4×C8×C53—21no—
65C4×C8×C53D412yes—
66#95×C53—22no—
67C24×C53—21no—
68C2×Q8×C53—21no—
69C2×Q8×C53—21no—
70C2×Q8×C53—21no—
71C2×Q8×C53—21no—
72C2×Q8×C53—21no—
73C2×Q8×C53D812yes—
74C2×D4×C53—21no—
75C2×D4×C53—21no—
76C2×D4×C53—21no—
77C2×D4×C53—21no—
78C2×D4×C53—21no—
79C2×D4×C53SD1612yes—
80C22×C4×C53—21no—
81C22×C4×C53—21no—
82C22×C4×C53—21no—
83C22×C4×C53—22no—
84C22×C4×C53—41no—
85C22×C4×C53—41no—
86C22×C4×C53—41no—
87C22×C4×C53—41no—
88C22×C4×C53—41no—
89C22×C4×C53—41no—
90C22×C4×C53—41no—
91C22×C4×C53C2×D411yescharacteristic
92C22×C4×C53C2×D411yescharacteristic
93C22×C4×C53C2×D411yescharacteristic
94C2×C8×C53—22no—
95C2×C8×C53—41no—
96C2×C8×C53—41no—
97C2×C8×C53—41no—
98C2×C8×C53—41no—
99C2×C8×C53—41no—
100C2×C8×C53—41no—
101C2×C8×C53—41no—
102C2×C8×C53—41no—
103C4⋊C4×C53—21no—
104C4⋊C4×C53—21no—
105C4⋊C4×C53—21no—
106C4⋊C4×C53—21no—
107C4⋊C4×C53—44no—
108C4⋊C4×C53—42no—
109C4⋊C4×C53—42no—
110C4⋊C4×C53—41no—
111C4⋊C4×C53—41no—
112C4⋊C4×C53—41no—
113C4⋊C4×C53—41no—
114C4⋊C4×C53—41no—
115C4⋊C4×C53—41no—
116C4⋊C4×C53—41no—
117C4⋊C4×C53—41no—
118C4⋊C4×C53—41no—
119C4⋊C4×C53—41no—
120C22⋊C4×C53—44no—
121C22⋊C4×C53—41no—
122C22⋊C4×C53—41no—
123C22⋊C4×C53—82no—
124C42×C53—41no—
125C42×C53—41no—
126C42×C53C2×D411yescharacteristic
127C42×C53#4111yescharacteristic
128C42×C53#4111yescharacteristic
129C42×C53#4111yescharacteristic
130C23×C53—22no—
131C23×C53—41no—
132C23×C53—41no—
133C23×C53—41no—
134C23×C53—41no—
135C23×C53—41no—
136C23×C53—41no—
137C23×C53#12011yescharacteristic
138Q8×C53—22no—
139Q8×C53—22no—
140Q8×C53—41no—
141Q8×C53—41no—
142D4×C53—22no—
143D4×C53—22no—
144D4×C53—41no—
145D4×C53—41no—
146C2×C4×C53—21no—
147C2×C4×C53—21no—
148C2×C4×C53—22no—
149C2×C4×C53—41no—
150C2×C4×C53—41no—
151C2×C4×C53—41no—
152C2×C4×C53—41no—
153C2×C4×C53—41no—
154C2×C4×C53—42no—
155C2×C4×C53—41no—
156C2×C4×C53—42no—
157C2×C4×C53—41no—
158C2×C4×C53—41no—
159C2×C4×C53—42no—
160C2×C4×C53—81no—
161C2×C4×C53—81no—
162C2×C4×C53—81no—
163C2×C4×C53—81no—
164C2×C4×C53—81no—
165C2×C4×C53—81no—
166C2×C4×C53—81no—
167C2×C4×C53#12111yescharacteristic
168C2×C4×C53#12111yescharacteristic
169C2×C4×C53#12111yescharacteristic
170C2×C4×C53#12311yescharacteristic
171C2×C4×C53#12311yescharacteristic
172C2×C4×C53#12411yescharacteristic
173C2×C4×C53C2×D811yescharacteristic
174C2×C4×C53C2×SD1611yescharacteristic
175C2×C4×C53#13511yescharacteristic
176C2×C4×C53#13511yescharacteristic
177C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C53#13711yescharacteristic
179C2×C4×C53#13711yescharacteristic
180C2×C4×C53#13711yescharacteristic
181C8×C53—42no—
182C8×C53—81no—
183C8×C53—81no—
184#10433C5311yesmaximal, characteristic, direct product factor, Sylow
185C22×C53—42no—
186C22×C53—42no—
187C22×C53—42no—
188C22×C53—81no—
189C22×C53—81no—
190C22×C53—81no—
191C22×C53—81no—
192C22×C53#39411yescharacteristic
193C22×C53#44711yescharacteristic
194C22×C53#44811yescharacteristic
195C22×C53#45211yescharacteristic
196C22×C53#45211yescharacteristic
197C22×C53#45411yescharacteristic
198C22×C53#45511yescharacteristic
199C4×C53—21no—
200C4×C53—21no—
201C4×C53—42no—
202C4×C53—82no—
203C4×C53—81no—
204C4×C53—81no—
205C4×C53—161no—
206C4×C53#46511yescharacteristic
207C4×C53#46611yescharacteristic
208C4×C53#46811yescharacteristic
209C4×C53#47011yescharacteristic
210C4×C53#48011yescharacteristic
211C4×C53#48211yescharacteristic
212C4×C53#48311yescharacteristic
213C4×C53#48511yescharacteristic
214#2538C2×C5311yescharacteristic
215#1834C2×C5311yescharacteristic, complemented
216#1803C2×C5311yescharacteristic, complemented
217#1802C2×C5311yescharacteristic
218C2×Q8⋊C8C2×C5311yescharacteristic, complemented
219C2×D4⋊C8C2×C5311yescharacteristic
220#1296C2×C5311yescharacteristic, complemented
221C2×C53—82no—
222C2×C53#162711yescharacteristic
223C2×C53#163811yescharacteristic
224C2×C53#164111yescharacteristic
225C2×C53#164311yescharacteristic
226C2×C53#203311yescharacteristic
227C2×C53#203511yescharacteristic
228C2×C53#204011yescharacteristic
229C2×C22⋊Q8—21no—
230C2×C4×Q8C22×C5311yescharacteristic
231C2×C4×D4C22×C5311yescharacteristic
232C2×C4⋊C8C22×C5311yescharacteristic
233C2×C4⋊C8C22×C5311yescharacteristic
234C2×#103—21no—
235C2×#102—21no—
236C2×C4×C8C22×C5311yescharacteristic
237#396—22no—
238#390—21no—
239#389—21no—
240#384C22×C5311yescharacteristic
241#384C22×C5311yescharacteristic
242#380—21no—
243#340—21no—
244#340—21no—
245#340—22no—
246Q8⋊C8—22no—
247D4⋊C8—22no—
248C53#1043311yescharacteristic, direct product factor, Sylow
249C22×Q8D4×C5311yescharacteristic
250C22×D4D4×C5311yescharacteristic
251C23×C4—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22⋊Q8—42no—
256C22⋊Q8—42no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C5311yescharacteristic
273C2×C4⋊C4D4×C5311yescharacteristic
274C2×C4⋊C4D4×C5312yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C42—21no—
279C2×C42C23×C5311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284#103—42no—
285#102—42no—
286C4×C8—21no—
287C4×C8D4×C5312yes—
288#95—22no—
289C24—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8D8×C5312yes—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4SD16×C5312yes—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C2×D4×C5311yescharacteristic
314C22×C4C2×D4×C5311yescharacteristic
315C22×C4C2×D4×C5311yescharacteristic
316C2×C8—22no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—44no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C22⋊C4—44no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—82no—
346C42—41no—
347C42—41no—
348C42C2×D4×C5311yescharacteristic
349C42#41×C5311yescharacteristic
350C42#41×C5311yescharacteristic
351C42#41×C5311yescharacteristic
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23#120×C5311yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—41no—
363Q8—41no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4#121×C5311yescharacteristic
390C2×C4#121×C5311yescharacteristic
391C2×C4#121×C5311yescharacteristic
392C2×C4#123×C5311yescharacteristic
393C2×C4#123×C5311yescharacteristic
394C2×C4#124×C5311yescharacteristic
395C2×C4C2×D8×C5311yescharacteristic
396C2×C4C2×SD16×C5311yescharacteristic
397C2×C4#135×C5311yescharacteristic
398C2×C4#135×C5311yescharacteristic
399C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
400C2×C4#137×C5311yescharacteristic
401C2×C4#137×C5311yescharacteristic
402C2×C4#137×C5311yescharacteristic
403C8—42no—
404C8—81no—
405C8—81no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22C53×#39411yescharacteristic
414C22C53×#44711yescharacteristic
415C22C53×#44811yescharacteristic
416C22C53×#45211yescharacteristic
417C22C53×#45211yescharacteristic
418C22C53×#45411yescharacteristic
419C22C53×#45511yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—81no—
425C4—82no—
426C4—161no—
427C4C53×#46511yescharacteristic
428C4C53×#46611yescharacteristic
429C4C53×#46811yescharacteristic
430C4C53×#47011yescharacteristic
431C4C53×#48011yescharacteristic
432C4C53×#48211yescharacteristic
433C4C53×#48311yescharacteristic
434C4C53×#48511yescharacteristic
435C2—82no—
436C2C53×#162711yescharacteristic
437C2C53×#163811yescharacteristic
438C2C53×#164111yescharacteristic
439C2C53×#164311yescharacteristic
440C2C53×#203311yescharacteristic
441C2C53×#203511yescharacteristic
442C2C53×#204011yescharacteristic
subgroupG/H
center, socleC23×C53#120
commutator, Frattini, cosocleC2×C42C23×C53
prime radicalC22×D4×C53D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#1834C2semidirect
3. C53×#1803C2semidirect
5. C2×C53×Q8⋊C8C2semidirect
7. C53×#1296C2semidirect
184. #10433C53direct (N × H)
215. #1834C2×C53semidirect
216. #1803C2×C53semidirect
218. C2×Q8⋊C8C2×C53semidirect
220. #1296C2×C53semidirect
248. C53#10433direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#25382
C53×#18342
C53×#18032
C53×#18022
C2×C53×Q8⋊C82
C2×C53×D4⋊C82
C53×#12962
#1043353