Finite Group Databasebeta

← C53×#10475 #27217987

Subgroups — C53×#10475 #27217987

Order 13568.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#460C211yesmaximal, characteristic
2C53×#1984C211yesmaximal, characteristic, complemented
3C53×#1957C211yesmaximal, characteristic
4C53×#1803C211yesmaximal, characteristic, complemented
5C2×C53×#334C211yesmaximal, characteristic, complemented
6C2×C53×#331C211yesmaximal, characteristic
7C53×#1296C211yesmaximal, characteristic, complemented
8C22×SD16×C53—21no—
9C2×#127×C53C2211yescharacteristic
10C2×C4×Q8×C53C2211yescharacteristic
11C53×#460—22no—
12C53×#460—22no—
13C2×C4⋊C8×C53C2211yescharacteristic
14C2×C4⋊C8×C53C2211yescharacteristic
15C2×C4⋊C8×C53C2211yescharacteristic
16C2×#103×C53—21no—
17C2×#102×C53—21no—
18C2×#102×C53—21no—
19C2×#102×C53—21no—
20C2×C4×C8×C53C2211yescharacteristic
21C53×#384C2211yescharacteristic
22C53×#340—21no—
23C53×#336—21no—
24C53×#336—21no—
25C53×#334—22no—
26C53×#331—22no—
27C22×Q8×C53D411yescharacteristic
28C22×D4×C53—21no—
29C22×D4×C53—21no—
30C22×D4×C53—21no—
31C2×SD16×C53—24no—
32C2×SD16×C53—42no—
33C2×SD16×C53—42no—
34C22×C8×C53—21no—
35C22×C8×C53—21no—
36C22×C8×C53—21no—
37C22×C8×C53D411yescharacteristic
38C22×C8×C53D411yescharacteristic
39#127×C53—21no—
40#127×C53—21no—
41#127×C53—21no—
42#127×C53D412yes—
43C4×Q8×C53—21no—
44C4×Q8×C53—21no—
45C4×Q8×C53—21no—
46C4×Q8×C53—21no—
47C2×C4⋊C4×C53—21no—
48C2×C4⋊C4×C53—21no—
49C2×C4⋊C4×C53—21no—
50C2×C4⋊C4×C53—21no—
51C2×C4⋊C4×C53D411yescharacteristic
52C2×C42×C53—21no—
53C2×C42×C53C2311yescharacteristic
54C4⋊C8×C53—21no—
55C4⋊C8×C53—21no—
56C4⋊C8×C53—21no—
57C4⋊C8×C53—21no—
58C4⋊C8×C53—21no—
59C4⋊C8×C53D412yes—
60#103×C53—42no—
61#102×C53—24no—
62#102×C53—42no—
63#102×C53—42no—
64C4×C8×C53—21no—
65C4×C8×C53—21no—
66C24×C53—41no—
67C2×Q8×C53—21no—
68C2×Q8×C53—21no—
69C2×Q8×C53—21no—
70C2×Q8×C53—21no—
71C2×Q8×C53—21no—
72C2×Q8×C53SD1612yes—
73C2×D4×C53—22no—
74C2×D4×C53—22no—
75C2×D4×C53—22no—
76C2×D4×C53—41no—
77C2×D4×C53—41no—
78C2×D4×C53—41no—
79C2×D4×C53—41no—
80C2×D4×C53—41no—
81C2×D4×C53—41no—
82C2×D4×C53—41no—
83C2×D4×C53—41no—
84C2×D4×C53—41no—
85C2×D4×C53—41no—
86C2×D4×C53—41no—
87C2×D4×C53—81no—
88C2×D4×C53—81no—
89C22×C4×C53—21no—
90C22×C4×C53—21no—
91C22×C4×C53—41no—
92C22×C4×C53C2×D411yescharacteristic
93C22×C4×C53C2×D411yescharacteristic
94C22×C4×C53#4111yescharacteristic
95SD16×C53—48no—
96C2×C8×C53—21no—
97C2×C8×C53—21no—
98C2×C8×C53—22no—
99C2×C8×C53—21no—
100C2×C8×C53—21no—
101C2×C8×C53—21no—
102C2×C8×C53—41no—
103C2×C8×C53—41no—
104C2×C8×C53—41no—
105C2×C8×C53—41no—
106C2×C8×C53—41no—
107C2×C8×C53—41no—
108C2×C8×C53—41no—
109C2×C8×C53—41no—
110C2×C8×C53SD1612yescomplemented
111C4⋊C4×C53—21no—
112C4⋊C4×C53—21no—
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—81no—
120C42×C53—41no—
121C42×C53—41no—
122C42×C53C2×D411yescharacteristic
123C42×C53C2×D411yescharacteristic
124C42×C53#4111yescharacteristic
125C42×C53#4111yescharacteristic
126C23×C53—42no—
127C23×C53—81no—
128C23×C53—81no—
129C23×C53—81no—
130C23×C53—81no—
131C23×C53—81no—
132C23×C53—81no—
133C23×C53#12111yescharacteristic
134Q8×C53—22no—
135Q8×C53—22no—
136Q8×C53—41no—
137Q8×C53—41no—
138D4×C53—42no—
139D4×C53—42no—
140D4×C53—42no—
141D4×C53—42no—
142D4×C53—82no—
143D4×C53—82no—
144D4×C53—81no—
145D4×C53—81no—
146D4×C53—81no—
147D4×C53—81no—
148C2×C4×C53—21no—
149C2×C4×C53—21no—
150C2×C4×C53—22no—
151C2×C4×C53—41no—
152C2×C4×C53—41no—
153C2×C4×C53—41no—
154C2×C4×C53—41no—
155C2×C4×C53—41no—
156C2×C4×C53—81no—
157C2×C4×C53—81no—
158C2×C4×C53—81no—
159C2×C4×C53#12011yescharacteristic
160C2×C4×C53#12111yescharacteristic
161C2×C4×C53#12111yescharacteristic
162C2×C4×C53#12311yescharacteristic
163C2×C4×C53#12311yescharacteristic
164C2×C4×C53#12411yescharacteristic
165C2×C4×C53C2×SD1611yescharacteristic
166C2×C4×C53C2×SD1611yescharacteristic
167C2×C4×C53#13511yescharacteristic
168C2×C4×C53#13511yescharacteristic
169C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C53#13711yescharacteristic
173C8×C53—22no—
174C8×C53—42no—
175C8×C53—41no—
176C8×C53—81no—
177C8×C53—81no—
178#10475C5311yesmaximal, characteristic, direct product factor, Sylow
179C22×C53—82no—
180C22×C53—82no—
181C22×C53—82no—
182C22×C53—161no—
183C22×C53—161no—
184C22×C53—161no—
185C22×C53—161no—
186C22×C53#39411yescharacteristic
187C22×C53#46011yescharacteristic
188C22×C53#46411yescharacteristic
189C22×C53#46511yescharacteristic
190C22×C53#46911yescharacteristic
191C22×C53#47111yescharacteristic
192C22×C53#47211yescharacteristic
193C4×C53—21no—
194C4×C53—21no—
195C4×C53—42no—
196C4×C53—81no—
197C4×C53—161no—
198C4×C53#44911yescharacteristic
199C4×C53#45011yescharacteristic
200C4×C53#46111yescharacteristic
201C4×C53#46311yescharacteristic
202C4×C53#46511yescharacteristic
203C4×C53#46811yescharacteristic
204C4×C53#48111yescharacteristic
205C4×C53#48211yescharacteristic
206C2×#460C2×C5311yescharacteristic
207#1984C2×C5311yescharacteristic, complemented
208#1957C2×C5311yescharacteristic
209#1803C2×C5311yescharacteristic, complemented
210C2×#334C2×C5311yescharacteristic, complemented
211C2×#331C2×C5311yescharacteristic
212#1296C2×C5311yescharacteristic, complemented
213C2×C53—162no—
214C2×C53#166611yescharacteristic
215C2×C53#167811yescharacteristic
216C2×C53#168811yescharacteristic
217C2×C53#170211yescharacteristic
218C2×C53#203411yescharacteristic
219C2×C53#205111yescharacteristic
220C2×C53#205511yescharacteristic
221C22×SD16—21no—
222C2×#127C22×C5311yescharacteristic
223C2×C4×Q8C22×C5311yescharacteristic
224#460—22no—
225#460—22no—
226C2×C4⋊C8C22×C5311yescharacteristic
227C2×C4⋊C8C22×C5311yescharacteristic
228C2×C4⋊C8C22×C5311yescharacteristic
229C2×#103—21no—
230C2×#102—21no—
231C2×#102—21no—
232C2×#102—21no—
233C2×C4×C8C22×C5311yescharacteristic
234#384C22×C5311yescharacteristic
235#340—21no—
236#336—21no—
237#336—21no—
238#334—22no—
239#331—22no—
240C53#1047511yescharacteristic, direct product factor, Sylow
241C22×Q8D4×C5311yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C2×SD16—24no—
246C2×SD16—42no—
247C2×SD16—42no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8D4×C5311yescharacteristic
252C22×C8D4×C5311yescharacteristic
253#127—21no—
254#127—21no—
255#127—21no—
256#127D4×C5312yes—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C5311yescharacteristic
266C2×C42—21no—
267C2×C42C23×C5311yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C5312yes—
274#103—42no—
275#102—24no—
276#102—42no—
277#102—42no—
278C4×C8—21no—
279C4×C8—21no—
280C24—41no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8SD16×C5312yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—81no—
302C2×D4—81no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4C2×D4×C5311yescharacteristic
307C22×C4C2×D4×C5311yescharacteristic
308C22×C4#41×C5311yescharacteristic
309SD16—48no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8SD16×C5312yescomplemented
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42C2×D4×C5311yescharacteristic
337C42C2×D4×C5311yescharacteristic
338C42#41×C5311yescharacteristic
339C42#41×C5311yescharacteristic
340C23—42no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23#121×C5311yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#120×C5311yescharacteristic
374C2×C4#121×C5311yescharacteristic
375C2×C4#121×C5311yescharacteristic
376C2×C4#123×C5311yescharacteristic
377C2×C4#123×C5311yescharacteristic
378C2×C4#124×C5311yescharacteristic
379C2×C4C2×SD16×C5311yescharacteristic
380C2×C4C2×SD16×C5311yescharacteristic
381C2×C4#135×C5311yescharacteristic
382C2×C4#135×C5311yescharacteristic
383C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
384C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
385C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
386C2×C4#137×C5311yescharacteristic
387C8—22no—
388C8—42no—
389C8—41no—
390C8—81no—
391C8—81no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—161no—
396C22—161no—
397C22—161no—
398C22—161no—
399C22C53×#39411yescharacteristic
400C22C53×#46011yescharacteristic
401C22C53×#46411yescharacteristic
402C22C53×#46511yescharacteristic
403C22C53×#46911yescharacteristic
404C22C53×#47111yescharacteristic
405C22C53×#47211yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4C53×#44911yescharacteristic
412C4C53×#45011yescharacteristic
413C4C53×#46111yescharacteristic
414C4C53×#46311yescharacteristic
415C4C53×#46511yescharacteristic
416C4C53×#46811yescharacteristic
417C4C53×#48111yescharacteristic
418C4C53×#48211yescharacteristic
419C2—162no—
420C2C53×#166611yescharacteristic
421C2C53×#167811yescharacteristic
422C2C53×#168811yescharacteristic
423C2C53×#170211yescharacteristic
424C2C53×#203411yescharacteristic
425C2C53×#205111yescharacteristic
426C2C53×#205511yescharacteristic
subgroupG/H
center, socleC23×C53#121
commutator, Frattini, cosocleC2×C42C23×C53
prime radicalC2×#127×C53C22
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×#1984C2semidirect
4. C53×#1803C2semidirect
5. C2×C53×#334C2semidirect
7. C53×#1296C2semidirect
110. C2×C8×C53SD16semidirect
178. #10475C53direct (N × H)
207. #1984C2×C53semidirect
209. #1803C2×C53semidirect
210. C2×#334C2×C53semidirect
212. #1296C2×C53semidirect
240. C53#10475direct (N × H)
324. C2×C8SD16×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#4602
C53×#19842
C53×#19572
C53×#18032
C2×C53×#3342
C2×C53×#3312
C53×#12962
#1047553