Finite Group Databasebeta

← C53×#10547 #27218059

Subgroups — C53×#10547 #27218059

Order 13568.

386 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3135C211yesmaximal, characteristic
2C53×#1940C211yesmaximal, characteristic, complemented
3C53×#1542C211yesmaximal, characteristic, complemented
4C53×#1540C211yesmaximal, characteristic
5C53×#1503C211yesmaximal, characteristic, complemented
6C53×#1502C211yesmaximal, characteristic
7C53×#1275C211yesmaximal, characteristic, complemented
8C53×#533C2211yescharacteristic
9C53×#532C2211yescharacteristic
10C53×#491—21no—
11C53×#490—21no—
12C53×#489—21no—
13C53×#489—21no—
14C53×#431C2211yescharacteristic
15C53×#431C2211yescharacteristic
16C2×C4⋊C8×C53—21no—
17C2×C4⋊C8×C53C2211yescharacteristic
18C53×#416—21no—
19C53×#416—21no—
20C2×#97×C53C2211yescharacteristic
21C4×C4⋊C4×C53C2211yescharacteristic
22C53×#336—21no—
23C53×#333—21no—
24C53×#332—21no—
25C53×#332—21no—
26C53×#331—21no—
27C53×#328—21no—
28C53×#328—21no—
29C53×#327—21no—
30C53×#327—21no—
31C2×#41×C53—21no—
32C22×C8×C53—21no—
33C22×C8×C53D411yescharacteristic
34C22×C8×C53D411yescharacteristic
35C4⋊Q8×C53D411yescharacteristic
36C4⋊Q8×C53D411yescharacteristic
37C4⋊Q8×C53D411yescharacteristic
38#127×C53D411yescharacteristic
39#125×C53—21no—
40#124×C53—21no—
41C22⋊Q8×C53—21no—
42C22⋊Q8×C53—21no—
43#121×C53—21no—
44#121×C53—21no—
45C4×Q8×C53—21no—
46C4×Q8×C53—21no—
47C4×D4×C53—21no—
48C4×D4×C53—21no—
49#117×C53—21no—
50C2×C4⋊C4×C53—21no—
51C2×C42×C53—21no—
52C2×C42×C53C2311yescharacteristic
53C4⋊C8×C53—21no—
54C4⋊C8×C53—21no—
55C4⋊C8×C53—21no—
56C4⋊C8×C53—21no—
57C4⋊C8×C53—42no—
58#103×C53—21no—
59#103×C53—21no—
60#103×C53—21no—
61#103×C53—21no—
62#102×C53—21no—
63#102×C53—21no—
64#102×C53—21no—
65#102×C53—21no—
66C22⋊C8×C53—21no—
67C22⋊C8×C53—21no—
68#97×C53—21no—
69#97×C53—21no—
70C4×C8×C53—21no—
71C4×C8×C53—21no—
72#95×C53D411yescharacteristic
73#95×C53D411yescharacteristic
74#41×C53—41no—
75#41×C53—41no—
76#41×C53—41no—
77#41×C53—41no—
78C2×Q8×C53—21no—
79C2×Q8×C53—21no—
80C2×Q8×C53—21no—
81C2×D4×C53—21no—
82C2×D4×C53—21no—
83C2×D4×C53—21no—
84C2×D4×C53—41no—
85C22×C4×C53—21no—
86C22×C4×C53—21no—
87C22×C4×C53—41no—
88C22×C4×C53C2×D411yescharacteristic
89C22×C4×C53C2×D411yescharacteristic
90C22×C4×C53#4111yescharacteristic
91C2×C8×C53—21no—
92C2×C8×C53—21no—
93C2×C8×C53—21no—
94C2×C8×C53—21no—
95C2×C8×C53—21no—
96C2×C8×C53—21no—
97C2×C8×C53—41no—
98C2×C8×C53—41no—
99C2×C8×C53—41no—
100C2×C8×C53—41no—
101C2×C8×C53—41no—
102C4⋊C4×C53—21no—
103C4⋊C4×C53—21no—
104C4⋊C4×C53—21no—
105C4⋊C4×C53—21no—
106C4⋊C4×C53—21no—
107C4⋊C4×C53—21no—
108C4⋊C4×C53—42no—
109C4⋊C4×C53—41no—
110C4⋊C4×C53—41no—
111C22⋊C4×C53—41no—
112C22⋊C4×C53—41no—
113C22⋊C4×C53—41no—
114C42×C53—41no—
115C42×C53—41no—
116C42×C53—41no—
117C42×C53C2×D411yescharacteristic
118C42×C53C2×D411yescharacteristic
119C42×C53#4111yescharacteristic
120C42×C53#4111yescharacteristic
121C23×C53—41no—
122C23×C53#12111yescharacteristic
123Q8×C53—41no—
124Q8×C53—41no—
125Q8×C53—81no—
126Q8×C53—81no—
127D4×C53—41no—
128D4×C53—41no—
129D4×C53—81no—
130D4×C53—81no—
131D4×C53—81no—
132D4×C53—81no—
133C2×C4×C53—22no—
134C2×C4×C53—41no—
135C2×C4×C53—41no—
136C2×C4×C53—41no—
137C2×C4×C53—41no—
138C2×C4×C53—41no—
139C2×C4×C53—41no—
140C2×C4×C53—41no—
141C2×C4×C53—41no—
142C2×C4×C53—41no—
143C2×C4×C53—41no—
144C2×C4×C53—81no—
145C2×C4×C53—81no—
146C2×C4×C53#12011yescharacteristic
147C2×C4×C53#12111yescharacteristic
148C2×C4×C53#12111yescharacteristic
149C2×C4×C53#12311yescharacteristic
150C2×C4×C53#12311yescharacteristic
151C2×C4×C53#12411yescharacteristic
152C2×C4×C53#13511yescharacteristic
153C2×C4×C53#13511yescharacteristic
154C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C53#13711yescharacteristic
156C8×C53—41no—
157C8×C53—41no—
158C8×C53—81no—
159C8×C53—81no—
160C8×C53—81no—
161#10547C5311yesmaximal, characteristic, direct product factor, Sylow
162C22×C53—21no—
163C22×C53—21no—
164C22×C53—81no—
165C22×C53—81no—
166C22×C53—81no—
167C22×C53#39411yescharacteristic
168C22×C53#46311yescharacteristic
169C22×C53#46411yescharacteristic
170C4×C53—21no—
171C4×C53—21no—
172C4×C53—21no—
173C4×C53—21no—
174C4×C53—42no—
175C4×C53—81no—
176C4×C53—81no—
177C4×C53—81no—
178C4×C53—81no—
179C4×C53#44911yescharacteristic
180C4×C53#45211yescharacteristic
181C4×C53#48811yescharacteristic
182C4×C53#48911yescharacteristic
183#3135C2×C5311yescharacteristic
184#1940C2×C5311yescharacteristic, complemented
185#1542C2×C5311yescharacteristic, complemented
186#1540C2×C5311yescharacteristic
187#1503C2×C5311yescharacteristic, complemented
188#1502C2×C5311yescharacteristic
189#1275C2×C5311yescharacteristic, complemented
190C2×C53—21no—
191C2×C53—21no—
192C2×C53—161no—
193C2×C53#204211yescharacteristic
194C2×C53#205011yescharacteristic
195C2×C53#205311yescharacteristic
196#533C22×C5311yescharacteristic
197#532C22×C5311yescharacteristic
198#491—21no—
199#490—21no—
200#489—21no—
201#489—21no—
202#431C22×C5311yescharacteristic
203#431C22×C5311yescharacteristic
204C2×C4⋊C8—21no—
205C2×C4⋊C8C22×C5311yescharacteristic
206#416—21no—
207#416—21no—
208C2×#97C22×C5311yescharacteristic
209C4×C4⋊C4C22×C5311yescharacteristic
210#336—21no—
211#333—21no—
212#332—21no—
213#332—21no—
214#331—21no—
215#328—21no—
216#328—21no—
217#327—21no—
218#327—21no—
219C53#1054711yescharacteristic, direct product factor, Sylow
220C2×#41—21no—
221C22×C8—21no—
222C22×C8D4×C5311yescharacteristic
223C22×C8D4×C5311yescharacteristic
224C4⋊Q8D4×C5311yescharacteristic
225C4⋊Q8D4×C5311yescharacteristic
226C4⋊Q8D4×C5311yescharacteristic
227#127D4×C5311yescharacteristic
228#125—21no—
229#124—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—21no—
233#121—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C5311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—42no—
247#103—21no—
248#103—21no—
249#103—21no—
250#103—21no—
251#102—21no—
252#102—21no—
253#102—21no—
254#102—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257#97—21no—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261#95D4×C5311yescharacteristic
262#95D4×C5311yescharacteristic
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4C2×D4×C5311yescharacteristic
278C22×C4C2×D4×C5311yescharacteristic
279C22×C4#41×C5311yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C42C2×D4×C5311yescharacteristic
307C42C2×D4×C5311yescharacteristic
308C42#41×C5311yescharacteristic
309C42#41×C5311yescharacteristic
310C23—41no—
311C23#121×C5311yescharacteristic
312Q8—41no—
313Q8—41no—
314Q8—81no—
315Q8—81no—
316D4—41no—
317D4—41no—
318D4—81no—
319D4—81no—
320D4—81no—
321D4—81no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#120×C5311yescharacteristic
336C2×C4#121×C5311yescharacteristic
337C2×C4#121×C5311yescharacteristic
338C2×C4#123×C5311yescharacteristic
339C2×C4#123×C5311yescharacteristic
340C2×C4#124×C5311yescharacteristic
341C2×C4#135×C5311yescharacteristic
342C2×C4#135×C5311yescharacteristic
343C2×C4AGL(1,ℤ/8)×C5311yescharacteristic
344C2×C4#137×C5311yescharacteristic
345C8—41no—
346C8—41no—
347C8—81no—
348C8—81no—
349C8—81no—
350C22—21no—
351C22—21no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22C53×#39411yescharacteristic
356C22C53×#46311yescharacteristic
357C22C53×#46411yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4C53×#44911yescharacteristic
368C4C53×#45211yescharacteristic
369C4C53×#48811yescharacteristic
370C4C53×#48911yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2C53×#204211yescharacteristic
375C2C53×#205011yescharacteristic
376C2C53×#205311yescharacteristic
subgroupG/H
centerC2×C4×C53#124
commutator, Frattini, cosocleC2×C42C23×C53
socleC22×C53#394
prime radicalC53×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C53 ◁ C2×C42×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C53×#1940C2semidirect
3. C53×#1542C2semidirect
5. C53×#1503C2semidirect
7. C53×#1275C2semidirect
161. #10547C53direct (N × H)
184. #1940C2×C53semidirect
185. #1542C2×C53semidirect
187. #1503C2×C53semidirect
189. #1275C2×C53semidirect
219. C53#10547direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#31352
C53×#19402
C53×#15422
C53×#15402
C53×#15032
C53×#15022
C53×#12752
#1054753