Finite Group Databasebeta

← C53×#7693 #27215205

Subgroups — C53×#7693 #27215205

Order 13568.

390 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#2863C211yesmaximal, characteristic
2C53×#1745C211yesmaximal, characteristic
3C53×#1744C211yesmaximal, characteristic
4C53×#1272C212yesmaximal
5C53×#1271C212yesmaximal
6C2×#97×C53—21no—
7C2×C4×C8×C53—21no—
8C53×#391C411yescharacteristic
9C53×#391C411yescharacteristic
10C53×#391C2211yescharacteristic
11C53×#389C411yescharacteristic
12C53×#389C411yescharacteristic
13C53×#389C2211yescharacteristic
14C53×#387—21no—
15C53×#387—21no—
16C53×#387—21no—
17C53×#383—21no—
18C43×C53C2211yescharacteristic
19C53×#336—21no—
20C53×#336—21no—
21C53×#336C2212yes—
22C53×#336C2212yes—
23C22×Q8×C53C2×C411yescharacteristic
24C22×C8×C53—22no—
25C22×C8×C53—22no—
26C2×C4⋊C4×C53—21no—
27C2×C4⋊C4×C53—21no—
28C2×C4⋊C4×C53—21no—
29C2×C4⋊C4×C53C2×C411yescharacteristic
30C2×C4⋊C4×C53C2×C411yescharacteristic
31C2×C4⋊C4×C53C2×C411yescharacteristic
32C2×C42×C53C2×C411yescharacteristic
33C2×C42×C53C2×C411yescharacteristic
34C2×C42×C53D411yescharacteristic
35C2×C42×C53D411yescharacteristic
36C2×C42×C53D411yescharacteristic
37C2×C42×C53D411yescharacteristic
38C2×C42×C53C2311yescharacteristic
39#97×C53—24no—
40C4×C8×C53—24no—
41#95×C53—21no—
42#95×C53—21no—
43#95×C53—21no—
44#95×C53—21no—
45#95×C53—21no—
46#95×C53—21no—
47#95×C53—21no—
48#95×C53—21no—
49#95×C53—21no—
50C2×Q8×C53—22no—
51C2×Q8×C53—41no—
52C2×Q8×C53—41no—
53C22×C4×C53—21no—
54C22×C4×C53—21no—
55C22×C4×C53—21no—
56C22×C4×C53—21no—
57C22×C4×C53C22⋊C411yescharacteristic
58C22×C4×C53C22⋊C411yescharacteristic
59C22×C4×C53C22⋊C411yescharacteristic
60C22×C4×C53C22⋊C411yescharacteristic
61C22×C4×C53C22×C411yescharacteristic
62C22×C4×C53C2×D411yescharacteristic
63C22×C4×C53C2×D411yescharacteristic
64C2×C8×C53—24no—
65C2×C8×C53—24no—
66C2×C8×C53—42no—
67C2×C8×C53—42no—
68C2×C8×C53—42no—
69C2×C8×C53—42no—
70C4⋊C4×C53—22no—
71C4⋊C4×C53—41no—
72C4⋊C4×C53—41no—
73C4⋊C4×C53—42no—
74C4⋊C4×C53—42no—
75C4⋊C4×C53—42no—
76C42×C53—22no—
77C42×C53—22no—
78C42×C53—22no—
79C42×C53—22no—
80C42×C53—22no—
81C42×C53—41no—
82C42×C53—41no—
83C23×C53C2×C22⋊C411yescharacteristic
84Q8×C53—82no—
85C2×C4×C53—21no—
86C2×C4×C53—21no—
87C2×C4×C53—21no—
88C2×C4×C53—21no—
89C2×C4×C53—21no—
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—21no—
93C2×C4×C53—21no—
94C2×C4×C53—21no—
95C2×C4×C53—21no—
96C2×C4×C53—21no—
97C2×C4×C53—21no—
98C2×C4×C53—21no—
99C2×C4×C53—21no—
100C2×C4×C53—21no—
101C2×C4×C53—41no—
102C2×C4×C53—41no—
103C2×C4×C53—41no—
104C2×C4×C53—41no—
105C2×C4×C53—41no—
106C2×C4×C53—41no—
107C2×C4×C53—41no—
108C2×C4×C53—41no—
109C2×C4×C53—41no—
110C2×C4×C53—41no—
111C2×C4×C53—41no—
112C2×C4×C53—41no—
113C2×C4×C53#10412yes—
114C2×C4×C53#10412yes—
115C2×C4×C53#13112yes—
116C2×C4×C53#13512yes—
117C2×C4×C53#13712yes—
118C8×C53—44no—
119C8×C53—44no—
120#7693C5311yesmaximal, characteristic, direct product factor, Sylow
121C22×C53#40811yescharacteristic
122C22×C53#41011yescharacteristic
123C22×C53#41311yescharacteristic
124C22×C53#41611yescharacteristic
125C22×C53#41911yescharacteristic
126C22×C53C2×#10411yescharacteristic
127C22×C53C2×#10411yescharacteristic
128C4×C53—22no—
129C4×C53—22no—
130C4×C53—22no—
131C4×C53—22no—
132C4×C53—22no—
133C4×C53—41no—
134C4×C53—41no—
135C4×C53—81no—
136C4×C53—81no—
137C4×C53—81no—
138C4×C53—81no—
139#2863C2×C5311yescharacteristic
140#1745C2×C5311yescharacteristic
141#1744C2×C5311yescharacteristic
142#1272C2×C5312yes—
143#1271C2×C5312yes—
144C2×C53#147311yescharacteristic
145C2×C53#148511yescharacteristic
146C2×C53#149411yescharacteristic
147C2×C53#150011yescharacteristic
148C2×C53#150611yescharacteristic
149C2×C53#152411yescharacteristic
150C2×C53#155411yescharacteristic
151C2×#97—21no—
152C2×C4×C8—21no—
153#391C4×C5311yescharacteristic
154#391C4×C5311yescharacteristic
155#391C22×C5311yescharacteristic
156#389C4×C5311yescharacteristic
157#389C4×C5311yescharacteristic
158#389C22×C5311yescharacteristic
159#387—21no—
160#387—21no—
161#387—21no—
162#383—21no—
163C43C22×C5311yescharacteristic
164#336—21no—
165#336—21no—
166#336C22×C5312yes—
167#336C22×C5312yes—
168C53#769311yescharacteristic, direct product factor, Sylow
169C22×Q8C2×C4×C5311yescharacteristic
170C22×C8—22no—
171C22×C8—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C2×C4×C5311yescharacteristic
176C2×C4⋊C4C2×C4×C5311yescharacteristic
177C2×C4⋊C4C2×C4×C5311yescharacteristic
178C2×C42C2×C4×C5311yescharacteristic
179C2×C42C2×C4×C5311yescharacteristic
180C2×C42D4×C5311yescharacteristic
181C2×C42D4×C5311yescharacteristic
182C2×C42D4×C5311yescharacteristic
183C2×C42D4×C5311yescharacteristic
184C2×C42C23×C5311yescharacteristic
185#97—24no—
186C4×C8—24no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C22⋊C4×C5311yescharacteristic
204C22×C4C22⋊C4×C5311yescharacteristic
205C22×C4C22⋊C4×C5311yescharacteristic
206C22×C4C22⋊C4×C5311yescharacteristic
207C22×C4C22×C4×C5311yescharacteristic
208C22×C4C2×D4×C5311yescharacteristic
209C22×C4C2×D4×C5311yescharacteristic
210C2×C8—24no—
211C2×C8—24no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—22no—
226C42—22no—
227C42—41no—
228C42—41no—
229C23C2×C22⋊C4×C5311yescharacteristic
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4#104×C5312yes—
260C2×C4#104×C5312yes—
261C2×C4#131×C5312yes—
262C2×C4#135×C5312yes—
263C2×C4#137×C5312yes—
264C8—44no—
265C8—44no—
266C22C53×#40811yescharacteristic
267C22C53×#41011yescharacteristic
268C22C53×#41311yescharacteristic
269C22C53×#41611yescharacteristic
270C22C53×#41911yescharacteristic
271C22C2×#104×C5311yescharacteristic
272C22C2×#104×C5311yescharacteristic
273C4—22no—
274C4—22no—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—41no—
279C4—41no—
280C4—81no—
281C4—81no—
282C4—81no—
283C4—81no—
284C2C53×#147311yescharacteristic
285C2C53×#148511yescharacteristic
286C2C53×#149411yescharacteristic
287C2C53×#150011yescharacteristic
288C2C53×#150611yescharacteristic
289C2C53×#152411yescharacteristic
290C2C53×#155411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C53C2×C22⋊C4
commutatorC22×C4C22×C4×C53
Frattini, cosocleC2×C42C23×C53
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C53 ◁ C43×C53 ◁ G

Complements

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

NH ≅ G/Ntype
120. #7693C53direct (N × H)
168. C53#7693direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#28632
C53×#17452
C53×#17442
C53×#12722
C53×#12712
#769353