Finite Group Databasebeta

← C53×#11571 #27219083

Subgroups — C53×#11571 #27219083

Order 13568.

350 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#2565C211yesmaximal, characteristic
2C53×#1467C211yesmaximal, characteristic
3C53×#1461C211yesmaximal, characteristic
4C53×#1325C212yesmaximal
5C53×#1324C212yesmaximal
6C2×#125×C53C411yescharacteristic
7C2×C4×Q8×C53C2211yescharacteristic
8C53×#432—21no—
9C53×#431—21no—
10C53×#398—21no—
11C53×#398—21no—
12C53×#391C411yescharacteristic
13C53×#391C411yescharacteristic
14C53×#387—21no—
15C53×#387—21no—
16C53×#384C2211yescharacteristic
17C53×#382C2211yescharacteristic
18C4×C4⋊C4×C53C411yescharacteristic
19C53×#324—21no—
20C53×#324—21no—
21C53×#324C2212yes—
22C53×#324C2212yes—
23C22×Q8×C53C2×C411yescharacteristic
24#125×C53—41no—
25#125×C53—41no—
26C4×Q8×C53—41no—
27C4×Q8×C53—41no—
28C2×C4⋊C4×C53—21no—
29C2×C4⋊C4×C53—21no—
30C2×C4⋊C4×C53—21no—
31C2×C4⋊C4×C53—21no—
32C2×C4⋊C4×C53—21no—
33C2×C4⋊C4×C53C2×C411yescharacteristic
34C2×C4⋊C4×C53C2×C411yescharacteristic
35C2×C4⋊C4×C53D411yescharacteristic
36C2×C4⋊C4×C53D411yescharacteristic
37C2×C4⋊C4×C53C2311yescharacteristic
38C2×C42×C53C2×C411yescharacteristic
39C2×C42×C53C2×C411yescharacteristic
40C2×C42×C53C2×C411yescharacteristic
41C2×C42×C53D411yescharacteristic
42C2×C42×C53D411yescharacteristic
43C4⋊C8×C53—41no—
44C4⋊C8×C53—41no—
45C22⋊C8×C53—22no—
46C22⋊C8×C53—22no—
47#97×C53—41no—
48C4×C8×C53—41no—
49#95×C53—21no—
50#95×C53—21no—
51#95×C53—21no—
52#95×C53—21no—
53#95×C53—21no—
54#95×C53—21no—
55#95×C53—21no—
56C2×Q8×C53—22no—
57C2×Q8×C53—22no—
58C2×Q8×C53—41no—
59C22×C4×C53—21no—
60C22×C4×C53—21no—
61C22×C4×C53—21no—
62C22×C4×C53—21no—
63C22×C4×C53C22⋊C411yescharacteristic
64C22×C4×C53C22⋊C411yescharacteristic
65C22×C4×C53C22⋊C411yescharacteristic
66C22×C4×C53C22⋊C411yescharacteristic
67C22×C4×C53C22×C411yescharacteristic
68C22×C4×C53C2×D411yescharacteristic
69C22×C4×C53C2×D411yescharacteristic
70C2×C8×C53—42no—
71C2×C8×C53—42no—
72C4⋊C4×C53—41no—
73C4⋊C4×C53—41no—
74C4⋊C4×C53—41no—
75C4⋊C4×C53—42no—
76C4⋊C4×C53—42no—
77C4⋊C4×C53—42no—
78C4⋊C4×C53—42no—
79C4⋊C4×C53—41no—
80C4⋊C4×C53—41no—
81C4⋊C4×C53—41no—
82C4⋊C4×C53—41no—
83C42×C53—21no—
84C42×C53—21no—
85C42×C53—21no—
86C42×C53—21no—
87C42×C53—21no—
88C42×C53—21no—
89C42×C53—22no—
90C42×C53—22no—
91C23×C53C2×C22⋊C411yescharacteristic
92Q8×C53—44no—
93C2×C4×C53—21no—
94C2×C4×C53—21no—
95C2×C4×C53—21no—
96C2×C4×C53—21no—
97C2×C4×C53—22no—
98C2×C4×C53—21no—
99C2×C4×C53—21no—
100C2×C4×C53—21no—
101C2×C4×C53—21no—
102C2×C4×C53—21no—
103C2×C4×C53—21no—
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—42no—
112C2×C4×C53—41no—
113C2×C4×C53—41no—
114C2×C4×C53—41no—
115C2×C4×C53—41no—
116C2×C4×C53—41no—
117C2×C4×C53—41no—
118C2×C4×C53#9911yescharacteristic
119C2×C4×C53#9911yescharacteristic
120C2×C4×C53#10112yes—
121C2×C4×C53#13112yes—
122C8×C53—82no—
123C8×C53—82no—
124#11571C5311yesmaximal, characteristic, direct product factor, Sylow
125C22×C53—21no—
126C22×C53—21no—
127C22×C53#40811yescharacteristic
128C22×C53C2×#9911yescharacteristic
129C22×C53C2×#10111yescharacteristic
130C4×C53—21no—
131C4×C53—21no—
132C4×C53—22no—
133C4×C53—22no—
134C4×C53—42no—
135C4×C53—41no—
136C4×C53—41no—
137C4×C53—41no—
138C4×C53—41no—
139C4×C53—81no—
140C4×C53—81no—
141C4×C53—81no—
142#2565C2×C5311yescharacteristic
143#1467C2×C5311yescharacteristic
144#1461C2×C5311yescharacteristic
145#1325C2×C5312yes—
146#1324C2×C5312yes—
147C2×C53—21no—
148C2×C53—21no—
149C2×C53#147211yescharacteristic
150C2×C53#212611yescharacteristic
151C2×C53#213311yescharacteristic
152C2×#125C4×C5311yescharacteristic
153C2×C4×Q8C22×C5311yescharacteristic
154#432—21no—
155#431—21no—
156#398—21no—
157#398—21no—
158#391C4×C5311yescharacteristic
159#391C4×C5311yescharacteristic
160#387—21no—
161#387—21no—
162#384C22×C5311yescharacteristic
163#382C22×C5311yescharacteristic
164C4×C4⋊C4C4×C5311yescharacteristic
165#324—21no—
166#324—21no—
167#324C22×C5312yes—
168#324C22×C5312yes—
169C53#1157111yescharacteristic, direct product factor, Sylow
170C22×Q8C2×C4×C5311yescharacteristic
171#125—41no—
172#125—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×C4×C5311yescharacteristic
181C2×C4⋊C4C2×C4×C5311yescharacteristic
182C2×C4⋊C4D4×C5311yescharacteristic
183C2×C4⋊C4D4×C5311yescharacteristic
184C2×C4⋊C4C23×C5311yescharacteristic
185C2×C42C2×C4×C5311yescharacteristic
186C2×C42C2×C4×C5311yescharacteristic
187C2×C42C2×C4×C5311yescharacteristic
188C2×C42D4×C5311yescharacteristic
189C2×C42D4×C5311yescharacteristic
190C4⋊C8—41no—
191C4⋊C8—41no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194#97—41no—
195C4×C8—41no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4C22⋊C4×C5311yescharacteristic
211C22×C4C22⋊C4×C5311yescharacteristic
212C22×C4C22⋊C4×C5311yescharacteristic
213C22×C4C22⋊C4×C5311yescharacteristic
214C22×C4C22×C4×C5311yescharacteristic
215C22×C4C2×D4×C5311yescharacteristic
216C22×C4C2×D4×C5311yescharacteristic
217C2×C8—42no—
218C2×C8—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—22no—
237C42—22no—
238C23C2×C22⋊C4×C5311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
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—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#99×C5311yescharacteristic
266C2×C4#99×C5311yescharacteristic
267C2×C4#101×C5312yes—
268C2×C4#131×C5312yes—
269C8—82no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22C53×#40811yescharacteristic
274C22C2×#99×C5311yescharacteristic
275C22C2×#101×C5311yescharacteristic
276C4—22no—
277C4—22no—
278C4—21no—
279C4—21no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2C53×#147211yescharacteristic
291C2C53×#212611yescharacteristic
292C2C53×#213311yescharacteristic
subgroupG/H
center, socleC22×C53C2×#99
commutatorC22×C4C22×C4×C53
Frattini, cosocleC2×C4⋊C4C23×C53
prime radicalC23×C53C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×C4×Q8×C53 ◁ G

Complements

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

NH ≅ G/Ntype
124. #11571C53direct (N × H)
169. C53#11571direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#25652
C53×#14672
C53×#14612
C53×#13252
C53×#13242
#1157153