Finite Group Databasebeta

← D53×#1324 #27293241

Subgroups — D53×#1324 #27293241

Order 13568.

510 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#382×D53C211yesmaximal, characteristic
2#324×D53C212yesmaximal
3#20272659C211yesmaximal, characteristic, complemented
4#20272658C212yesmaximal, complemented
5C53×#1324C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D53C411yescharacteristic
7C2×C4⋊C4×D53C2211yescharacteristic
8C2×C42×D53C411yescharacteristic
9C22⋊C8×D53—22no—
10#16810489C411yescharacteristic
11#16810488C411yescharacteristic
12#16810488C2211yescharacteristic
13#16810487—22no—
14#95×D53—22no—
15#16810349C2212yes—
16#16810348—22no—
17C53×#382C2211yescharacteristic
18C53×#324C2212yes—
19C22×C4×D53—21no—
20C22×C4×D53—21no—
21C22×C4×D53C2×C411yescharacteristic
22C22×C4×D53D412yes—
23C2×C8×D53—42no—
24C2×C4⋊Dic53C2×C411yescharacteristic
25C2×C4⋊Dic53C2×C411yescharacteristic
26C2×#11719919—21no—
27C2×#11719919D412yes—
28C4⋊C4×D53—41no—
29C4⋊C4×D53—41no—
30C4⋊C4×D53—41no—
31C4⋊C4×D53—41no—
32C2×C4×Dic53—21no—
33C2×C4×Dic53C2×C411yescharacteristic
34C42×D53—22no—
35C42×D53C814yescomplemented
36C22⋊#88322—22no—
37#13133129—42no—
38#13133124—22no—
39#13133124—22no—
40#13133124—22no—
41C2×C4⋊C4×C53C2×C411yescharacteristic
42C2×C4⋊C4×C53C2311yescharacteristic
43C2×C42×C53C2×C411yescharacteristic
44C22⋊C8×C53—22no—
45#95×C53—22no—
46C23×D53C22⋊C411yescharacteristic
47C22×C4×C53—21no—
48C22×C4×C53—21no—
49C22×C4×C53C22×C411yescharacteristic
50C22×C4×C53C2×D412yes—
51C22×Dic53—21no—
52C22×Dic53—21no—
53C22×Dic53C22⋊C411yescharacteristic
54C22×Dic53C22⋊C412yes—
55C2×C4×D53—21no—
56C2×C4×D53—21no—
57C2×C4×D53—22no—
58C2×C4×D53—24no—
59C2×C4×D53—22no—
60C2×C4×D53—22no—
61C2×C4×D53—42no—
62C2×C4×D53—42no—
63C2×C4×D53—44no—
64C2×C4×D53—44no—
65C2×C4×D53—41no—
66C2×C4×D53—41no—
67C2×C4×D53C2×C812yes—
68C2×C4×D53M1612yes—
69C2×C8×C53—42no—
70C4⋊C4×C53—41no—
71C4⋊C4×C53—41no—
72C42×C53—21no—
73C42×C53C2×C812yescomplemented
74C4⋊Dic53—41no—
75C4⋊Dic53—41no—
76#11719919—42no—
77#11719919—42no—
78C4×Dic53—21no—
79C4×Dic53—24no—
80C4×Dic53C2×C812yescomplemented
81C2×#88322—42no—
82C8×D53—84no—
83C23×C53C2×C22⋊C411yescharacteristic
84C22×D53—22no—
85C22×D53—22no—
86C22×D53C22⋊C812yes—
87C22×D53#9911yescharacteristic
88C22×D53#9911yescharacteristic
89C22×D53#10112yes—
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—22no—
93C2×C4×C53—22no—
94C2×C4×C53—41no—
95C2×C4×C53—41no—
96C2×C4×C53—42no—
97C2×C4×C53—42no—
98C2×C4×C53—41no—
99C2×C4×C53C22×C811yescharacteristic
100C2×C4×C53C2×M1611yescharacteristic
101C2×Dic53—21no—
102C2×Dic53—21no—
103C2×Dic53—22no—
104C2×Dic53—22no—
105C2×Dic53—41no—
106C2×Dic53—41no—
107C2×Dic53—42no—
108C2×Dic53—42no—
109C2×Dic53—41no—
110C2×Dic53C22⋊C812yes—
111C4×D53—22no—
112C4×D53—22no—
113C4×D53—22no—
114C4×D53—22no—
115C4×D53—48no—
116C4×D53—44no—
117C4×D53—82no—
118C4×D53—82no—
119C4×D53—82no—
120C8×C53—82no—
121#88322—82no—
122C2×#1324—531nomaximal, Sylow
123C22×C53—21no—
124C22×C53—21no—
125C22×C53C2×C22⋊C811yescharacteristic
126C22×C53C2×#9911yescharacteristic
127C22×C53C2×#10111yescharacteristic
128C2×D53—21no—
129C2×D53—21no—
130C2×D53—24no—
131C2×D53—24no—
132C2×D53#32412yes—
133C2×D53#32412yes—
134C2×D53#35412yes—
135C2×D53#35512yes—
136C4×C53—21no—
137C4×C53—21no—
138C4×C53—42no—
139C4×C53—42no—
140C4×C53—81no—
141Dic53—22no—
142Dic53—42no—
143Dic53—42no—
144Dic53—81no—
145C2×#382—531no—
146C2×#324—532no—
147#1324—531no—
148#1324—532no—
149#1324D5311yescharacteristic, direct product factor
150C2×C53—21no—
151C2×C53—21no—
152C2×C53C2×#32411yescharacteristic
153C2×C53C2×#35411yescharacteristic
154C2×C53C2×#35511yescharacteristic
155D53—22no—
156D53#132414yesdirect product factor
157C22×C4⋊C4—531no—
158C22×C4⋊C4—531no—
159C22×C42—531no—
160C2×C22⋊C8—1062no—
161#382—531no—
162#382—531no—
163#382—531no—
164#382—1062no—
165#382C2×D5311yescharacteristic
166C2×#95—1062no—
167#324—532no—
168#324—1062no—
169#324C2×D5312yes—
170C53C2×#132411yescharacteristic, complemented, Sylow
171C23×C4—531no—
172C23×C4—532no—
173C23×C4—1061no—
174C23×C4—1061no—
175C22×C8—2122no—
176C2×C4⋊C4—531no—
177C2×C4⋊C4—532no—
178C2×C4⋊C4—531no—
179C2×C4⋊C4—1061no—
180C2×C4⋊C4—2121no—
181C2×C4⋊C4—2121no—
182C2×C4⋊C4—2121no—
183C2×C4⋊C4—2121no—
184C2×C4⋊C4C4×D5311yescharacteristic
185C2×C4⋊C4C22×D5311yescharacteristic
186C2×C42—531no—
187C2×C42—534no—
188C2×C42—1062no—
189C2×C42—1061no—
190C2×C42C4×D5311yescharacteristic
191C22⋊C8—22no—
192C22⋊C8—1062no—
193C22⋊C8—2122no—
194#95—22no—
195#95—1062no—
196#95—1062no—
197#95—1062no—
198C24—531no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—531no—
202C22×C4—532no—
203C22×C4—532no—
204C22×C4—532no—
205C22×C4—1061no—
206C22×C4—1061no—
207C22×C4—1062no—
208C22×C4—1062no—
209C22×C4—1064no—
210C22×C4—1062no—
211C22×C4—1061no—
212C22×C4—1061no—
213C22×C4—2121no—
214C22×C4—2121no—
215C22×C4—2124no—
216C22×C4—2124no—
217C22×C4—2122no—
218C22×C4—2122no—
219C22×C4C2×C4×D5311yescharacteristic
220C22×C4D4×D5312yes—
221C2×C8—42no—
222C2×C8—4244no—
223C2×C8—2122no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—2122no—
227C4⋊C4—2121no—
228C4⋊C4—2121no—
229C4⋊C4—2122no—
230C42—21no—
231C42—532no—
232C42—1064no—
233C42—1061no—
234C42C8×D5312yescomplemented
235C23—531no—
236C23—532no—
237C23—531no—
238C23—532no—
239C23—1062no—
240C23—1062no—
241C23C22⋊C4×D5311yescharacteristic
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—532no—
252C2×C4—1062no—
253C2×C4—1062no—
254C2×C4—1062no—
255C2×C4—1062no—
256C2×C4—1061no—
257C2×C4—1061no—
258C2×C4—1062no—
259C2×C4—1062no—
260C2×C4—4242no—
261C2×C4—4242no—
262C2×C4—4242no—
263C2×C4—2124no—
264C2×C4—2128no—
265C2×C4—2122no—
266C2×C4—2121no—
267C2×C4—2121no—
268C2×C4—2121no—
269C2×C4—2122no—
270C2×C4C2×C8×D5311yescharacteristic
271C2×C4M16×D5311yescharacteristic
272C8—82no—
273C8—4242no—
274C22—21no—
275C22—21no—
276C22—532no—
277C22—532no—
278C22—532no—
279C22—532no—
280C22—1064no—
281C22—1064no—
282C22—1061no—
283C22—1061no—
284C22C22⋊C8×D5311yescharacteristic
285C22#99×D5311yescharacteristic
286C22#101×D5311yescharacteristic
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—81no—
292C4—1062no—
293C4—4241no—
294C4—2122no—
295C4—2122no—
296C2—21no—
297C2—21no—
298C2—534no—
299C2—1062no—
300C2#324×D5311yescharacteristic
301C2#354×D5311yescharacteristic
302C2#355×D5311yescharacteristic
subgroupG/H
centerC22#99×D53
commutatorC2×C4×C53C22×C8
FrattiniC2×C4⋊C4C22×D53
FittingC53×#1324C2
socleC22×C53C2×#99
prime radicalC23×D53C22⋊C4
cosocleC2×C4⋊C4×C53C23
hypercenter#1324D53
hypocenterC53C2×#1324
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #20272659C2semidirect
4. #20272658C2semidirect
5. C53×#1324C2semidirect
35. C42×D53C8semidirect
73. C42×C53C2×C8semidirect
80. C4×Dic53C2×C8semidirect
149. #1324D53direct (N × H)
156. D53#1324direct (N × H)
170. C53C2×#1324semidirect
234. C42C8×D53semidirect

Maximal subgroups

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

subgroupindex
#382×D532
#324×D532
#202726592
#202726582
C53×#13242
C2×#132453