Finite Group Databasebeta

← D53⋊#1325 #28307963

Subgroups — D53⋊#1325 #28307963

Order 13568.

598 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 98 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
1D53⋊#324C212yesmaximal
2#20289658C212yesmaximal, complemented
3#20289657C212yesmaximal, complemented
4#384×D53C211yesmaximal, characteristic
5D53⋊(C22⋊C8)—22no—
6#16811469—22no—
7#16811468C2214yes—
8C2×C4⋊C4×D53—22no—
9C2×C4⋊C4×D53C411yescharacteristic
10C2×C4⋊C4×D53C2211yescharacteristic
11C2×C42×D53C411yescharacteristic
12#16810493C2211yescharacteristic
13#16810492—22no—
14#16810492C411yescharacteristic
15#16810492C2211yescharacteristic
16C53×#384C411yescharacteristic
17C2×D53⋊C8—42no—
18#13133274—42no—
19C22⋊#88324—24no—
20C22×C4×D53—21no—
21C22×C4×D53—21no—
22C22×C4×D53C2×C411yescharacteristic
23C22×C4×D53D412yes—
24C2×C4⋊Dic53—22no—
25C2×C4⋊Dic53C2×C411yescharacteristic
26C2×C4⋊Dic53C2311yescharacteristic
27C2×#11719919—22no—
28C2×#11719919—21no—
29C2×#11719919—22no—
30C2×#11719919D412yes—
31C4⋊C4×D53—41no—
32C4⋊C4×D53—41no—
33C4⋊C4×D53—48no—
34C4⋊C4×D53—41no—
35C4⋊C4×D53—41no—
36C2×C4×Dic53—21no—
37C2×C4×Dic53C2×C411yescharacteristic
38C42×D53—22no—
39C42×D53C814yescomplemented
40C2×C4⋊C4×C53—22no—
41C2×C4⋊C4×C53C2×C411yescharacteristic
42C2×C4⋊C4×C53C2×C411yescharacteristic
43C2×C42×C53C2×C411yescharacteristic
44C23×D53C22⋊C411yescharacteristic
45C22×C4×C53—21no—
46C22×C4×C53—21no—
47C22×C4×C53C22⋊C412yes—
48C22×C4×C53C22×C411yescharacteristic
49C22×Dic53—21no—
50C22×Dic53—21no—
51C22×Dic53C22⋊C411yescharacteristic
52C22×Dic53C2×D412yes—
53C2×C4×D53—24no—
54C2×C4×D53—24no—
55C2×C4×D53—24no—
56C2×C4×D53—21no—
57C2×C4×D53—21no—
58C2×C4×D53—22no—
59C2×C4×D53—22no—
60C2×C4×D53—22no—
61C2×C4×D53—44no—
62C2×C4×D53—44no—
63C2×C4×D53—41no—
64C2×C4×D53—41no—
65C2×C4×D53C2×C812yes—
66C2×C4×D53M1612yes—
67C2×#88324—44no—
68D53⋊C8—84no—
69C4⋊C4×C53—41no—
70C4⋊C4×C53—44no—
71C4⋊C4×C53—41no—
72C42×C53—21no—
73C42×C53C2×C812yescomplemented
74C4⋊Dic53—41no—
75C4⋊Dic53—44no—
76C4⋊Dic53—41no—
77#11719919—42no—
78#11719919—44no—
79#11719919—44no—
80#11719919—42no—
81C4×Dic53—21no—
82C4×Dic53—24no—
83C4×Dic53C2×C812yescomplemented
84C23×C53C2×C22⋊C411yescharacteristic
85C22×D53—22no—
86C22×D53—22no—
87C22×D53C22⋊C812yes—
88C22×D53#9911yescharacteristic
89C22×D53#9911yescharacteristic
90C22×D53#10112yes—
91C2×C4×C53—22no—
92C2×C4×C53—22no—
93C2×C4×C53—22no—
94C2×C4×C53—21no—
95C2×C4×C53—21no—
96C2×C4×C53—22no—
97C2×C4×C53—42no—
98C2×C4×C53—42no—
99C2×C4×C53—41no—
100C2×C4×C53C22×C811yescharacteristic
101C2×C4×C53C2×M1611yescharacteristic
102C2×Dic53—22no—
103C2×Dic53—22no—
104C2×Dic53—22no—
105C2×Dic53—21no—
106C2×Dic53—21no—
107C2×Dic53—22no—
108C2×Dic53—42no—
109C2×Dic53—42no—
110C2×Dic53—41no—
111C2×Dic53C22⋊C812yes—
112C4×D53—216no—
113C4×D53—22no—
114C4×D53—22no—
115C4×D53—22no—
116C4×D53—22no—
117C4×D53—44no—
118C4×D53—82no—
119C4×D53—82no—
120C4×D53—82no—
121#88324—84no—
122C2×#1325—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#35312yes—
135C2×D53#35612yes—
136C4×C53—24no—
137C4×C53—21no—
138C4×C53—21no—
139C4×C53—42no—
140C4×C53—81no—
141Dic53—24no—
142Dic53—22no—
143Dic53—42no—
144Dic53—81no—
145C2×#384—531no—
146C2×#324—532no—
147#1325—532no—
148#1325—532no—
149C2×C53—21no—
150C2×C53—21no—
151C2×C53C2×#32411yescharacteristic
152C2×C53C2×#35311yescharacteristic
153C2×C53C2×#35611yescharacteristic
154D53—22no—
155D53#132514yescomplemented
156C22×C4⋊C4—531no—
157C22×C4⋊C4—531no—
158C22×C4⋊C4—1062no—
159C22×C42—531no—
160C2×C22⋊C8—1062no—
161#384—531no—
162#384—531no—
163#384—531no—
164#384—1062no—
165#384#615711yescharacteristic
166#324—534no—
167#324—1062no—
168C53C2×#132511yescharacteristic, complemented, Sylow
169C23×C4—531no—
170C23×C4—532no—
171C23×C4—1061no—
172C23×C4—1061no—
173C22×C8—2122no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—532no—
176C2×C4⋊C4—531no—
177C2×C4⋊C4—531no—
178C2×C4⋊C4—1061no—
179C2×C4⋊C4—1062no—
180C2×C4⋊C4—1062no—
181C2×C4⋊C4—1062no—
182C2×C4⋊C4—2121no—
183C2×C4⋊C4—2121no—
184C2×C4⋊C4—2121no—
185C2×C4⋊C4—2121no—
186C2×C4⋊C4—2128no—
187C2×C4⋊C4C2×#615711yescharacteristic
188C2×C4⋊C4C2×#615711yescharacteristic
189C2×C42—531no—
190C2×C42—534no—
191C2×C42—1062no—
192C2×C42—1061no—
193C2×C42C2×#615711yescharacteristic
194C22⋊C8—1064no—
195C22⋊C8—2122no—
196C24—531no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—531no—
200C22×C4—532no—
201C22×C4—532no—
202C22×C4—532no—
203C22×C4—1064no—
204C22×C4—1061no—
205C22×C4—1061no—
206C22×C4—1062no—
207C22×C4—1064no—
208C22×C4—1064no—
209C22×C4—1062no—
210C22×C4—1062no—
211C22×C4—1061no—
212C22×C4—1061no—
213C22×C4—2121no—
214C22×C4—2121no—
215C22×C4—2124no—
216C22×C4—2124no—
217C22×C4C22⋊#615712yes—
218C22×C4C22×#615711yescharacteristic
219C2×C8—4244no—
220C2×C8—2124no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—44no—
224C4⋊C4—2122no—
225C4⋊C4—2121no—
226C4⋊C4—2121no—
227C4⋊C4—2124no—
228C4⋊C4—2124no—
229C4⋊C4—2124no—
230C4⋊C4—2122no—
231C42—21no—
232C42—532no—
233C42—1064no—
234C42—1061no—
235C42D53⋊C812yescomplemented
236C23—531no—
237C23—532no—
238C23—531no—
239C23—532no—
240C23—1062no—
241C23—1062no—
242C23C2×C22⋊#615711yescharacteristic
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—532no—
253C2×C4—1062no—
254C2×C4—1062no—
255C2×C4—1062no—
256C2×C4—1062no—
257C2×C4—10616no—
258C2×C4—1062no—
259C2×C4—1062no—
260C2×C4—1062no—
261C2×C4—1061no—
262C2×C4—1061no—
263C2×C4—1062no—
264C2×C4—4242no—
265C2×C4—4242no—
266C2×C4—4242no—
267C2×C4—2124no—
268C2×C4—2122no—
269C2×C4—2121no—
270C2×C4—2122no—
271C2×C4C2×D53⋊C811yescharacteristic
272C2×C4D53⋊M1611yescharacteristic
273C8—4244no—
274C22—21no—
275C22—21no—
276C22—532no—
277C22—532no—
278C22—532no—
279C22—532no—
280C22—1064no—
281C22—1064no—
282C22—1061no—
283C22—1061no—
284C22D53⋊(C22⋊C8)11yescharacteristic
285C22D53⋊#9911yescharacteristic
286C22D53⋊#10111yescharacteristic
287C4—24no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—81no—
292C4—1064no—
293C4—1062no—
294C4—4241no—
295C4—2122no—
296C2—21no—
297C2—21no—
298C2—534no—
299C2—1062no—
300C2D53⋊#32411yescharacteristic
301C2D53⋊#35311yescharacteristic
302C2D53⋊#35611yescharacteristic
subgroupG/H
centerC22D53⋊#99
commutatorC2×C4×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC53×#384C4
socleC22×C53C2×#99
prime radicalC23×D53C22⋊C4
cosocleC2×C4⋊Dic53C23
hypercenter#384#6157
hypocenterC53C2×#1325
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #20289658C2semidirect
3. #20289657C2semidirect
39. C42×D53C8semidirect
73. C42×C53C2×C8semidirect
83. C4×Dic53C2×C8semidirect
155. D53#1325semidirect
168. C53C2×#1325semidirect
235. C42D53⋊C8semidirect

Maximal subgroups

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

subgroupindex
D53⋊#3242
#202896582
#202896572
#384×D532
C2×#132553