Finite Group Databasebeta

← D53×#1325 #27293244

Subgroups — D53×#1325 #27293244

Order 13568.

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

normal subgroups only

This group has 598 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#384×D53C211yesmaximal, characteristic
2#324×D53C212yesmaximal
3#20272661C211yesmaximal, characteristic, complemented
4#20272660C212yesmaximal, complemented
5C53×#1325C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D53—22no—
7C2×C4⋊C4×D53C411yescharacteristic
8C2×C4⋊C4×D53C2211yescharacteristic
9C2×C42×D53C411yescharacteristic
10C22⋊C8×D53—22no—
11#16810493C411yescharacteristic
12#16810492—22no—
13#16810492C411yescharacteristic
14#16810492C2211yescharacteristic
15#16810349C2212yes—
16#16810348—22no—
17C53×#384C2211yescharacteristic
18C53×#324C2212yes—
19C22×C4×D53—21no—
20C22×C4×D53—21no—
21C22×C4×D53C2×C411yescharacteristic
22C22×C4×D53D412yes—
23C2×C8×D53—42no—
24C2×C4⋊Dic53—22no—
25C2×C4⋊Dic53C2×C411yescharacteristic
26C2×C4⋊Dic53C2×C411yescharacteristic
27C2×#11719919—22no—
28C2×#11719919—22no—
29C2×#11719919—21no—
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
40C22⋊#88322—22no—
41#13133129—42no—
42C2×C4⋊C4×C53—22no—
43C2×C4⋊C4×C53C2×C411yescharacteristic
44C2×C4⋊C4×C53C2311yescharacteristic
45C2×C42×C53C2×C411yescharacteristic
46C22⋊C8×C53—22no—
47C23×D53C22⋊C411yescharacteristic
48C22×C4×C53—21no—
49C22×C4×C53—21no—
50C22×C4×C53C22×C411yescharacteristic
51C22×C4×C53C2×D412yes—
52C22×Dic53—21no—
53C22×Dic53—21no—
54C22×Dic53C22⋊C411yescharacteristic
55C22×Dic53C22⋊C412yes—
56C2×C4×D53—24no—
57C2×C4×D53—24no—
58C2×C4×D53—24no—
59C2×C4×D53—21no—
60C2×C4×D53—21no—
61C2×C4×D53—22no—
62C2×C4×D53—22no—
63C2×C4×D53—22no—
64C2×C4×D53—44no—
65C2×C4×D53—44no—
66C2×C4×D53—41no—
67C2×C4×D53—41no—
68C2×C4×D53C2×C812yes—
69C2×C4×D53M1612yes—
70C2×C8×C53—42no—
71C4⋊C4×C53—41no—
72C4⋊C4×C53—44no—
73C4⋊C4×C53—41no—
74C42×C53—21no—
75C42×C53C2×C812yescomplemented
76C4⋊Dic53—41no—
77C4⋊Dic53—44no—
78C4⋊Dic53—41no—
79#11719919—42no—
80#11719919—44no—
81#11719919—44no—
82#11719919—42no—
83C4×Dic53—21no—
84C4×Dic53—24no—
85C4×Dic53C2×C812yescomplemented
86C2×#88322—42no—
87C8×D53—84no—
88C23×C53C2×C22⋊C411yescharacteristic
89C22×D53—22no—
90C22×D53—22no—
91C22×D53C22⋊C812yes—
92C22×D53#9911yescharacteristic
93C22×D53#9911yescharacteristic
94C22×D53#10112yes—
95C2×C4×C53—22no—
96C2×C4×C53—22no—
97C2×C4×C53—22no—
98C2×C4×C53—21no—
99C2×C4×C53—21no—
100C2×C4×C53—22no—
101C2×C4×C53—42no—
102C2×C4×C53—42no—
103C2×C4×C53—41no—
104C2×C4×C53C22×C811yescharacteristic
105C2×C4×C53C2×M1611yescharacteristic
106C2×Dic53—22no—
107C2×Dic53—22no—
108C2×Dic53—22no—
109C2×Dic53—21no—
110C2×Dic53—21no—
111C2×Dic53—22no—
112C2×Dic53—42no—
113C2×Dic53—42no—
114C2×Dic53—41no—
115C2×Dic53C22⋊C812yes—
116C4×D53—216no—
117C4×D53—22no—
118C4×D53—22no—
119C4×D53—22no—
120C4×D53—22no—
121C4×D53—44no—
122C4×D53—82no—
123C4×D53—82no—
124C4×D53—82no—
125C8×C53—82no—
126#88322—82no—
127C2×#1325—531nomaximal, Sylow
128C22×C53—21no—
129C22×C53—21no—
130C22×C53C2×C22⋊C811yescharacteristic
131C22×C53C2×#9911yescharacteristic
132C22×C53C2×#10111yescharacteristic
133C2×D53—21no—
134C2×D53—21no—
135C2×D53—24no—
136C2×D53—24no—
137C2×D53#32412yes—
138C2×D53#32412yes—
139C2×D53#35312yes—
140C2×D53#35612yes—
141C4×C53—24no—
142C4×C53—21no—
143C4×C53—21no—
144C4×C53—42no—
145C4×C53—81no—
146Dic53—24no—
147Dic53—22no—
148Dic53—42no—
149Dic53—81no—
150C2×#384—531no—
151C2×#324—532no—
152#1325—531no—
153#1325—532no—
154#1325D5311yescharacteristic, direct product factor
155C2×C53—21no—
156C2×C53—21no—
157C2×C53C2×#32411yescharacteristic
158C2×C53C2×#35311yescharacteristic
159C2×C53C2×#35611yescharacteristic
160D53—22no—
161D53#132514yesdirect product factor
162C22×C4⋊C4—531no—
163C22×C4⋊C4—531no—
164C22×C4⋊C4—1062no—
165C22×C42—531no—
166C2×C22⋊C8—1062no—
167#384—531no—
168#384—531no—
169#384—531no—
170#384—1062no—
171#384C2×D5311yescharacteristic
172#324—532no—
173#324—1062no—
174#324C2×D5312yes—
175C53C2×#132511yescharacteristic, complemented, Sylow
176C23×C4—531no—
177C23×C4—532no—
178C23×C4—1061no—
179C23×C4—1061no—
180C22×C8—2122no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—531no—
183C2×C4⋊C4—532no—
184C2×C4⋊C4—531no—
185C2×C4⋊C4—1061no—
186C2×C4⋊C4—1062no—
187C2×C4⋊C4—1062no—
188C2×C4⋊C4—1062no—
189C2×C4⋊C4—2121no—
190C2×C4⋊C4—2121no—
191C2×C4⋊C4—2121no—
192C2×C4⋊C4—2121no—
193C2×C4⋊C4—2128no—
194C2×C4⋊C4C4×D5311yescharacteristic
195C2×C4⋊C4C22×D5311yescharacteristic
196C2×C42—531no—
197C2×C42—534no—
198C2×C42—1062no—
199C2×C42—1061no—
200C2×C42C4×D5311yescharacteristic
201C22⋊C8—22no—
202C22⋊C8—1062no—
203C22⋊C8—2122no—
204C24—531no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—531no—
208C22×C4—532no—
209C22×C4—532no—
210C22×C4—532no—
211C22×C4—1064no—
212C22×C4—1061no—
213C22×C4—1061no—
214C22×C4—1062no—
215C22×C4—1064no—
216C22×C4—1064no—
217C22×C4—1062no—
218C22×C4—1062no—
219C22×C4—1061no—
220C22×C4—1061no—
221C22×C4—2121no—
222C22×C4—2121no—
223C22×C4—2124no—
224C22×C4—2124no—
225C22×C4C2×C4×D5311yescharacteristic
226C22×C4D4×D5312yes—
227C2×C8—42no—
228C2×C8—4244no—
229C2×C8—2122no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—44no—
233C4⋊C4—2122no—
234C4⋊C4—2121no—
235C4⋊C4—2121no—
236C4⋊C4—2124no—
237C4⋊C4—2124no—
238C4⋊C4—2124no—
239C4⋊C4—2122no—
240C42—21no—
241C42—532no—
242C42—1064no—
243C42—1061no—
244C42C8×D5312yescomplemented
245C23—531no—
246C23—532no—
247C23—531no—
248C23—532no—
249C23—1062no—
250C23—1062no—
251C23C22⋊C4×D5311yescharacteristic
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—532no—
262C2×C4—1062no—
263C2×C4—1062no—
264C2×C4—1062no—
265C2×C4—1062no—
266C2×C4—10616no—
267C2×C4—1062no—
268C2×C4—1062no—
269C2×C4—1062no—
270C2×C4—1061no—
271C2×C4—1061no—
272C2×C4—1062no—
273C2×C4—4242no—
274C2×C4—4242no—
275C2×C4—4242no—
276C2×C4—2124no—
277C2×C4—2122no—
278C2×C4—2121no—
279C2×C4—2122no—
280C2×C4C2×C8×D5311yescharacteristic
281C2×C4M16×D5311yescharacteristic
282C8—82no—
283C8—4242no—
284C22—21no—
285C22—21no—
286C22—532no—
287C22—532no—
288C22—532no—
289C22—532no—
290C22—1064no—
291C22—1064no—
292C22—1061no—
293C22—1061no—
294C22C22⋊C8×D5311yescharacteristic
295C22#99×D5311yescharacteristic
296C22#101×D5311yescharacteristic
297C4—24no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—81no—
302C4—1064no—
303C4—1062no—
304C4—4241no—
305C4—2122no—
306C2—21no—
307C2—21no—
308C2—534no—
309C2—1062no—
310C2#324×D5311yescharacteristic
311C2#353×D5311yescharacteristic
312C2#356×D5311yescharacteristic
subgroupG/H
centerC22#99×D53
commutatorC2×C4×C53C22×C8
FrattiniC2×C4⋊C4C22×D53
FittingC53×#1325C2
socleC22×C53C2×#99
prime radicalC23×D53C22⋊C4
cosocleC2×C4⋊C4×C53C23
hypercenter#1325D53
hypocenterC53C2×#1325
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #20272661C2semidirect
4. #20272660C2semidirect
5. C53×#1325C2semidirect
39. C42×D53C8semidirect
75. C42×C53C2×C8semidirect
85. C4×Dic53C2×C8semidirect
154. #1325D53direct (N × H)
161. D53#1325direct (N × H)
175. C53C2×#1325semidirect
244. C42C8×D53semidirect

Maximal subgroups

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

subgroupindex
#384×D532
#324×D532
#202726612
#202726602
C53×#13252
C2×#132553