Finite Group Databasebeta

← D13×#1325 #15772071

Subgroups — D13×#1325 #15772071

Order 3328.

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
1D13×#384C211yesmaximal, characteristic
2D13×#324C212yesmaximal
3#13112782C211yesmaximal, characteristic, complemented
4#13112781C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D13—22no—
7C2×C4⋊C4×D13C411yescharacteristic
8C2×C4⋊C4×D13C2211yescharacteristic
9C2×C42×D13C411yescharacteristic
10C13×#384C2211yescharacteristic
11#11718637—22no—
12#11718637C411yescharacteristic
13#11718637C2211yescharacteristic
14#11718596C411yescharacteristic
15D13×C22⋊C8—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718061—22no—
19C22×C4×D13—21no—
20C22×C4×D13—21no—
21C22×C4×D13C2×C411yescharacteristic
22C22×C4×D13D412yes—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—22no—
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101—21no—
33C2×#6101D412yes—
34C2×C4×Dic13—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C8×D13—42no—
37C4⋊C4×D13—41no—
38C4⋊C4×D13—41no—
39C4⋊C4×D13—41no—
40C4⋊C4×D13—41no—
41C4⋊C4×D13—48no—
42C42×D13—22no—
43C42×D13C814yescomplemented
44C13×C22⋊C8—22no—
45C22⋊#1055—22no—
46#88060—42no—
47C2×#1325—131nomaximal, Sylow
48C23×D13C22⋊C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22×C411yescharacteristic
52C22×C4×C13C2×D412yes—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C22⋊C412yes—
57C2×C4×D13—24no—
58C2×C4×D13—24no—
59C2×C4×D13—24no—
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13—44no—
66C2×C4×D13—44no—
67C2×C4×D13—41no—
68C2×C4×D13—41no—
69C2×C4×D13C2×C812yes—
70C2×C4×D13M1612yes—
71C2×C8×C13—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—44no—
75C42×C13—21no—
76C42×C13C2×C812yescomplemented
77C4⋊Dic13—41no—
78C4⋊Dic13—44no—
79C4⋊Dic13—41no—
80#6101—42no—
81#6101—44no—
82#6101—44no—
83#6101—42no—
84C4×Dic13—21no—
85C4×Dic13—24no—
86C4×Dic13C2×C812yescomplemented
87C2×#1055—42no—
88C8×D13—84no—
89C2×#384—131no—
90C2×#324—132no—
91#1325—131no—
92#1325—132no—
93#1325D1311yescharacteristic, direct product factor
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—22no—
96C22×D13—22no—
97C22×D13C22⋊C812yes—
98C22×D13#9911yescharacteristic
99C22×D13#9911yescharacteristic
100C22×D13#10112yes—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13C22×C811yescharacteristic
111C2×C4×C13C2×M1611yescharacteristic
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—22no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—41no—
121C2×Dic13C22⋊C812yes—
122C4×D13—216no—
123C4×D13—22no—
124C4×D13—22no—
125C4×D13—22no—
126C4×D13—22no—
127C4×D13—44no—
128C4×D13—82no—
129C4×D13—82no—
130C4×D13—82no—
131C8×C13—82no—
132#1055—82no—
133C22×C4⋊C4—131no—
134C22×C4⋊C4—131no—
135C22×C4⋊C4—262no—
136C22×C42—131no—
137C2×C22⋊C8—262no—
138#384—131no—
139#384—131no—
140#384—131no—
141#384—262no—
142#384C2×D1311yescharacteristic
143#324—132no—
144#324—262no—
145#324C2×D1312yes—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13C2×C22⋊C811yescharacteristic
149C22×C13C2×#9911yescharacteristic
150C22×C13C2×#10111yescharacteristic
151C2×D13—21no—
152C2×D13—21no—
153C2×D13—24no—
154C2×D13—24no—
155C2×D13#32412yes—
156C2×D13#32412yes—
157C2×D13#35312yes—
158C2×D13#35612yes—
159C4×C13—24no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—42no—
163C4×C13—81no—
164Dic13—24no—
165Dic13—22no—
166Dic13—42no—
167Dic13—81no—
168C23×C4—131no—
169C23×C4—132no—
170C23×C4—261no—
171C23×C4—261no—
172C22×C8—522no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—132no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4—262no—
180C2×C4⋊C4—262no—
181C2×C4⋊C4—521no—
182C2×C4⋊C4—521no—
183C2×C4⋊C4—521no—
184C2×C4⋊C4—521no—
185C2×C4⋊C4—528no—
186C2×C4⋊C4C4×D1311yescharacteristic
187C2×C4⋊C4C22×D1311yescharacteristic
188C2×C42—131no—
189C2×C42—134no—
190C2×C42—262no—
191C2×C42—261no—
192C2×C42C4×D1311yescharacteristic
193C22⋊C8—22no—
194C22⋊C8—262no—
195C22⋊C8—522no—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13C2×#32411yescharacteristic
199C2×C13C2×#35311yescharacteristic
200C2×C13C2×#35611yescharacteristic
201D13—22no—
202D13#132514yesdirect product factor
203C24—131no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—131no—
207C22×C4—132no—
208C22×C4—132no—
209C22×C4—132no—
210C22×C4—264no—
211C22×C4—261no—
212C22×C4—261no—
213C22×C4—262no—
214C22×C4—264no—
215C22×C4—264no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4—524no—
221C22×C4—521no—
222C22×C4—521no—
223C22×C4—524no—
224C22×C4C2×C4×D1311yescharacteristic
225C22×C4D4×D1312yes—
226C2×C8—42no—
227C2×C8—522no—
228C2×C8—1044no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—44no—
232C4⋊C4—522no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—524no—
236C4⋊C4—524no—
237C4⋊C4—524no—
238C4⋊C4—522no—
239C42—21no—
240C42—132no—
241C42—264no—
242C42—261no—
243C42C8×D1312yescomplemented
244C13C2×#132511yescharacteristic, complemented, Sylow
245C23—131no—
246C23—131no—
247C23—132no—
248C23—132no—
249C23—262no—
250C23—262no—
251C23C22⋊C4×D1311yescharacteristic
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—132no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—2616no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—524no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—521no—
277C2×C4—1042no—
278C2×C4—1042no—
279C2×C4—1042no—
280C2×C4C2×C8×D1311yescharacteristic
281C2×C4M16×D1311yescharacteristic
282C8—82no—
283C8—1042no—
284C22—21no—
285C22—21no—
286C22—132no—
287C22—132no—
288C22—132no—
289C22—132no—
290C22—264no—
291C22—264no—
292C22—261no—
293C22—261no—
294C22D13×C22⋊C811yescharacteristic
295C22D13×#9911yescharacteristic
296C22D13×#10111yescharacteristic
297C4—24no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—81no—
302C4—264no—
303C4—262no—
304C4—522no—
305C4—1041no—
306C2—21no—
307C2—21no—
308C2—134no—
309C2—262no—
310C2D13×#32411yescharacteristic
311C2D13×#35311yescharacteristic
312C2D13×#35611yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1325C2
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1325D13
hypocenterC13C2×#1325
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #13112782C2semidirect
4. #13112781C2semidirect
5. C13×#1325C2semidirect
43. C42×D13C8semidirect
76. C42×C13C2×C8semidirect
86. C4×Dic13C2×C8semidirect
93. #1325D13direct (N × H)
202. D13#1325direct (N × H)
243. C42C8×D13semidirect
244. C13C2×#1325semidirect

Maximal subgroups

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

subgroupindex
D13×#3842
D13×#3242
#131127822
#131127812
C13×#13252
C2×#132513