Finite Group Databasebeta

← C13×#11535 #15697874

Subgroups — C13×#11535 #15697874

Order 3328.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C13×#2326C211yesmaximal, characteristic
2C13×#1465C212yesmaximal
3C13×#1325C212yesmaximal, complemented
4C13×#1319C212yesmaximal, complemented
5C2×C13×#124C411yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#407—22no—
9C13×#391C2211yescharacteristic
10C13×#390C411yescharacteristic
11C13×#388—22no—
12C13×#385—22no—
13C13×#384C2211yescharacteristic
14C13×#376C411yescharacteristic
15C13×#324C2214yes—
16C13×#323—22no—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13D412yes—
20C2×C13×M16—42no—
21C13×#124—22no—
22C13×#124—22no—
23C4×Q8×C13—42no—
24C4×D4×C13—42no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4D412yes—
32C2×C42×C13—21no—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C13×C22⋊C8—24no—
37C13×C22⋊C8—42no—
38C13×#95—21no—
39C13×#95—21no—
40C13×#95—22no—
41#11535C1311yesmaximal, characteristic, direct product factor, Sylow
42C24×C13C22⋊C412yes—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13M1612yescomplemented
47C2×D4×C13—21no—
48C2×D4×C13—21no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—82no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×M16—84no—
63C2×C8×C13—44no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—82no—
68C13×C22⋊C4—28no—
69C13×C22⋊C4—42no—
70C13×C22⋊C4—82no—
71C42×C13—22no—
72C42×C13—21no—
73C42×C13—41no—
74C42×C13—42no—
75C42×C13M1612yescomplemented
76#2326C2×C1311yescharacteristic
77#1465C2×C1312yes—
78#1325C2×C1312yescomplemented
79#1319C2×C1312yescomplemented
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—42no—
84C23×C13—42no—
85C23×C13C2×C22⋊C411yescharacteristic
86Q8×C13—42no—
87Q8×C13—42no—
88D4×C13—42no—
89D4×C13—42no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—41no—
97C2×C4×C13—44no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—82no—
110C2×C4×C13#9912yes—
111C2×C4×C13C2×M1611yescharacteristic
112C2×C4×C13C2×M1611yescharacteristic
113C8×C13—84no—
114C2×#124C4×C1311yescharacteristic
115C2×C4×Q8C4×C1311yescharacteristic
116C2×C4×D4C22×C1311yescharacteristic
117#407—22no—
118#391C22×C1311yescharacteristic
119#390C4×C1311yescharacteristic
120#388—22no—
121#385—22no—
122#384C22×C1311yescharacteristic
123#376C4×C1311yescharacteristic
124#324C22×C1314yes—
125#323—22no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13—44no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—82no—
133C22×C13#40711yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C22×C13#41311yescharacteristic
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—42no—
140C4×C13—42no—
141C4×C13—41no—
142C4×C13—42no—
143C4×C13—81no—
144C4×C13—81no—
145C22×Q8C2×C4×C1311yescharacteristic
146C22×D4C2×C4×C1311yescharacteristic
147C23×C4D4×C1312yes—
148C2×M16—42no—
149#124—22no—
150#124—22no—
151C4×Q8—42no—
152C4×D4—42no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4C2×C4×C1311yescharacteristic
156C2×C4⋊C4C23×C1311yescharacteristic
157C2×C22⋊C4—22no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4D4×C1312yes—
160C2×C42—21no—
161C2×C42C2×C4×C1311yescharacteristic
162C2×C42C2×C4×C1311yescharacteristic
163C2×C42C2×C4×C1311yescharacteristic
164C22⋊C8—24no—
165C22⋊C8—42no—
166#95—21no—
167#95—21no—
168#95—22no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13—82no—
172C2×C13#146511yescharacteristic
173C2×C13#212711yescharacteristic
174C2×C13#213511yescharacteristic
175C24C13×C22⋊C412yes—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C13×M1612yescomplemented
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—41no—
183C2×D4—41no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—82no—
191C22×C4C13×C22⋊C411yescharacteristic
192C22×C4C13×C22⋊C411yescharacteristic
193C22×C4C22×C4×C1311yescharacteristic
194C22×C4C2×D4×C1312yes—
195M16—84no—
196C2×C8—44no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—82no—
201C22⋊C4—28no—
202C22⋊C4—42no—
203C22⋊C4—82no—
204C42—22no—
205C42—21no—
206C42—41no—
207C42—42no—
208C42C13×M1612yescomplemented
209C13#1153511yescharacteristic, direct product factor, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C13×C22⋊C411yescharacteristic
216Q8—42no—
217Q8—42no—
218D4—42no—
219D4—42no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4C13×#9912yes—
241C2×C4C2×C13×M1611yescharacteristic
242C2×C4C2×C13×M1611yescharacteristic
243C8—84no—
244C22—21no—
245C22—21no—
246C22—44no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—82no—
251C22C13×#40711yescharacteristic
252C22C2×C13×#9911yescharacteristic
253C22C13×#41311yescharacteristic
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—81no—
262C4—81no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2C13×#146511yescharacteristic
267C2C13×#212711yescharacteristic
268C2C13×#213511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1325C2semidirect
4. C13×#1319C2semidirect
41. #11535C13direct (N × H)
46. C2×Q8×C13M16semidirect
75. C42×C13M16semidirect
78. #1325C2×C13semidirect
79. #1319C2×C13semidirect
179. C2×Q8C13×M16semidirect
208. C42C13×M16semidirect
209. C13#11535direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23262
C13×#14652
C13×#13252
C13×#13192
#1153513