Finite Group Databasebeta

← C13×#9460 #15695799

Subgroups — C13×#9460 #15695799

Order 3328.

512 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2503C211yesmaximal, characteristic
2C13×#2313C211yesmaximal, characteristic
3C13×#1821C211yesmaximal, characteristic
4C13×#1511C212yesmaximal
5C13×#1284C212yesmaximal
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#407C2212yes—
9C13×#400—22no—
10C13×#391C412yescomplemented
11C13×#387—24no—
12C13×#382C412yescomplemented
13C13×#381—21no—
14C13×#381—21no—
15C13×#381C2212yes—
16C13×#380—21no—
17C4×C13×C22⋊C4—21no—
18C4×C13×C22⋊C4C2211yescharacteristic
19C13×#343—22no—
20C13×#328—24no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C2×C13×M16—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4D412yes—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C42×C13—22no—
39C2×C42×C13C2×C412yes—
40C13×C22⋊C8—22no—
41C13×C22⋊C8—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—21no—
49C13×#95—22no—
50C13×#95D414yes—
51#9460C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13C2×D411yescharacteristic
53C2×Q8×C13—22no—
54C2×Q8×C13—42no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D412yes—
71C22×C4×C13#4112yes—
72C13×M16—44no—
73C2×C8×C13—42no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—82no—
79C13×C22⋊C4—44no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C42×C13—42no—
84C42×C13—82no—
85#2503C2×C1311yescharacteristic
86#2313C2×C1311yescharacteristic
87#1821C2×C1311yescharacteristic
88#1511C2×C1312yes—
89#1284C2×C1312yes—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—41no—
93C23×C13C2×C22⋊C411yescharacteristic
94C23×C13#12011yescharacteristic
95C23×C13#12311yescharacteristic
96Q8×C13—82no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—44no—
109C2×C4×C13—42no—
110C2×C4×C13—44no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—44no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13C4×D412yes—
120C2×C4×C13#12112yes—
121C8×C13—82no—
122C2×C22⋊Q8C22×C1311yescharacteristic
123C22×C4⋊C4C22×C1311yescharacteristic
124#407C22×C1312yes—
125#400—22no—
126#391C4×C1312yescomplemented
127#387—24no—
128#382C4×C1312yescomplemented
129#381—21no—
130#381—21no—
131#381C22×C1312yes—
132#380—21no—
133C4×C22⋊C4—21no—
134C4×C22⋊C4C22×C1311yescharacteristic
135#343—22no—
136#328—24no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—44no—
145C22×C13#38611yescharacteristic
146C22×C13#41012yes—
147C22×C13#45512yes—
148C4×C13—22no—
149C4×C13—22no—
150C4×C13—42no—
151C4×C13—42no—
152C4×C13—84no—
153C4×C13—82no—
154C4×C13—81no—
155C4×C13—81no—
156C22×Q8C2×C4×C1311yescharacteristic
157C23×C4D4×C1311yescharacteristic
158C23×C4D4×C1311yescharacteristic
159C23×C4C23×C1311yescharacteristic
160C2×M16—22no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×C4×C1311yescharacteristic
168C2×C4⋊C4C2×C4×C1312yes—
169C2×C4⋊C4D4×C1312yes—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—21no—
173C2×C42—22no—
174C2×C42C2×C4×C1312yes—
175C22⋊C8—22no—
176C22⋊C8—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—21no—
184#95—22no—
185#95D4×C1314yes—
186C2×C13—22no—
187C2×C13—22no—
188C2×C13—41no—
189C2×C13#188511yescharacteristic
190C2×C13#189911yescharacteristic
191C2×C13#191211yescharacteristic
192C24C2×D4×C1311yescharacteristic
193C2×Q8—22no—
194C2×Q8—42no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—24no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4C13×C22⋊C412yes—
207C22×C4C13×C22⋊C412yes—
208C22×C4C22×C4×C1311yescharacteristic
209C22×C4C2×D4×C1311yescharacteristic
210C22×C4C2×D4×C1312yes—
211C22×C4C13×#4112yes—
212M16—44no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—22no—
217C4⋊C4—42no—
218C4⋊C4—82no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C42—42no—
224C42—82no—
225C13#946011yescharacteristic, direct product factor, Sylow
226C23—22no—
227C23—22no—
228C23—41no—
229C23C2×C13×C22⋊C411yescharacteristic
230C23C13×#12011yescharacteristic
231C23C13×#12311yescharacteristic
232Q8—82no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—44no—
245C2×C4—42no—
246C2×C4—44no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—44no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4C4×D4×C1312yes—
256C2×C4C13×#12112yes—
257C8—82no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22C13×#38611yescharacteristic
267C22C13×#41012yes—
268C22C13×#45512yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—82no—
275C4—81no—
276C4—81no—
277C2—22no—
278C2—22no—
279C2—41no—
280C2C13×#188511yescharacteristic
281C2C13×#189911yescharacteristic
282C2C13×#191211yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
10. C13×#391C4semidirect
12. C13×#382C4semidirect
51. #9460C13direct (N × H)
126. #391C4×C13semidirect
128. #382C4×C13semidirect
225. C13#9460direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25032
C13×#23132
C13×#18212
C13×#15112
C13×#12842
#946013