Finite Group Databasebeta

← C13×#9482 #15695821

Subgroups — C13×#9482 #15695821

Order 3328.

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

normal subgroups only

This group has 518 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×#2484C211yesmaximal, characteristic
2C13×#2313C211yesmaximal, characteristic
3C13×#1826C212yesmaximal
4C13×#1463C211yesmaximal, characteristic
5C13×#1284C212yesmaximal
6C2×C13×#117C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#407C2212yes—
9C13×#400C412yescomplemented
10C13×#398C412yescomplemented
11C13×#387—22no—
12C13×#387—24no—
13C13×#385—21no—
14C13×#381—21no—
15C13×#381—21no—
16C13×#381C2211yescharacteristic
17C13×#380—21no—
18C4×C13×C22⋊C4C2212yes—
19C13×#339—24no—
20C13×#324—22no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C2×C13×M16—22no—
25C13×#117—22no—
26C13×#117—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
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—21no—
39C2×C42×C13D414yes—
40C13×C22⋊C8—22no—
41C13×C22⋊C8—22no—
42C13×#95—22no—
43C13×#95—24no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—21no—
49C13×#95C2×C412yes—
50#9482C1311yesmaximal, characteristic, direct product factor, Sylow
51C24×C13C2×D411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—24no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13#4112yes—
69C13×M16—44no—
70C2×C8×C13—42no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—82no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C42×C13—44no—
82C42×C13—42no—
83#2484C2×C1311yescharacteristic
84#2313C2×C1311yescharacteristic
85#1826C2×C1312yes—
86#1463C2×C1311yescharacteristic
87#1284C2×C1312yes—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—41no—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13#12011yescharacteristic
93C23×C13#12311yescharacteristic
94C2×C4×C13—24no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
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—44no—
108C2×C4×C13—42no—
109C2×C4×C13—44no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—44no—
116C2×C4×C13—81no—
117C2×C4×C13C4×D412yes—
118C2×C4×C13#12112yes—
119C8×C13—82no—
120C2×#117C22×C1311yescharacteristic
121C22×C4⋊C4C22×C1311yescharacteristic
122#407C22×C1312yes—
123#400C4×C1312yescomplemented
124#398C4×C1312yescomplemented
125#387—22no—
126#387—24no—
127#385—21no—
128#381—21no—
129#381—21no—
130#381C22×C1311yescharacteristic
131#380—21no—
132C4×C22⋊C4C22×C1312yes—
133#339—24no—
134#324—22no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—44no—
143C22×C13#38611yescharacteristic
144C22×C13#42112yes—
145C22×C13#45812yes—
146C4×C13—22no—
147C4×C13—22no—
148C4×C13—42no—
149C4×C13—42no—
150C4×C13—84no—
151C4×C13—82no—
152C4×C13—81no—
153C4×C13—81no—
154C23×C4D4×C1311yescharacteristic
155C23×C4D4×C1311yescharacteristic
156C23×C4C23×C1311yescharacteristic
157C2×M16—22no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C2×C4×C1311yescharacteristic
165C2×C4⋊C4C2×C4×C1311yescharacteristic
166C2×C4⋊C4C2×C4×C1312yes—
167C2×C4⋊C4D4×C1312yes—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—21no—
171C2×C42—21no—
172C2×C42D4×C1314yes—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—22no—
176#95—24no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—21no—
182#95C2×C4×C1312yes—
183C2×C13—22no—
184C2×C13—22no—
185C2×C13—41no—
186C2×C13#189011yescharacteristic
187C2×C13#189711yescharacteristic
188C2×C13#191211yescharacteristic
189C24C2×D4×C1311yescharacteristic
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—24no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4C13×C22⋊C412yes—
202C22×C4C13×C22⋊C412yes—
203C22×C4C22×C4×C1311yescharacteristic
204C22×C4C2×D4×C1312yes—
205C22×C4C2×D4×C1311yescharacteristic
206C22×C4C13×#4112yes—
207M16—44no—
208C2×C8—42no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—44no—
214C4⋊C4—82no—
215C22⋊C4—44no—
216C22⋊C4—42no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C42—44no—
220C42—42no—
221C13#948211yescharacteristic, direct product factor, Sylow
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×C13×C22⋊C411yescharacteristic
226C23C13×#12011yescharacteristic
227C23C13×#12311yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—44no—
250C2×C4—81no—
251C2×C4C4×D4×C1312yes—
252C2×C4C13×#12112yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22C13×#38611yescharacteristic
263C22C13×#42112yes—
264C22C13×#45812yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—84no—
270C4—82no—
271C4—81no—
272C4—81no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2C13×#189011yescharacteristic
277C2C13×#189711yescharacteristic
278C2C13×#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
9. C13×#400C4semidirect
10. C13×#398C4semidirect
50. #9482C13direct (N × H)
123. #400C4×C13semidirect
124. #398C4×C13semidirect
221. C13#9482direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24842
C13×#23132
C13×#18262
C13×#14632
C13×#12842
#948213