Finite Group Databasebeta

← C13×#11519 #15697858

Subgroups — C13×#11519 #15697858

Order 3328.

542 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2315C211yesmaximal, characteristic
2C13×#1462C212yesmaximal
3C13×#1326C214yesmaximal, complemented
4C22×C13×C22⋊C4C411yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C13×#407—22no—
8C13×#385—22no—
9C13×#385C412yes—
10C13×#385C2212yes—
11C13×#380—22no—
12C13×#323—22no—
13C13×#323C2214yes—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×C4×C13C2×C412yes—
17C23×C4×C13D412yes—
18C2×C13×M16—42no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C22⋊C4—21no—
22C2×C13×C22⋊C4—24no—
23C2×C13×C22⋊C4—21no—
24C2×C13×C22⋊C4—21no—
25C2×C13×C22⋊C4—41no—
26C2×C13×C22⋊C4—41no—
27C2×C13×C22⋊C4—41no—
28C2×C13×C22⋊C4—41no—
29C2×C13×C22⋊C4C2×C412yes—
30C2×C13×C22⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4D412yes—
32C2×C13×C22⋊C4C2311yescharacteristic
33C13×C22⋊C8—24no—
34C13×C22⋊C8—42no—
35C13×#95—22no—
36C13×#95—22no—
37#11519C1311yesmaximal, characteristic, direct product factor, Sylow
38C24×C13—21no—
39C24×C13—21no—
40C24×C13—22no—
41C24×C13—22no—
42C24×C13—82no—
43C24×C13C22⋊C411yescharacteristic
44C24×C13C22⋊C411yescharacteristic
45C24×C13C22×C411yescharacteristic
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—24no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—42no—
52C22×C4×C13—82no—
53C22×C4×C13—82no—
54C22×C4×C13—82no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C2×D412yes—
57C13×M16—84no—
58C2×C8×C13—44no—
59C13×C4⋊C4—82no—
60C13×C4⋊C4—82no—
61C13×C22⋊C4—24no—
62C13×C22⋊C4—22no—
63C13×C22⋊C4—41no—
64C13×C22⋊C4—42no—
65C13×C22⋊C4—41no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—41no—
68C13×C22⋊C4—41no—
69C13×C22⋊C4M1614yescomplemented
70#2315C2×C1311yescharacteristic
71#1462C2×C1312yes—
72#1326C2×C1314yescomplemented
73C23×C13—24no—
74C23×C13—24no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—42no—
82C23×C13—42no—
83C23×C13—42no—
84C23×C13—82no—
85C23×C13—82no—
86C23×C13—84no—
87C23×C13—84no—
88C23×C13#9911yescharacteristic
89C23×C13#9911yescharacteristic
90C23×C13#10112yes—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13C2×M1612yes—
93C2×C4×C13—24no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—44no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—82no—
105C2×C4×C13—84no—
106C2×C4×C13—84no—
107C8×C13—84no—
108C22×C22⋊C4C4×C1311yescharacteristic
109C22×C22⋊C4C4×C1311yescharacteristic
110C22×C22⋊C4C22×C1311yescharacteristic
111#407—22no—
112#385—22no—
113#385C4×C1312yes—
114#385C22×C1312yes—
115#380—22no—
116#323—22no—
117#323C22×C1314yes—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—84no—
134C22×C13—84no—
135C22×C13#40711yescharacteristic
136C22×C13C2×#9911yescharacteristic
137C22×C13C2×#10111yescharacteristic
138C4×C13—44no—
139C4×C13—42no—
140C4×C13—42no—
141C4×C13—82no—
142C25C2×C4×C1311yescharacteristic
143C23×C4—21no—
144C23×C4C2×C4×C1312yes—
145C23×C4D4×C1312yes—
146C2×M16—42no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—24no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—41no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4C2×C4×C1312yes—
158C2×C22⋊C4C2×C4×C1311yescharacteristic
159C2×C22⋊C4D4×C1312yes—
160C2×C22⋊C4C23×C1311yescharacteristic
161C22⋊C8—24no—
162C22⋊C8—42no—
163#95—22no—
164#95—22no—
165C2×C13—21no—
166C2×C13—21no—
167C2×C13—41no—
168C2×C13—41no—
169C2×C13—42no—
170C2×C13—42no—
171C2×C13#146311yescharacteristic
172C2×C13#212112yes—
173C24—21no—
174C24—21no—
175C24—22no—
176C24—22no—
177C24—82no—
178C24C13×C22⋊C411yescharacteristic
179C24C13×C22⋊C411yescharacteristic
180C24C22×C4×C1311yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—82no—
188C22×C4—82no—
189C22×C4—82no—
190C22×C4C13×C22⋊C412yes—
191C22×C4C2×D4×C1312yes—
192M16—84no—
193C2×C8—44no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C22⋊C4—24no—
197C22⋊C4—22no—
198C22⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4C13×M1614yescomplemented
205C13#1151911yescharacteristic, direct product factor, Sylow
206C23—24no—
207C23—24no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—42no—
215C23—42no—
216C23—42no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23C13×#9911yescharacteristic
222C23C13×#9911yescharacteristic
223C23C13×#10112yes—
224C23C2×C13×C22⋊C411yescharacteristic
225C23C2×C13×M1612yes—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4—84no—
239C2×C4—84no—
240C8—84no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—22no—
247C22—22no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—84no—
257C22—84no—
258C22C13×#40711yescharacteristic
259C22C2×C13×#9911yescharacteristic
260C22C2×C13×#10111yescharacteristic
261C4—44no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—41no—
268C2—41no—
269C2—42no—
270C2—42no—
271C2C13×#146311yescharacteristic
272C2C13×#212112yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC25×C13C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1326C2semidirect
37. #11519C13direct (N × H)
69. C13×C22⋊C4M16semidirect
72. #1326C2×C13semidirect
204. C22⋊C4C13×M16semidirect
205. C13#11519direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23152
C13×#14622
C13×#13262
#1151913