Finite Group Databasebeta

← C13×#8756 #15695095

Subgroups — C13×#8756 #15695095

Order 3328.

546 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 118 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×#1305C214yesmaximal, complemented
4C22×C13×C22⋊C4C411yescharacteristic
5C22×C13×C22⋊C4C411yescharacteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C13×#407C2214yes—
8C13×#385—22no—
9C13×#385—22no—
10C13×#380C412yes—
11C13×#380C2212yes—
12C13×#323—22no—
13C13×#323—22no—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×C4×C13—21no—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13C2311yescharacteristic
19C2×C13×M16—24no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C22⋊C4—24no—
23C2×C13×C22⋊C4—21no—
24C2×C13×C22⋊C4—21no—
25C2×C13×C22⋊C4—42no—
26C2×C13×C22⋊C4—42no—
27C2×C13×C22⋊C4C2×C412yes—
28C2×C13×C22⋊C4C2×C412yes—
29C2×C13×C22⋊C4D412yes—
30C2×C13×C22⋊C4D412yes—
31C13×C22⋊C8—24no—
32C13×C22⋊C8—24no—
33C13×#95—22no—
34C13×#95—22no—
35#8756C1311yesmaximal, characteristic, direct product factor, Sylow
36C24×C13—22no—
37C24×C13—22no—
38C24×C13—22no—
39C24×C13—81no—
40C24×C13—81no—
41C24×C13C22⋊C411yescharacteristic
42C24×C13C22⋊C411yescharacteristic
43C24×C13C22×C411yescharacteristic
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—42no—
48C22×C4×C13—42no—
49C22×C4×C13—81no—
50C22×C4×C13—81no—
51C22×C4×C13—81no—
52C22×C4×C13—81no—
53C22×C4×C13—81no—
54C22×C4×C13—81no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C2×D412yes—
57C22×C4×C13#4114yes—
58C13×M16—84no—
59C2×C8×C13—44no—
60C13×C4⋊C4—82no—
61C13×C4⋊C4—82no—
62C13×C22⋊C4—24no—
63C13×C22⋊C4—24no—
64C13×C22⋊C4—42no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68#2315C2×C1311yescharacteristic
69#1462C2×C1312yes—
70#1305C2×C1314yescomplemented
71C23×C13—28no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—41no—
79C23×C13—41no—
80C23×C13—41no—
81C23×C13—41no—
82C23×C13—41no—
83C23×C13—41no—
84C23×C13—82no—
85C23×C13—82no—
86C23×C13—84no—
87C23×C13—84no—
88C23×C13#10012yes—
89C23×C13#10112yes—
90C23×C13C2×C22⋊C411yescharacteristic
91C23×C13#11712yes—
92C2×C4×C13—22no—
93C2×C4×C13—42no—
94C2×C4×C13—44no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—82no—
103C2×C4×C13—84no—
104C2×C4×C13—84no—
105C2×C4×C13#12314yes—
106C8×C13—84no—
107C22×C22⋊C4C4×C1311yescharacteristic
108C22×C22⋊C4C4×C1311yescharacteristic
109C22×C22⋊C4C22×C1311yescharacteristic
110#407C22×C1314yes—
111#385—22no—
112#385—22no—
113#380C4×C1312yes—
114#380C22×C1312yes—
115#323—22no—
116#323—22no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—41no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13—41no—
134C22×C13—88no—
135C22×C13#38111yescharacteristic
136C22×C13C2×#10011yescharacteristic
137C22×C13C2×#10111yescharacteristic
138C4×C13—24no—
139C4×C13—42no—
140C4×C13—82no—
141C4×C13—82no—
142C25C2×C4×C1311yescharacteristic
143C23×C4—21no—
144C23×C4—21no—
145C23×C4C2×C4×C1311yescharacteristic
146C23×C4C23×C1311yescharacteristic
147C2×M16—24no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C22⋊C4—24no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—42no—
154C2×C22⋊C4—42no—
155C2×C22⋊C4C2×C4×C1312yes—
156C2×C22⋊C4C2×C4×C1312yes—
157C2×C22⋊C4D4×C1312yes—
158C2×C22⋊C4D4×C1312yes—
159C22⋊C8—24no—
160C22⋊C8—24no—
161#95—22no—
162#95—22no—
163C2×C13—21no—
164C2×C13—21no—
165C2×C13—42no—
166C2×C13—42no—
167C2×C13—42no—
168C2×C13#182111yescharacteristic
169C2×C13#182811yescharacteristic
170C2×C13#182911yescharacteristic
171C24—22no—
172C24—22no—
173C24—22no—
174C24—81no—
175C24—81no—
176C24C13×C22⋊C411yescharacteristic
177C24C13×C22⋊C411yescharacteristic
178C24C22×C4×C1311yescharacteristic
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4—81no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4C13×C22⋊C412yes—
191C22×C4C2×D4×C1312yes—
192C22×C4C13×#4114yes—
193M16—84no—
194C2×C8—44no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C22⋊C4—24no—
198C22⋊C4—24no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C13#875611yescharacteristic, direct product factor, Sylow
204C23—28no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—41no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23C13×#10012yes—
222C23C13×#10112yes—
223C23C2×C13×C22⋊C411yescharacteristic
224C23C13×#11712yes—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—84no—
237C2×C4—84no—
238C2×C4C13×#12314yes—
239C8—84no—
240C22—21no—
241C22—21no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—88no—
258C22C13×#38111yescharacteristic
259C22C2×C13×#10011yescharacteristic
260C22C2×C13×#10111yescharacteristic
261C4—24no—
262C4—42no—
263C4—82no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—42no—
269C2—42no—
270C2C13×#182111yescharacteristic
271C2C13×#182811yescharacteristic
272C2C13×#182911yescharacteristic
subgroupG/H
center, socleC22×C13#381
commutatorC24C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1305C2semidirect
35. #8756C13direct (N × H)
70. #1305C2×C13semidirect
203. C13#8756direct (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×#13052
#875613