Finite Group Databasebeta

← C13×#11562 #15697901

Subgroups — C13×#11562 #15697901

Order 3328.

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

normal subgroups only

This group has 444 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×#2486C211yesmaximal, characteristic
2C13×#1465C211yesmaximal, characteristic
3C13×#1460C211yesmaximal, characteristic
4C13×#1317C214yesmaximal, complemented
5C2×C13×#123C412yes—
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C13×#431—21no—
9C13×#407—21no—
10C13×#398—21no—
11C13×#397—21no—
12C13×#389—21no—
13C13×#381C2212yes—
14C13×#380—21no—
15C13×#380C411yescharacteristic
16C13×#324—21no—
17C13×#323—21no—
18C13×#323C2212yes—
19C13×#323C2212yes—
20C22×D4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C412yes—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C2×C13×M16—41no—
25C13×#123—44no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4C2×C412yes—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4C2311yescharacteristic
39C2×C42×C13D411yescharacteristic
40C13×C4⋊C8—41no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—41no—
44C4×C8×C13—41no—
45C13×#95—21no—
46C13×#95—22no—
47C13×#95—22no—
48#11562C1311yesmaximal, characteristic, direct product factor, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C22×C411yescharacteristic
51C2×D4×C13—22no—
52C2×D4×C13—22no—
53C2×D4×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—24no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×M16—82no—
71C2×C8×C13—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—44no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—44no—
82C13×C22⋊C4—42no—
83C42×C13—21no—
84C42×C13—21no—
85#2486C2×C1311yescharacteristic
86#1465C2×C1311yescharacteristic
87#1460C2×C1311yescharacteristic
88#1317C2×C1314yescomplemented
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13#13112yes—
100D4×C13—44no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—81no—
120C2×C4×C13—84no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#10012yes—
124C8×C13—82no—
125C8×C13—82no—
126C2×#123C4×C1312yes—
127C2×C4×D4C22×C1311yescharacteristic
128C22×C4⋊C4C4×C1311yescharacteristic
129#431—21no—
130#407—21no—
131#398—21no—
132#397—21no—
133#389—21no—
134#381C22×C1312yes—
135#380—21no—
136#380C4×C1311yescharacteristic
137#324—21no—
138#323—21no—
139#323C22×C1312yes—
140#323C22×C1312yes—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—81no—
153C22×C13#40811yescharacteristic
154C22×C13C2×#9911yescharacteristic
155C22×C13C2×#10011yescharacteristic
156C4×C13—21no—
157C4×C13—22no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—82no—
162C4×C13—82no—
163C4×C13#35212yes—
164C22×D4C2×C4×C1311yescharacteristic
165C23×C4C2×C4×C1312yes—
166C23×C4C2×C4×C1311yescharacteristic
167C23×C4D4×C1311yescharacteristic
168C2×M16—41no—
169#123—44no—
170C4×D4—41no—
171C4×D4—41no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4D4×C1311yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4C2×C4×C1312yes—
181C2×C22⋊C4D4×C1311yescharacteristic
182C2×C22⋊C4C23×C1311yescharacteristic
183C2×C42D4×C1311yescharacteristic
184C4⋊C8—41no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—41no—
188C4×C8—41no—
189#95—21no—
190#95—22no—
191#95—22no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13—42no—
195C2×C13—81no—
196C2×C13#147111yescharacteristic
197C2×C13C2×#35211yescharacteristic
198C2×C13#212311yescharacteristic
199C24C13×C22⋊C411yescharacteristic
200C24C22×C4×C1311yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4C13×C22⋊C411yescharacteristic
216C22×C4C13×C22⋊C411yescharacteristic
217C22×C4C13×C22⋊C411yescharacteristic
218C22×C4C2×D4×C1311yescharacteristic
219C22×C4C2×D4×C1311yescharacteristic
220M16—82no—
221C2×C8—42no—
222C2×C8—42no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—44no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—44no—
232C22⋊C4—42no—
233C42—21no—
234C42—21no—
235C13#1156211yescharacteristic, direct product factor, Sylow
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23C2×C13×C22⋊C411yescharacteristic
246C23C13×#13112yes—
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—81no—
267C2×C4—84no—
268C2×C4C13×#9911yescharacteristic
269C2×C4C13×#9911yescharacteristic
270C2×C4C13×#10012yes—
271C8—82no—
272C8—82no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22C13×#40811yescharacteristic
286C22C2×C13×#9911yescharacteristic
287C22C2×C13×#10011yescharacteristic
288C4—22no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4C13×#35212yes—
296C2—21no—
297C2—21no—
298C2—42no—
299C2—81no—
300C2C13×#147111yescharacteristic
301C2C2×C13×#35211yescharacteristic
302C2C13×#212311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C24 ▷ 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
4. C13×#1317C2semidirect
48. #11562C13direct (N × H)
88. #1317C2×C13semidirect
235. C13#11562direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#24862
C13×#14652
C13×#14602
C13×#13172
#1156213