Finite Group Databasebeta

← C13×#11569 #15697908

Subgroups — C13×#11569 #15697908

Order 3328.

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

normal subgroups only

This group has 424 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×#2563C211yesmaximal, characteristic
2C13×#1465C211yesmaximal, characteristic
3C13×#1459C211yesmaximal, characteristic
4C13×#1324C214yesmaximal, complemented
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#407—21no—
8C2×C13×C22⋊C8—21no—
9C13×#393—21no—
10C13×#393—21no—
11C13×#390C412yes—
12C13×#382C2212yes—
13C13×#380—21no—
14C13×#380—21no—
15C4×C13×C4⋊C4C411yescharacteristic
16C13×#324C2212yes—
17C13×#324C2212yes—
18C13×#323—21no—
19C13×#323—21no—
20C22×Q8×C13—21no—
21C22×D4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C2×C13×M16—41no—
25C22×C8×C13—41no—
26C13×C4⋊Q8—41no—
27C13×C4⋊Q8—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C42×C13C2×C412yes—
39C2×C42×C13C2×C411yescharacteristic
40C13×C22⋊C8—22no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8—41no—
43C13×C22⋊C8—41no—
44C13×#95—21no—
45C13×#95—22no—
46C13×#95—22no—
47#11569C1311yesmaximal, characteristic, direct product factor, Sylow
48C24×C13C22⋊C411yescharacteristic
49C24×C13C22⋊C411yescharacteristic
50C2×Q8×C13—42no—
51C2×Q8×C13—82no—
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C13×M16—82no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—82no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—82no—
80C13×C22⋊C4—82no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—24no—
84#2563C2×C1311yescharacteristic
85#1465C2×C1311yescharacteristic
86#1459C2×C1311yescharacteristic
87#1324C2×C1314yescomplemented
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13#10112yes—
98C23×C13C2×C22⋊C411yescharacteristic
99Q8×C13—84no—
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—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#13112yes—
123C8×C13—82no—
124C8×C13—82no—
125C2×C4⋊Q8C4×C1311yescharacteristic
126C2×C4×D4C22×C1311yescharacteristic
127#407—21no—
128C2×C22⋊C8—21no—
129#393—21no—
130#393—21no—
131#390C4×C1312yes—
132#382C22×C1312yes—
133#380—21no—
134#380—21no—
135C4×C4⋊C4C4×C1311yescharacteristic
136#324C22×C1312yes—
137#324C22×C1312yes—
138#323—21no—
139#323—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—22no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—81no—
151C22×C13—81no—
152C22×C13#40811yescharacteristic
153C22×C13C2×#9911yescharacteristic
154C22×C13C2×#10111yescharacteristic
155C4×C13—21no—
156C4×C13—22no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—82no—
161C4×C13—82no—
162C4×C13#35412yes—
163C22×Q8—21no—
164C22×D4C2×C4×C1311yescharacteristic
165C23×C4D4×C1311yescharacteristic
166C23×C4D4×C1311yescharacteristic
167C2×M16—41no—
168C22×C8—41no—
169C4⋊Q8—41no—
170C4⋊Q8—41no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C2×C4×C1312yes—
176C2×C4⋊C4C23×C1311yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4D4×C1311yescharacteristic
180C2×C22⋊C4D4×C1311yescharacteristic
181C2×C42C2×C4×C1312yes—
182C2×C42C2×C4×C1311yescharacteristic
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187#95—21no—
188#95—22no—
189#95—22no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—42no—
193C2×C13—81no—
194C2×C13#147211yescharacteristic
195C2×C13C2×#35411yescharacteristic
196C2×C13#213411yescharacteristic
197C24C13×C22⋊C411yescharacteristic
198C24C13×C22⋊C411yescharacteristic
199C2×Q8—42no—
200C2×Q8—82no—
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—42no—
211C22×C4—42no—
212C22×C4C13×C22⋊C411yescharacteristic
213C22×C4C13×C22⋊C411yescharacteristic
214C22×C4C22×C4×C1311yescharacteristic
215C22×C4C2×D4×C1311yescharacteristic
216C22×C4C2×D4×C1311yescharacteristic
217M16—82no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—82no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C42—21no—
231C42—21no—
232C42—24no—
233C13#1156911yescharacteristic, direct product factor, Sylow
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23C13×#10112yes—
244C23C2×C13×C22⋊C411yescharacteristic
245Q8—84no—
246D4—44no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4C13×#9911yescharacteristic
267C2×C4C13×#9911yescharacteristic
268C2×C4C13×#13112yes—
269C8—82no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—81no—
282C22—81no—
283C22C13×#40811yescharacteristic
284C22C2×C13×#9911yescharacteristic
285C22C2×C13×#10111yescharacteristic
286C4—22no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4C13×#35412yes—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2C13×#147211yescharacteristic
299C2C2×C13×#35411yescharacteristic
300C2C13×#213411yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ 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×#1324C2semidirect
47. #11569C13direct (N × H)
87. #1324C2×C13semidirect
233. C13#11569direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25632
C13×#14652
C13×#14592
C13×#13242
#1156913