Finite Group Databasebeta

← C13×#12965 #15699304

Subgroups — C13×#12965 #15699304

Order 3328.

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

normal subgroups only

This group has 536 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×#2372C211yesmaximal, characteristic
2C2×C13×#354C211yesmaximal, characteristic
3C13×#1885C211yesmaximal, characteristic
4C13×#1867C212yesmaximal
5C13×#1390C212yesmaximal
6C2×C13×#124C2211yescharacteristic
7C13×#518C2211yescharacteristic
8C13×#419—21no—
9C2×C13×#100C2211yescharacteristic
10C2×C13×#99C2212yes—
11C13×#391—21no—
12C13×#388—22no—
13C13×#386C2212yes—
14C13×#385—22no—
15C4×C13×C22⋊C4—22no—
16C13×#376—21no—
17C13×#354C414yescomplemented
18C13×#342—22no—
19C13×#339—21no—
20C22×Q8×C13D411yescharacteristic
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13D412yes—
23C2×C13×M16—21no—
24C13×#124—22no—
25C13×#124C2×C412yes—
26C13×#124Q812yes—
27C4×D4×C13—42no—
28C13×#117—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—42no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4D412yes—
36C2×C42×C13—22no—
37C2×C42×C13—21no—
38C2×C42×C13D411yescharacteristic
39C13×#103—42no—
40C13×#100—22no—
41C13×#99—22no—
42C13×#99C2×C414yes—
43C13×#95—21no—
44C13×#95—22no—
45C13×#95—21no—
46C13×#95—22no—
47C13×#95—42no—
48#12965C1311yesmaximal, characteristic, direct product factor, Sylow
49C24×C13C2×D412yes—
50C2×Q8×C13—21no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13C4⋊C412yescomplemented
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13C22×C411yescharacteristic
57C2×D4×C13C2×Q811yescharacteristic
58C2×D4×C13#4112yes—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—44no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13C2×D411yescharacteristic
69C13×M16—41no—
70C13×M16—41no—
71C2×C8×C13—41no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—81no—
74C13×C4⋊C4—84no—
75C13×C22⋊C4—24no—
76C13×C22⋊C4—24no—
77C13×C22⋊C4—24no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—42no—
83C42×C13—21no—
84C42×C13—44no—
85C42×C13—41no—
86C42×C13—81no—
87C42×C13C4⋊C412yescomplemented
88#2372C2×C1311yescharacteristic
89C2×#354C2×C1311yescharacteristic
90#1885C2×C1311yescharacteristic
91#1867C2×C1312yes—
92#1390C2×C1312yes—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13C4×D412yes—
98C23×C13#12011yescharacteristic
99C23×C13C22⋊Q812yes—
100Q8×C13—42no—
101Q8×C13—81no—
102D4×C13—41no—
103D4×C13—41no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—24no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—44no—
116C2×C4×C13—42no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—82no—
122C2×C4×C13—82no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13C2×C4⋊C411yescharacteristic
127C2×C4×C13#12311yescharacteristic
128C8×C13—81no—
129C2×#124C22×C1311yescharacteristic
130#518C22×C1311yescharacteristic
131#419—21no—
132C2×#100C22×C1311yescharacteristic
133C2×#99C22×C1312yes—
134#391—21no—
135#388—22no—
136#386C22×C1312yes—
137#385—22no—
138C4×C22⋊C4—22no—
139#376—21no—
140#354C4×C1314yescomplemented
141#342—22no—
142#339—21no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—82no—
151C22×C13#38511yescharacteristic
152C22×C13B(4,𝔽2)11yescharacteristic
153C22×C13#45811yescharacteristic
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—42no—
157C4×C13—42no—
158C4×C13—44no—
159C4×C13—82no—
160C4×C13—84no—
161C4×C13—82no—
162C22×Q8D4×C1311yescharacteristic
163C22×D4C23×C1311yescharacteristic
164C23×C4D4×C1312yes—
165C2×M16—21no—
166#124—22no—
167#124C2×C4×C1312yes—
168#124Q8×C1312yes—
169C4×D4—42no—
170#117—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—42no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4D4×C1312yes—
178C2×C42—22no—
179C2×C42—21no—
180C2×C42D4×C1311yescharacteristic
181#103—42no—
182#100—22no—
183#99—22no—
184#99C2×C4×C1314yes—
185#95—21no—
186#95—21no—
187#95—22no—
188#95—22no—
189#95—42no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—42no—
193C2×C13—42no—
194C2×C13#186711yescharacteristic
195C2×C13#219712yes—
196C24C2×D4×C1312yes—
197C2×Q8—21no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8C13×C4⋊C412yescomplemented
201C2×D4—41no—
202C2×D4—41no—
203C2×D4C22×C4×C1311yescharacteristic
204C2×D4C2×Q8×C1311yescharacteristic
205C2×D4C13×#4112yes—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—44no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4C2×D4×C1311yescharacteristic
216M16—41no—
217M16—41no—
218C2×C8—41no—
219C4⋊C4—22no—
220C4⋊C4—81no—
221C4⋊C4—84no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—44no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—41no—
229C22⋊C4—42no—
230C42—21no—
231C42—44no—
232C42—41no—
233C42—81no—
234C42C13×C4⋊C412yescomplemented
235C13#1296511yescharacteristic, direct product factor, Sylow
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23C4×D4×C1312yes—
241C23C13×#12011yescharacteristic
242C23C13×C22⋊Q812yes—
243Q8—42no—
244Q8—81no—
245D4—41no—
246D4—41no—
247D4—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4C2×C13×C4⋊C411yescharacteristic
270C2×C4C13×#12311yescharacteristic
271C8—81no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22C13×#38511yescharacteristic
281C22C13×B(4,𝔽2)11yescharacteristic
282C22C13×#45811yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—42no—
287C4—44no—
288C4—82no—
289C4—84no—
290C4—82no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2C13×#186711yescharacteristic
296C2C13×#219712yes—
subgroupG/H
center, socleC22×C13B(4,𝔽2)
commutatorC2×D4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
17. C13×#354C4semidirect
48. #12965C13direct (N × H)
53. C2×Q8×C13C4⋊C4semidirect
87. C42×C13C4⋊C4semidirect
140. #354C4×C13semidirect
200. C2×Q8C13×C4⋊C4semidirect
234. C42C13×C4⋊C4semidirect
235. C13#12965direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23722
C2×C13×#3542
C13×#18852
C13×#18672
C13×#13902
#1296513