Finite Group Databasebeta

← C13×#9388 #15695727

Subgroups — C13×#9388 #15695727

Order 3328.

532 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2873C211yesmaximal, characteristic
2C13×#2611C211yesmaximal, characteristic
3C13×#1528C212yesmaximal, complemented
4C13×#1464C211yesmaximal, characteristic
5C13×#1300C212yesmaximal, complemented
6C22×C13×M16—21no—
7C2×C13×#125C2211yescharacteristic
8C2×C13×#117C2211yescharacteristic
9C13×#432C2212yes—
10C13×#405—24no—
11C4×C13×M16—21no—
12C4×C13×M16C2212yes—
13C13×#400C411yescharacteristic
14C13×#399C411yescharacteristic
15C13×#398C411yescharacteristic
16C13×#397C411yescharacteristic
17C13×#389—21no—
18C13×#388—21no—
19C13×#387—21no—
20C13×#385—21no—
21C13×#376C2211yescharacteristic
22C13×#330—24no—
23C13×#324—21no—
24C13×#323—21no—
25C23×C4×C13D411yescharacteristic
26C2×C13×M16—22no—
27C2×C13×M16—24no—
28C2×C13×M16—24no—
29C2×C13×M16—22no—
30C22×C8×C13—22no—
31C13×#125—22no—
32C13×#125—22no—
33C13×#117—22no—
34C13×#117—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C42×C13—21no—
48C2×C42×C13D411yescharacteristic
49C2×C42×C13C2311yescharacteristic
50C13×C4⋊C8—22no—
51C13×C22⋊C8—22no—
52C13×#97—22no—
53C13×#97—22no—
54C13×#97D414yes—
55C4×C8×C13—22no—
56C4×C8×C13—22no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95C2×C411yescharacteristic
63C13×#95C2×C411yescharacteristic
64#9388C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13C22⋊C411yescharacteristic
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×M16—28no—
81C13×M16—24no—
82C13×M16—24no—
83C2×C8×C13—28no—
84C2×C8×C13—24no—
85C2×C8×C13—42no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—41no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—42no—
102C42×C13C2×D412yes—
103C42×C13#4112yes—
104#2873C2×C1311yescharacteristic
105#2611C2×C1311yescharacteristic
106#1528C2×C1312yescomplemented
107#1464C2×C1311yescharacteristic
108#1300C2×C1312yescomplemented
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—24no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13#10412yes—
141C2×C4×C13C4×D412yes—
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12112yes—
144C2×C4×C13#12311yescharacteristic
145C8×C13—28no—
146C8×C13—82no—
147C22×M16—21no—
148C2×#125C22×C1311yescharacteristic
149C2×#117C22×C1311yescharacteristic
150#432C22×C1312yes—
151#405—24no—
152C4×M16—21no—
153C4×M16C22×C1312yes—
154#400C4×C1311yescharacteristic
155#399C4×C1311yescharacteristic
156#398C4×C1311yescharacteristic
157#397C4×C1311yescharacteristic
158#389—21no—
159#388—21no—
160#387—21no—
161#385—21no—
162#376C22×C1311yescharacteristic
163#330—24no—
164#324—21no—
165#323—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—42no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13#38611yescharacteristic
174C22×C13C2×#10411yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C4×C13—22no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—42no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13—81no—
187C23×C4D4×C1311yescharacteristic
188C2×M16—22no—
189C2×M16—24no—
190C2×M16—24no—
191C2×M16—22no—
192C22×C8—22no—
193#125—22no—
194#125—22no—
195#117—22no—
196#117—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C1311yescharacteristic
202C2×C4⋊C4C2×C4×C1311yescharacteristic
203C2×C4⋊C4C2×C4×C1311yescharacteristic
204C2×C4⋊C4D4×C1311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4C2×C4×C1311yescharacteristic
208C2×C22⋊C4D4×C1311yescharacteristic
209C2×C42—21no—
210C2×C42D4×C1311yescharacteristic
211C2×C42C23×C1311yescharacteristic
212C4⋊C8—22no—
213C22⋊C8—22no—
214#97—22no—
215#97—22no—
216#97D4×C1314yes—
217C4×C8—22no—
218C4×C8—22no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C2×C4×C1311yescharacteristic
225#95C2×C4×C1311yescharacteristic
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13#188411yescharacteristic
230C2×C13#189611yescharacteristic
231C2×C13#191511yescharacteristic
232C24C13×C22⋊C411yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C13×C22⋊C411yescharacteristic
242C22×C4C13×C22⋊C411yescharacteristic
243C22×C4C13×C22⋊C411yescharacteristic
244C22×C4C22×C4×C1311yescharacteristic
245C22×C4C2×D4×C1311yescharacteristic
246C22×C4C2×D4×C1311yescharacteristic
247M16—28no—
248M16—24no—
249M16—24no—
250C2×C8—28no—
251C2×C8—24no—
252C2×C8—42no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C22⋊C4—22no—
263C22⋊C4—22no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—42no—
269C42C2×D4×C1312yes—
270C42C13×#4112yes—
271C13#938811yescharacteristic, direct product factor, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C13×#10412yes—
277C23C2×C13×C22⋊C411yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4C13×#10412yes—
304C2×C4C4×D4×C1312yes—
305C2×C4C13×#12011yescharacteristic
306C2×C4C13×#12112yes—
307C2×C4C13×#12311yescharacteristic
308C8—28no—
309C8—82no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22C13×#38611yescharacteristic
318C22C2×C13×#10411yescharacteristic
319C22C2×C13×#10411yescharacteristic
320C4—22no—
321C4—21no—
322C4—22no—
323C4—21no—
324C4—22no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—21no—
332C2—21no—
333C2—42no—
334C2C13×#188411yescharacteristic
335C2C13×#189611yescharacteristic
336C2C13×#191511yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1528C2semidirect
5. C13×#1300C2semidirect
64. #9388C13direct (N × H)
106. #1528C2×C13semidirect
108. #1300C2×C13semidirect
271. C13#9388direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28732
C13×#26112
C13×#15282
C13×#14642
C13×#13002
#938813