Finite Group Databasebeta

← C13×#9032 #15695371

Subgroups — C13×#9032 #15695371

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2983C211yesmaximal, characteristic, complemented
2C13×#2398C211yesmaximal, characteristic
3C4×C13×#101C211yesmaximal, characteristic, complemented
4C13×#1490C212yesmaximal
5C13×#1300C212yesmaximal, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#446—24no—
9C13×#432—21no—
10C13×#432C2212yes—
11C13×#431—21no—
12C2×C13×#101—21no—
13C4×C13×M16C2212yes—
14C13×#400C411yescharacteristic
15C13×#400C411yescharacteristic
16C13×#397—21no—
17C13×#394C411yescharacteristic
18C13×#394C411yescharacteristic
19C13×#393—21no—
20C4×C13×C22⋊C4—21no—
21C4×C13×C22⋊C4—21no—
22C13×#376C2211yescharacteristic
23C13×#343—21no—
24C13×D4⋊C8—24no—
25C22×Q8×C13D411yescharacteristic
26C22×D4×C13C2×C411yescharacteristic
27C23×C4×C13—21no—
28C2×C13×M16—22no—
29C4×Q8×C13—22no—
30C4×Q8×C13—22no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C42×C13—21no—
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C13×C4⋊C8—22no—
47C13×C4⋊C8—22no—
48C13×C4⋊C8D414yes—
49C13×#101—24no—
50C13×C22⋊C8—22no—
51C13×#97—22no—
52C13×#97—22no—
53C13×#97—22no—
54C4×C8×C13—22no—
55C4×C8×C13—22no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95C2×C411yescharacteristic
62C13×#95C2×C411yescharacteristic
63#9032C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13—21no—
65C2×Q8×C13—22no—
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C2×D4×C13—22no—
69C2×D4×C13—42no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C13×M16—24no—
85C13×M16—42no—
86C2×C8×C13—24no—
87C2×C8×C13—42no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—42no—
102C42×C13C2×D412yes—
103C42×C13#4112yes—
104#2983C2×C1311yescharacteristic, complemented
105#2398C2×C1311yescharacteristic
106C4×#101C2×C1311yescharacteristic, complemented
107#1490C2×C1312yes—
108#1300C2×C1312yescomplemented
109C23×C13—22no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—44no—
118D4×C13—24no—
119D4×C13—42no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
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—41no—
141C2×C4×C13—41no—
142C2×C4×C13—82no—
143C2×C4×C13—82no—
144C2×C4×C13#10412yes—
145C2×C4×C13C4×D412yes—
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12112yes—
148C2×C4×C13#12311yescharacteristic
149C8×C13—44no—
150C8×C13—44no—
151C2×C4×Q8C22×C1311yescharacteristic
152C2×C4×D4C22×C1311yescharacteristic
153#446—24no—
154#432—21no—
155#432C22×C1312yes—
156#431—21no—
157C2×#101—21no—
158C4×M16C22×C1312yes—
159#400C4×C1311yescharacteristic
160#400C4×C1311yescharacteristic
161#397—21no—
162#394C4×C1311yescharacteristic
163#394C4×C1311yescharacteristic
164#393—21no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—21no—
167#376C22×C1311yescharacteristic
168#343—21no—
169D4⋊C8—24no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13#38611yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C22×C13#42111yescharacteristic
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13#45412yes—
193C22×Q8D4×C1311yescharacteristic
194C22×D4C2×C4×C1311yescharacteristic
195C23×C4—21no—
196C2×M16—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×D4—22no—
200C4×D4—22no—
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⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42—21no—
211C2×C42D4×C1311yescharacteristic
212C2×C42D4×C1311yescharacteristic
213C2×C42C23×C1311yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8D4×C1314yes—
217#101—24no—
218C22⋊C8—22no—
219#97—22no—
220#97—22no—
221#97—22no—
222C4×C8—22no—
223C4×C8—22no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×C4×C1311yescharacteristic
230#95C2×C4×C1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—82no—
234C2×C13#187111yescharacteristic
235C2×C13#188811yescharacteristic
236C2×C13#189111yescharacteristic
237C24—21no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×D4—22no—
242C2×D4—42no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4C13×C22⋊C411yescharacteristic
251C22×C4C13×C22⋊C411yescharacteristic
252C22×C4C13×C22⋊C411yescharacteristic
253C22×C4C13×C22⋊C411yescharacteristic
254C22×C4C22×C4×C1311yescharacteristic
255C22×C4C2×D4×C1311yescharacteristic
256C22×C4C2×D4×C1311yescharacteristic
257M16—24no—
258M16—42no—
259C2×C8—24no—
260C2×C8—42no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—42no—
275C42C2×D4×C1312yes—
276C42C13×#4112yes—
277C13#903211yescharacteristic, direct product factor, Sylow
278C23—22no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C2×C13×C22⋊C411yescharacteristic
286Q8—44no—
287D4—24no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4C13×#10412yes—
314C2×C4C4×D4×C1312yes—
315C2×C4C13×#12011yescharacteristic
316C2×C4C13×#12112yes—
317C2×C4C13×#12311yescharacteristic
318C8—44no—
319C8—44no—
320C22—21no—
321C22—21no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22C13×#38611yescharacteristic
330C22C2×C13×#10411yescharacteristic
331C22C13×#42111yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4C13×#45412yes—
343C2—21no—
344C2—21no—
345C2—82no—
346C2C13×#187111yescharacteristic
347C2C13×#188811yescharacteristic
348C2C13×#189111yescharacteristic
subgroupG/H
centerC2×C4×C13#120
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2983C2semidirect
3. C4×C13×#101C2semidirect
5. C13×#1300C2semidirect
63. #9032C13direct (N × H)
104. #2983C2×C13semidirect
106. C4×#101C2×C13semidirect
108. #1300C2×C13semidirect
277. C13#9032direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29832
C13×#23982
C4×C13×#1012
C13×#14902
C13×#13002
#903213