Finite Group Databasebeta

← C13×#7676 #15694015

Subgroups — C13×#7676 #15694015

Order 3328.

458 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2861C211yesmaximal, characteristic
2C4×C13×C4⋊C8C211yesmaximal, characteristic, complemented
3C13×#1745C211yesmaximal, characteristic, complemented
4C13×#1272C212yesmaximal, complemented
5C13×#1270C212yesmaximal
6C2×C13×#125C411yescharacteristic
7C2×C13×#124C411yescharacteristic
8C2×C13×C4⋊C8—21no—
9C2×C13×#97—21no—
10C2×C4×C8×C13—21no—
11C13×#391C411yescharacteristic
12C13×#391C2211yescharacteristic
13C13×#390C411yescharacteristic
14C13×#390C2211yescharacteristic
15C13×#388—21no—
16C13×#388—21no—
17C13×#388—21no—
18C13×#388—21no—
19C43×C13C2211yescharacteristic
20C13×#336—21no—
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C22×C8×C13—22no—
26C22×C8×C13—22no—
27C13×#125—42no—
28C13×#124—42no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C13×C4⋊C8—24no—
47C13×#97—24no—
48C4×C8×C13—42no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53#7676C1311yesmaximal, characteristic, direct product factor, Sylow
54C24×C13—21no—
55C2×Q8×C13—22no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×D4×C13—22no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C2×C8×C13—24no—
72C2×C8×C13—24no—
73C2×C8×C13—42no—
74C2×C8×C13—42no—
75C2×C8×C13—42no—
76C2×C8×C13—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—22no—
89C42×C13—22no—
90C42×C13—22no—
91C42×C13—22no—
92C42×C13—22no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—41no—
96#2861C2×C1311yescharacteristic
97C4×C4⋊C8C2×C1311yescharacteristic, complemented
98#1745C2×C1311yescharacteristic, complemented
99#1272C2×C1312yescomplemented
100#1270C2×C1312yes—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109Q8×C13—82no—
110D4×C13—82no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
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#10012yes—
136C2×C4×C13#10412yes—
137C2×C4×C13#10412yes—
138C2×C4×C13#13112yes—
139C2×C4×C13#13512yes—
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C8×C13—44no—
143C8×C13—44no—
144C2×#125C4×C1311yescharacteristic
145C2×#124C4×C1311yescharacteristic
146C2×C4⋊C8—21no—
147C2×#97—21no—
148C2×C4×C8—21no—
149#391C4×C1311yescharacteristic
150#391C22×C1311yescharacteristic
151#390C4×C1311yescharacteristic
152#390C22×C1311yescharacteristic
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157C43C22×C1311yescharacteristic
158#336—21no—
159#336C22×C1312yes—
160#336C22×C1312yes—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13#40811yescharacteristic
169C22×C13#41011yescharacteristic
170C22×C13C2×#10011yescharacteristic
171C22×C13#41611yescharacteristic
172C22×C13#41711yescharacteristic
173C22×C13C2×#10411yescharacteristic
174C22×C13C2×#10411yescharacteristic
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13—81no—
186C22×Q8C2×C4×C1311yescharacteristic
187C22×D4C2×C4×C1311yescharacteristic
188C22×C8—22no—
189C22×C8—22no—
190#125—42no—
191#124—42no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×C4×C1311yescharacteristic
195C2×C4⋊C4C2×C4×C1311yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C42C2×C4×C1311yescharacteristic
203C2×C42C2×C4×C1311yescharacteristic
204C2×C42D4×C1311yescharacteristic
205C2×C42D4×C1311yescharacteristic
206C2×C42D4×C1311yescharacteristic
207C2×C42D4×C1311yescharacteristic
208C2×C42C23×C1311yescharacteristic
209C4⋊C8—24no—
210#97—24no—
211C4×C8—42no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216C2×C13—161no—
217C2×C13#146911yescharacteristic
218C2×C13#148311yescharacteristic
219C2×C13#149411yescharacteristic
220C2×C13#150011yescharacteristic
221C2×C13#150911yescharacteristic
222C2×C13#152511yescharacteristic
223C2×C13#155111yescharacteristic
224C24—21no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×D4—22no—
229C2×D4—41no—
230C2×D4—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4C13×C22⋊C411yescharacteristic
235C22×C4C13×C22⋊C411yescharacteristic
236C22×C4C13×C22⋊C411yescharacteristic
237C22×C4C13×C22⋊C411yescharacteristic
238C22×C4C22×C4×C1311yescharacteristic
239C22×C4C2×D4×C1311yescharacteristic
240C22×C4C2×D4×C1311yescharacteristic
241C2×C8—24no—
242C2×C8—24no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—21no—
264C42—21no—
265C42—41no—
266C13#767611yescharacteristic, direct product factor, Sylow
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C2×C13×C22⋊C411yescharacteristic
275Q8—82no—
276D4—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
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×C4C13×#10012yes—
302C2×C4C13×#10412yes—
303C2×C4C13×#10412yes—
304C2×C4C13×#13112yes—
305C2×C4C13×#13512yes—
306C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
307C2×C4C13×#13711yescharacteristic
308C8—44no—
309C8—44no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C13×#40811yescharacteristic
318C22C13×#41011yescharacteristic
319C22C2×C13×#10011yescharacteristic
320C22C13×#41611yescharacteristic
321C22C13×#41711yescharacteristic
322C22C2×C13×#10411yescharacteristic
323C22C2×C13×#10411yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—161no—
336C2C13×#146911yescharacteristic
337C2C13×#148311yescharacteristic
338C2C13×#149411yescharacteristic
339C2C13×#150011yescharacteristic
340C2C13×#150911yescharacteristic
341C2C13×#152511yescharacteristic
342C2C13×#155111yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C43×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C13×C4⋊C8C2semidirect
3. C13×#1745C2semidirect
4. C13×#1272C2semidirect
53. #7676C13direct (N × H)
97. C4×C4⋊C8C2×C13semidirect
98. #1745C2×C13semidirect
99. #1272C2×C13semidirect
266. C13#7676direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28612
C4×C13×C4⋊C82
C13×#17452
C13×#12722
C13×#12702
#767613