Finite Group Databasebeta

← C13×#7716 #15694055

Subgroups — C13×#7716 #15694055

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2861C211yesmaximal, characteristic
2C13×#1839C211yesmaximal, characteristic, complemented
3C13×#1831C211yesmaximal, characteristic, complemented
4C13×#1272C212yesmaximal, complemented
5C13×#1270C212yesmaximal
6C2×C13×#125C411yescharacteristic
7C2×C13×#124C411yescharacteristic
8C2×C13×C4⋊C8—21no—
9C13×#391C411yescharacteristic
10C13×#391C2211yescharacteristic
11C13×#390C411yescharacteristic
12C13×#390C2211yescharacteristic
13C13×#388—21no—
14C13×#388—21no—
15C13×#388—21no—
16C13×#388—21no—
17C43×C13C2211yescharacteristic
18C13×#336—21no—
19C13×#336—21no—
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—42no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51#7716C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C2×Q8×C13—22no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C2×C8×C13—42no—
73C2×C8×C13—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—22no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—41no—
92C42×C13—41no—
93C42×C13—41no—
94#2861C2×C1311yescharacteristic
95#1839C2×C1311yescharacteristic, complemented
96#1831C2×C1311yescharacteristic, complemented
97#1272C2×C1312yescomplemented
98#1270C2×C1312yes—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13C2×C22⋊C411yescharacteristic
107Q8×C13—82no—
108D4×C13—82no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
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#13112yes—
137C2×C4×C13#13512yes—
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C8×C13—82no—
141C8×C13—82no—
142C2×#125C4×C1311yescharacteristic
143C2×#124C4×C1311yescharacteristic
144C2×C4⋊C8—21no—
145#391C4×C1311yescharacteristic
146#391C22×C1311yescharacteristic
147#390C4×C1311yescharacteristic
148#390C22×C1311yescharacteristic
149#388—21no—
150#388—21no—
151#388—21no—
152#388—21no—
153C43C22×C1311yescharacteristic
154#336—21no—
155#336—21no—
156#336—21no—
157#336C22×C1312yes—
158#336C22×C1312yes—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13#40811yescharacteristic
167C22×C13#41011yescharacteristic
168C22×C13C2×#10011yescharacteristic
169C22×C13#41611yescharacteristic
170C22×C13#41711yescharacteristic
171C22×C13#42111yescharacteristic
172C22×C13#42111yescharacteristic
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—22no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184C22×Q8C2×C4×C1311yescharacteristic
185C22×D4C2×C4×C1311yescharacteristic
186C22×C8—22no—
187C22×C8—22no—
188#125—42no—
189#124—42no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×C4×C1311yescharacteristic
193C2×C4⋊C4C2×C4×C1311yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C42C2×C4×C1311yescharacteristic
201C2×C42C2×C4×C1311yescharacteristic
202C2×C42D4×C1311yescharacteristic
203C2×C42D4×C1311yescharacteristic
204C2×C42D4×C1311yescharacteristic
205C2×C42D4×C1311yescharacteristic
206C2×C42C23×C1311yescharacteristic
207C4⋊C8—42no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212C2×C13—161no—
213C2×C13#146911yescharacteristic
214C2×C13#148211yescharacteristic
215C2×C13#149511yescharacteristic
216C2×C13#151211yescharacteristic
217C2×C13#152111yescharacteristic
218C2×C13#153611yescharacteristic
219C2×C13#155111yescharacteristic
220C24—21no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×D4—22no—
225C2×D4—41no—
226C2×D4—41no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C13×C22⋊C411yescharacteristic
231C22×C4C13×C22⋊C411yescharacteristic
232C22×C4C13×C22⋊C411yescharacteristic
233C22×C4C13×C22⋊C411yescharacteristic
234C22×C4C22×C4×C1311yescharacteristic
235C22×C4C2×D4×C1311yescharacteristic
236C22×C4C2×D4×C1311yescharacteristic
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C42—22no—
255C42—22no—
256C42—22no—
257C42—21no—
258C42—21no—
259C42—41no—
260C42—41no—
261C42—41no—
262C13#771611yescharacteristic, direct product factor, Sylow
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23C2×C13×C22⋊C411yescharacteristic
271Q8—82no—
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
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—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×C4C13×#10012yes—
300C2×C4C13×#13112yes—
301C2×C4C13×#13512yes—
302C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
303C2×C4C13×#13711yescharacteristic
304C8—82no—
305C8—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C13×#40811yescharacteristic
314C22C13×#41011yescharacteristic
315C22C2×C13×#10011yescharacteristic
316C22C13×#41611yescharacteristic
317C22C13×#41711yescharacteristic
318C22C13×#42111yescharacteristic
319C22C13×#42111yescharacteristic
320C4—21no—
321C4—21no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2C13×#146911yescharacteristic
333C2C13×#148211yescharacteristic
334C2C13×#149511yescharacteristic
335C2C13×#151211yescharacteristic
336C2C13×#152111yescharacteristic
337C2C13×#153611yescharacteristic
338C2C13×#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. C13×#1839C2semidirect
3. C13×#1831C2semidirect
4. C13×#1272C2semidirect
51. #7716C13direct (N × H)
95. #1839C2×C13semidirect
96. #1831C2×C13semidirect
97. #1272C2×C13semidirect
262. C13#7716direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28612
C13×#18392
C13×#18312
C13×#12722
C13×#12702
#771613