Finite Group Databasebeta

← C13×#7712 #15694051

Subgroups — C13×#7712 #15694051

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2860C211yesmaximal, characteristic
2C13×#1839C211yesmaximal, characteristic, complemented
3C13×#1767C211yesmaximal, characteristic, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C212yesmaximal
6C2×C13×#126—21no—
7C2×C13×C4⋊C8—21no—
8C2×C13×#97—21no—
9C13×#390C411yescharacteristic
10C13×#390C411yescharacteristic
11C13×#390C2211yescharacteristic
12C13×#389C411yescharacteristic
13C13×#389C411yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#388—21no—
16C13×#388—21no—
17C13×#388—21no—
18C43×C13C2211yescharacteristic
19C13×#336—21no—
20C13×#336—21no—
21C13×#336C2212yes—
22C13×#336C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C22×C8×C13—22no—
25C22×C8×C13—22no—
26C13×#126—44no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
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—42no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51#7712C1311yesmaximal, characteristic, direct product factor, Sylow
52C24×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C2×C8×C13—24no—
67C2×C8×C13—42no—
68C2×C8×C13—42no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—41no—
85C42×C13—22no—
86C42×C13—22no—
87C42×C13—21no—
88C42×C13—22no—
89C42×C13—21no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13—41no—
93#2860C2×C1311yescharacteristic
94#1839C2×C1311yescharacteristic, complemented
95#1767C2×C1311yescharacteristic, complemented
96#1271C2×C1312yescomplemented
97#1270C2×C1312yes—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C2×C22⋊C411yescharacteristic
106D4×C13—82no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
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—41no—
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#10412yes—
134C2×C4×C13#13112yes—
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13AGL(1,ℤ/8)12yes—
137C2×C4×C13#13711yescharacteristic
138C8×C13—44no—
139C8×C13—82no—
140C2×#126—21no—
141C2×C4⋊C8—21no—
142C2×#97—21no—
143#390C4×C1311yescharacteristic
144#390C4×C1311yescharacteristic
145#390C22×C1311yescharacteristic
146#389C4×C1311yescharacteristic
147#389C4×C1311yescharacteristic
148#389C22×C1311yescharacteristic
149#388—21no—
150#388—21no—
151#388—21no—
152C43C22×C1311yescharacteristic
153#336—21no—
154#336—21no—
155#336C22×C1312yes—
156#336C22×C1312yes—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13#40811yescharacteristic
165C22×C13#41011yescharacteristic
166C22×C13#41311yescharacteristic
167C22×C13#41711yescharacteristic
168C22×C13#41811yescharacteristic
169C22×C13C2×#10411yescharacteristic
170C22×C13#42111yescharacteristic
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182C22×D4C2×C4×C1311yescharacteristic
183C22×C8—22no—
184C22×C8—22no—
185#126—44no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C1311yescharacteristic
190C2×C4⋊C4C2×C4×C1311yescharacteristic
191C2×C4⋊C4C2×C4×C1311yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42C2×C4×C1311yescharacteristic
199C2×C42C2×C4×C1311yescharacteristic
200C2×C42D4×C1311yescharacteristic
201C2×C42D4×C1311yescharacteristic
202C2×C42D4×C1311yescharacteristic
203C2×C42D4×C1311yescharacteristic
204C2×C42C23×C1311yescharacteristic
205C4⋊C8—24no—
206#97—42no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C13—161no—
211C2×C13#147311yescharacteristic
212C2×C13#148411yescharacteristic
213C2×C13#149511yescharacteristic
214C2×C13#150911yescharacteristic
215C2×C13#151411yescharacteristic
216C2×C13#153211yescharacteristic
217C2×C13#155711yescharacteristic
218C24—21no—
219C2×D4—22no—
220C2×D4—41no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C13×C22⋊C411yescharacteristic
226C22×C4C13×C22⋊C411yescharacteristic
227C22×C4C13×C22⋊C411yescharacteristic
228C22×C4C13×C22⋊C411yescharacteristic
229C22×C4C22×C4×C1311yescharacteristic
230C22×C4C2×D4×C1311yescharacteristic
231C22×C4C2×D4×C1311yescharacteristic
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—22no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C42—22no—
252C42—22no—
253C42—21no—
254C42—22no—
255C42—21no—
256C42—41no—
257C42—41no—
258C42—41no—
259C13#771211yescharacteristic, direct product factor, Sylow
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C2×C13×C22⋊C411yescharacteristic
268D4—82no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
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—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4C13×#10412yes—
296C2×C4C13×#13112yes—
297C2×C4C13×AGL(1,ℤ/8)11yescharacteristic
298C2×C4C13×AGL(1,ℤ/8)12yes—
299C2×C4C13×#13711yescharacteristic
300C8—44no—
301C8—82no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22C13×#40811yescharacteristic
310C22C13×#41011yescharacteristic
311C22C13×#41311yescharacteristic
312C22C13×#41711yescharacteristic
313C22C13×#41811yescharacteristic
314C22C2×C13×#10411yescharacteristic
315C22C13×#42111yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C2—161no—
328C2C13×#147311yescharacteristic
329C2C13×#148411yescharacteristic
330C2C13×#149511yescharacteristic
331C2C13×#150911yescharacteristic
332C2C13×#151411yescharacteristic
333C2C13×#153211yescharacteristic
334C2C13×#155711yescharacteristic
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×#1767C2semidirect
4. C13×#1271C2semidirect
51. #7712C13direct (N × H)
94. #1839C2×C13semidirect
95. #1767C2×C13semidirect
96. #1271C2×C13semidirect
259. C13#7712direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28602
C13×#18392
C13×#17672
C13×#12712
C13×#12702
#771213