Finite Group Databasebeta

← C13×#7666 #15694005

Subgroups — C13×#7666 #15694005

Order 3328.

438 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×#2860C211yesmaximal, characteristic
2C13×#1831C211yesmaximal, characteristic, complemented
3C13×#1744C211yesmaximal, characteristic, complemented
4C13×#1271C212yesmaximal, complemented
5C13×#1270C212yesmaximal
6C2×C13×#126—21no—
7C2×C13×C4⋊C8—21no—
8C2×C4×C8×C13—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—42no—
27C13×#126—42no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
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×C13×C22⋊C4—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13C2311yescharacteristic
47C13×C4⋊C8—42no—
48C4×C8×C13—24no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52#7666C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13—21no—
54C2×D4×C13—22no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C2×C8×C13—24no—
68C2×C8×C13—42no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13—22no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13—41no—
93C42×C13D812yes—
94C42×C13SD1612yes—
95#2860C2×C1311yescharacteristic
96#1831C2×C1311yescharacteristic, complemented
97#1744C2×C1311yescharacteristic, complemented
98#1271C2×C1312yescomplemented
99#1270C2×C1312yes—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13C2×C22⋊C411yescharacteristic
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—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#10212yes—
134C2×C4×C13#10212yes—
135C2×C4×C13#10412yes—
136C2×C4×C13#13112yes—
137C2×C4×C13C2×D811yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13#13512yes—
140C8×C13—44no—
141C8×C13—82no—
142C2×#126—21no—
143C2×C4⋊C8—21no—
144C2×C4×C8—21no—
145#390C4×C1311yescharacteristic
146#390C4×C1311yescharacteristic
147#390C22×C1311yescharacteristic
148#389C4×C1311yescharacteristic
149#389C4×C1311yescharacteristic
150#389C22×C1311yescharacteristic
151#388—21no—
152#388—21no—
153#388—21no—
154C43C22×C1311yescharacteristic
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×C13#41311yescharacteristic
169C22×C13C2×#10211yescharacteristic
170C22×C13#41611yescharacteristic
171C22×C13C2×#10411yescharacteristic
172C22×C13#42111yescharacteristic
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—22no—
180C4×C13—41no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184C22×D4C2×C4×C1311yescharacteristic
185C22×C8—22no—
186C22×C8—22no—
187#126—42no—
188#126—42no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×C4×C1311yescharacteristic
193C2×C4⋊C4C2×C4×C1311yescharacteristic
194C2×C4⋊C4C2×C4×C1311yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C42C2×C4×C1311yescharacteristic
202C2×C42C2×C4×C1311yescharacteristic
203C2×C42D4×C1311yescharacteristic
204C2×C42D4×C1311yescharacteristic
205C2×C42D4×C1311yescharacteristic
206C2×C42D4×C1311yescharacteristic
207C2×C42C23×C1311yescharacteristic
208C4⋊C8—42no—
209C4×C8—24no—
210#95—21no—
211#95—21no—
212#95—21no—
213C2×C13—161no—
214C2×C13#147311yescharacteristic
215C2×C13#148211yescharacteristic
216C2×C13#149211yescharacteristic
217C2×C13#150011yescharacteristic
218C2×C13#151711yescharacteristic
219C2×C13#153211yescharacteristic
220C2×C13#154011yescharacteristic
221C24—21no—
222C2×D4—22no—
223C2×D4—41no—
224C2×D4—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4C13×C22⋊C411yescharacteristic
229C22×C4C13×C22⋊C411yescharacteristic
230C22×C4C13×C22⋊C411yescharacteristic
231C22×C4C13×C22⋊C411yescharacteristic
232C22×C4C22×C4×C1311yescharacteristic
233C22×C4C2×D4×C1311yescharacteristic
234C22×C4C2×D4×C1311yescharacteristic
235C2×C8—24no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C42—22no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C42—41no—
261C42C13×D812yes—
262C42C13×SD1612yes—
263C13#766611yescharacteristic, direct product factor, Sylow
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C13×C22⋊C411yescharacteristic
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—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×C4C13×#10212yes—
298C2×C4C13×#10212yes—
299C2×C4C13×#10412yes—
300C2×C4C13×#13112yes—
301C2×C4C2×C13×D811yescharacteristic
302C2×C4C2×C13×SD1611yescharacteristic
303C2×C4C13×#13512yes—
304C8—44no—
305C8—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C13×#40811yescharacteristic
314C22C13×#41011yescharacteristic
315C22C13×#41311yescharacteristic
316C22C2×C13×#10211yescharacteristic
317C22C13×#41611yescharacteristic
318C22C2×C13×#10411yescharacteristic
319C22C13×#42111yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—21no—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2C13×#147311yescharacteristic
333C2C13×#148211yescharacteristic
334C2C13×#149211yescharacteristic
335C2C13×#150011yescharacteristic
336C2C13×#151711yescharacteristic
337C2C13×#153211yescharacteristic
338C2C13×#154011yescharacteristic
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×#1831C2semidirect
3. C13×#1744C2semidirect
4. C13×#1271C2semidirect
52. #7666C13direct (N × H)
96. #1831C2×C13semidirect
97. #1744C2×C13semidirect
98. #1271C2×C13semidirect
263. C13#7666direct (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×#18312
C13×#17442
C13×#12712
C13×#12702
#766613