Finite Group Databasebeta

← C13×#10856 #15697195

Subgroups — C13×#10856 #15697195

Order 3328.

810 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
1C2×C13×#423C211yesmaximal, characteristic
2C2×C13×#423C211yesmaximal, characteristic
3C4×C13×#117C211yesmaximal, characteristic
4C2×C13×#344C214yesmaximal
5C22×C13×M16C2212yes—
6C22×C13×M16C2212yes—
7C2×C13×#117C2212yes—
8C22×C42×C13C2211yescharacteristic
9C13×#423—22no—
10C13×#423—22no—
11C13×#423—21no—
12C13×#423—21no—
13C13×#423C412yescomplemented
14C13×#423C412yescomplemented
15C2×C13×C4⋊C8—22no—
16C2×C13×C4⋊C8C414yescomplemented
17C4×C13×C4⋊C4—22no—
18C4×C13×C22⋊C4C414yes—
19C13×#376—21no—
20C43×C13—21no—
21C13×#344—28no—
22C23×C4×C13C2×C412yes—
23C23×C4×C13C2311yescharacteristic
24C2×C13×M16—24no—
25C2×C13×M16—22no—
26C2×C13×M16—22no—
27C2×C13×M16—22no—
28C2×C13×M16—24no—
29C2×C13×M16—24no—
30C2×C13×M16—24no—
31C2×C13×M16C2×C414yes—
32C22×C8×C13—22no—
33C22×C8×C13C2×C414yes—
34C13×#117—22no—
35C13×#117—22no—
36C13×#117D414yes—
37C13×#117Q814yes—
38C2×C13×C4⋊C4—22no—
39C2×C13×C22⋊C4C2×C414yes—
40C2×C42×C13—22no—
41C2×C42×C13—24no—
42C2×C42×C13C2×C412yes—
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13D412yes—
46C2×C42×C13D412yes—
47C2×C42×C13D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13Q811yescharacteristic
50C2×C42×C13Q811yescharacteristic
51C13×C4⋊C8—24no—
52C13×C4⋊C8—24no—
53C13×C4⋊C8—24no—
54C13×C4⋊C8—24no—
55C13×#95—24no—
56#10856C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13C22×C411yescharacteristic
58C22×C4×C13—24no—
59C22×C4×C13—44no—
60C22×C4×C13C4212yes—
61C22×C4×C13C4212yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C4⋊C412yes—
65C22×C4×C13C4⋊C412yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×Q811yescharacteristic
73C22×C4×C13C2×Q812yes—
74C22×C4×C13#4112yes—
75C22×C4×C13#4112yes—
76C13×M16—28no—
77C13×M16—44no—
78C13×M16—44no—
79C13×M16—42no—
80C13×M16—42no—
81C2×C8×C13—24no—
82C2×C8×C13—24no—
83C2×C8×C13—28no—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—24no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4C4⋊C418yes—
90C42×C13—24no—
91C42×C13—24no—
92C42×C13—48no—
93C42×C13C22⋊C412yes—
94C42×C13C22⋊C412yes—
95C42×C13C22⋊C412yes—
96C42×C13C22⋊C412yes—
97C42×C13C4⋊C412yes—
98C42×C13C4⋊C411yescharacteristic
99C42×C13C4⋊C411yescharacteristic
100C42×C13C4⋊C411yescharacteristic
101C42×C13C4⋊C412yes—
102C42×C13C4⋊C411yescharacteristic
103C2×#423C2×C1311yescharacteristic
104C2×#423C2×C1311yescharacteristic
105C4×#117C2×C1311yescharacteristic
106C2×#344C2×C1314yes—
107C23×C13—42no—
108C23×C13C2×C4211yescharacteristic
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13C2×C4⋊C411yescharacteristic
111C23×C13C2×C4⋊C412yes—
112C23×C13#11712yes—
113C2×C4×C13—24no—
114C2×C4×C13—24no—
115C2×C4×C13—24no—
116C2×C4×C13—28no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—48no—
121C2×C4×C13#9512yes—
122C2×C4×C13#9512yes—
123C2×C4×C13#9512yes—
124C2×C4×C13#9512yes—
125C2×C4×C13C2×C22⋊C411yescharacteristic
126C2×C4×C13C2×C22⋊C411yescharacteristic
127C2×C4×C13C2×C4⋊C411yescharacteristic
128C2×C4×C13C2×C4⋊C411yescharacteristic
129C2×C4×C13C4×D412yes—
130C2×C4×C13C4×D412yes—
131C2×C4×C13C4×Q812yes—
132C2×C4×C13C4×Q812yes—
133C2×C4×C13#12112yes—
134C2×C4×C13#12112yes—
135C2×C4×C13C22⋊Q812yes—
136C2×C4×C13C22⋊Q812yes—
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13#12512yes—
140C2×C4×C13#12711yescharacteristic
141C2×C4×C13C4⋊Q812yes—
142C2×C4×C13C4⋊Q811yescharacteristic
143C8×C13—44no—
144C8×C13—44no—
145C22×M16C22×C1312yes—
146C22×M16C22×C1312yes—
147C2×#117C22×C1312yes—
148C22×C42C22×C1311yescharacteristic
149#423—22no—
150#423—22no—
151#423—21no—
152#423—21no—
153#423C4×C1312yescomplemented
154#423C4×C1312yescomplemented
155C2×C4⋊C8—22no—
156C2×C4⋊C8C4×C1314yescomplemented
157C4×C4⋊C4—22no—
158C4×C22⋊C4C4×C1314yes—
159#376—21no—
160C43—21no—
161#344—28no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13C2×#9511yescharacteristic
168C22×C13C4×C4⋊C412yes—
169C22×C13#38012yes—
170C22×C13#38211yescharacteristic
171C22×C13#38411yescharacteristic
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—48no—
176C4×C13#34414yescomplemented
177C4×C13#38912yes—
178C4×C13#38912yes—
179C4×C13#39011yescharacteristic
180C4×C13#39011yescharacteristic
181C4×C13#39111yescharacteristic
182C4×C13#39111yescharacteristic
183C23×C4C2×C4×C1312yes—
184C23×C4C23×C1311yescharacteristic
185C2×M16—24no—
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—24no—
190C2×M16—24no—
191C2×M16—24no—
192C2×M16C2×C4×C1314yes—
193C22×C8—22no—
194C22×C8C2×C4×C1314yes—
195#117—22no—
196#117—22no—
197#117D4×C1314yes—
198#117Q8×C1314yes—
199C2×C4⋊C4—22no—
200C2×C22⋊C4C2×C4×C1314yes—
201C2×C42—22no—
202C2×C42—24no—
203C2×C42C2×C4×C1312yes—
204C2×C42C2×C4×C1311yescharacteristic
205C2×C42C2×C4×C1311yescharacteristic
206C2×C42D4×C1312yes—
207C2×C42D4×C1311yescharacteristic
208C2×C42D4×C1311yescharacteristic
209C2×C42D4×C1312yes—
210C2×C42Q8×C1311yescharacteristic
211C2×C42Q8×C1311yescharacteristic
212C4⋊C8—24no—
213C4⋊C8—24no—
214C4⋊C8—24no—
215C4⋊C8—24no—
216#95—24no—
217C2×C13—22no—
218C2×C13—22no—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13C4⋊#9511yescharacteristic
222C2×C13C2×#34412yes—
223C24C22×C4×C1311yescharacteristic
224C22×C4—24no—
225C22×C4—44no—
226C22×C4C42×C1312yes—
227C22×C4C42×C1312yes—
228C22×C4C13×C22⋊C412yes—
229C22×C4C13×C22⋊C412yes—
230C22×C4C13×C4⋊C412yes—
231C22×C4C13×C4⋊C412yes—
232C22×C4C22×C4×C1311yescharacteristic
233C22×C4C22×C4×C1311yescharacteristic
234C22×C4C2×D4×C1311yescharacteristic
235C22×C4C2×D4×C1311yescharacteristic
236C22×C4C2×D4×C1311yescharacteristic
237C22×C4C2×D4×C1312yes—
238C22×C4C2×Q8×C1311yescharacteristic
239C22×C4C2×Q8×C1312yes—
240C22×C4C13×#4112yes—
241C22×C4C13×#4112yes—
242M16—28no—
243M16—44no—
244M16—44no—
245M16—42no—
246M16—42no—
247C2×C8—24no—
248C2×C8—24no—
249C2×C8—28no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C22⋊C4—24no—
255C22⋊C4C13×C4⋊C418yes—
256C42—24no—
257C42—24no—
258C42—48no—
259C42C13×C22⋊C412yes—
260C42C13×C22⋊C412yes—
261C42C13×C22⋊C412yes—
262C42C13×C22⋊C412yes—
263C42C13×C4⋊C412yes—
264C42C13×C4⋊C411yescharacteristic
265C42C13×C4⋊C411yescharacteristic
266C42C13×C4⋊C411yescharacteristic
267C42C13×C4⋊C412yes—
268C42C13×C4⋊C411yescharacteristic
269C13#1085611yescharacteristic, direct product factor, Sylow
270C23—42no—
271C23C2×C42×C1311yescharacteristic
272C23C2×C13×C22⋊C411yescharacteristic
273C23C2×C13×C4⋊C411yescharacteristic
274C23C2×C13×C4⋊C412yes—
275C23C13×#11712yes—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—48no—
284C2×C4C13×#9512yes—
285C2×C4C13×#9512yes—
286C2×C4C13×#9512yes—
287C2×C4C13×#9512yes—
288C2×C4C2×C13×C22⋊C411yescharacteristic
289C2×C4C2×C13×C22⋊C411yescharacteristic
290C2×C4C2×C13×C4⋊C411yescharacteristic
291C2×C4C2×C13×C4⋊C411yescharacteristic
292C2×C4C4×D4×C1312yes—
293C2×C4C4×D4×C1312yes—
294C2×C4C4×Q8×C1312yes—
295C2×C4C4×Q8×C1312yes—
296C2×C4C13×#12112yes—
297C2×C4C13×#12112yes—
298C2×C4C13×C22⋊Q812yes—
299C2×C4C13×C22⋊Q812yes—
300C2×C4C13×#12411yescharacteristic
301C2×C4C13×#12411yescharacteristic
302C2×C4C13×#12512yes—
303C2×C4C13×#12711yescharacteristic
304C2×C4C13×C4⋊Q812yes—
305C2×C4C13×C4⋊Q811yescharacteristic
306C8—44no—
307C8—44no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—42no—
312C22—42no—
313C22C2×C13×#9511yescharacteristic
314C22C4×C13×C4⋊C412yes—
315C22C13×#38012yes—
316C22C13×#38211yescharacteristic
317C22C13×#38411yescharacteristic
318C4—22no—
319C4—22no—
320C4—22no—
321C4—48no—
322C4C13×#34414yescomplemented
323C4C13×#38912yes—
324C4C13×#38912yes—
325C4C13×#39011yescharacteristic
326C4C13×#39011yescharacteristic
327C4C13×#39111yescharacteristic
328C4C13×#39111yescharacteristic
329C2—22no—
330C2—22no—
331C2—21no—
332C2—21no—
333C2C13×C4⋊#9511yescharacteristic
334C2C2×C13×#34412yes—
subgroupG/H
centerC2×C4×C13C2×C22⋊C4
commutatorC23C2×C42×C13
Frattini, cosocleC23×C4C23×C13
socleC22×C13C2×#95
prime radicalC24×C13C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
13. C13×#423C4semidirect
14. C13×#423C4semidirect
16. C2×C13×C4⋊C8C4semidirect
56. #10856C13direct (N × H)
153. #423C4×C13semidirect
154. #423C4×C13semidirect
156. C2×C4⋊C8C4×C13semidirect
176. C4×C13#344semidirect
269. C13#10856direct (N × H)
322. C4C13×#344semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#4232
C4×C13×#1172
C2×C13×#3442
#1085613