Finite Group Databasebeta

← C13×#9491 #15695830

Subgroups — C13×#9491 #15695830

Order 3328.

544 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2873C211yesmaximal, characteristic
2C13×#2599C211yesmaximal, characteristic
3C13×#1491C212yesmaximal, complemented
4C13×#1464C211yesmaximal, characteristic
5C13×#1288C212yesmaximal, complemented
6C22×C13×M16—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C2×C13×#117C2211yescharacteristic
9C13×#432C2212yes—
10C13×#405—24no—
11C4×C13×M16—21no—
12C4×C13×M16C2212yes—
13C13×#398C411yescharacteristic
14C13×#397C411yescharacteristic
15C13×#395C411yescharacteristic
16C13×#393C411yescharacteristic
17C13×#388—21no—
18C13×#387—21no—
19C13×#387—21no—
20C13×#385—21no—
21C13×#383C2211yescharacteristic
22C13×Q8⋊C8—24no—
23C13×#324—21no—
24C13×#323—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C2×C13×M16—22no—
28C2×C13×M16—24no—
29C2×C13×M16—24no—
30C2×C13×M16—22no—
31C22×C8×C13—22no—
32C4×Q8×C13—22no—
33C4×Q8×C13—22no—
34C13×#117—22no—
35C13×#117—22no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C42×C13—21no—
47C2×C42×C13D411yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C13×C4⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×#97—22no—
52C13×#97—22no—
53C13×#97—22no—
54C4×C8×C13—22no—
55C4×C8×C13D414yes—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95C2×C411yescharacteristic
63C13×#95C2×C411yescharacteristic
64#9491C1311yesmaximal, characteristic, direct product factor, Sylow
65C24×C13C22⋊C411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—42no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C13×M16—28no—
83C13×M16—24no—
84C13×M16—24no—
85C2×C8×C13—28no—
86C2×C8×C13—24no—
87C2×C8×C13—42no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—42no—
102C42×C13C2×D412yes—
103C42×C13#4112yes—
104#2873C2×C1311yescharacteristic
105#2599C2×C1311yescharacteristic
106#1491C2×C1312yescomplemented
107#1464C2×C1311yescharacteristic
108#1288C2×C1312yescomplemented
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115Q8×C13—24no—
116Q8×C13—42no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
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—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13#10412yes—
143C2×C4×C13C4×D412yes—
144C2×C4×C13#12011yescharacteristic
145C2×C4×C13#12112yes—
146C2×C4×C13#12311yescharacteristic
147C8×C13—28no—
148C8×C13—82no—
149C22×M16—21no—
150C2×C4×Q8C22×C1311yescharacteristic
151C2×#117C22×C1311yescharacteristic
152#432C22×C1312yes—
153#405—24no—
154C4×M16—21no—
155C4×M16C22×C1312yes—
156#398C4×C1311yescharacteristic
157#397C4×C1311yescharacteristic
158#395C4×C1311yescharacteristic
159#393C4×C1311yescharacteristic
160#388—21no—
161#387—21no—
162#387—21no—
163#385—21no—
164#383C22×C1311yescharacteristic
165Q8⋊C8—24no—
166#324—21no—
167#323—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13#38611yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—41no—
184C4×C13—42no—
185C4×C13—41no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—81no—
189C22×Q8C2×C4×C1311yescharacteristic
190C23×C4D4×C1311yescharacteristic
191C2×M16—22no—
192C2×M16—24no—
193C2×M16—24no—
194C2×M16—22no—
195C22×C8—22no—
196C4×Q8—22no—
197C4×Q8—22no—
198#117—22no—
199#117—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C1311yescharacteristic
204C2×C4⋊C4C2×C4×C1311yescharacteristic
205C2×C4⋊C4D4×C1311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4C2×C4×C1311yescharacteristic
209C2×C22⋊C4D4×C1311yescharacteristic
210C2×C42—21no—
211C2×C42D4×C1311yescharacteristic
212C2×C42C23×C1311yescharacteristic
213C4⋊C8—22no—
214C22⋊C8—22no—
215#97—22no—
216#97—22no—
217#97—22no—
218C4×C8—22no—
219C4×C8D4×C1314yes—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×C4×C1311yescharacteristic
227#95C2×C4×C1311yescharacteristic
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—42no—
231C2×C13#189111yescharacteristic
232C2×C13#189611yescharacteristic
233C2×C13#190911yescharacteristic
234C24C13×C22⋊C411yescharacteristic
235C2×Q8—22no—
236C2×Q8—42no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4C13×C22⋊C411yescharacteristic
246C22×C4C13×C22⋊C411yescharacteristic
247C22×C4C13×C22⋊C411yescharacteristic
248C22×C4C22×C4×C1311yescharacteristic
249C22×C4C2×D4×C1311yescharacteristic
250C22×C4C2×D4×C1311yescharacteristic
251M16—28no—
252M16—24no—
253M16—24no—
254C2×C8—28no—
255C2×C8—24no—
256C2×C8—42no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C42—21no—
269C42—21no—
270C42—42no—
271C42C2×D4×C1312yes—
272C42C13×#4112yes—
273C13#949111yescharacteristic, direct product factor, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23C13×#10412yes—
279C23C2×C13×C22⋊C411yescharacteristic
280Q8—24no—
281Q8—42no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
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×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4C13×#10412yes—
308C2×C4C4×D4×C1312yes—
309C2×C4C13×#12011yescharacteristic
310C2×C4C13×#12112yes—
311C2×C4C13×#12311yescharacteristic
312C8—28no—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C13×#38611yescharacteristic
322C22C2×C13×#10411yescharacteristic
323C22C2×C13×#10411yescharacteristic
324C4—22no—
325C4—21no—
326C4—22no—
327C4—21no—
328C4—22no—
329C4—41no—
330C4—42no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C13×#189111yescharacteristic
339C2C13×#189611yescharacteristic
340C2C13×#190911yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1491C2semidirect
5. C13×#1288C2semidirect
64. #9491C13direct (N × H)
106. #1491C2×C13semidirect
108. #1288C2×C13semidirect
273. C13#9491direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28732
C13×#25992
C13×#14912
C13×#14642
C13×#12882
#949113