Finite Group Databasebeta

← C13×#11528 #15697867

Subgroups — C13×#11528 #15697867

Order 3328.

442 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2322C211yesmaximal, characteristic
2C13×#1466C211yesmaximal, characteristic
3C13×#1465C211yesmaximal, characteristic
4C13×#1326C212yesmaximal, complemented
5C13×#1317C212yesmaximal, complemented
6C2×C13×#123C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C13×C4⋊C4C411yescharacteristic
9C13×#432—21no—
10C13×#407—21no—
11C13×#389—21no—
12C13×#388—21no—
13C13×#387—21no—
14C13×#386C411yescharacteristic
15C13×#385—21no—
16C13×#385C2211yescharacteristic
17C13×#381C2211yescharacteristic
18C4×C13×C22⋊C4C411yescharacteristic
19C13×#324—21no—
20C13×#323—21no—
21C13×#323C2212yes—
22C13×#323C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C2×C13×M16—41no—
29C13×#123—22no—
30C13×#123—22no—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—41no—
38C2×C13×C4⋊C4—41no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4C2311yescharacteristic
46C2×C42×C13—21no—
47C2×C42×C13D411yescharacteristic
48C13×C4⋊C8—41no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—41no—
52C13×#97—41no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58#11528C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13C22⋊C411yescharacteristic
60C24×C13C22×C411yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13—81no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13M1612yescomplemented
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×M16—82no—
87C2×C8×C13—42no—
88C2×C8×C13—42no—
89C13×C4⋊C4—24no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C22⋊C4—24no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—81no—
101C13×C22⋊C4M1612yescomplemented
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—81no—
105#2322C2×C1311yescharacteristic
106#1466C2×C1311yescharacteristic
107#1465C2×C1311yescharacteristic
108#1326C2×C1312yescomplemented
109#1317C2×C1312yescomplemented
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13C2×M1611yescharacteristic
121C23×C13C2×M1611yescharacteristic
122D4×C13—42no—
123D4×C13—42no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—82no—
153C2×C4×C13#9911yescharacteristic
154C2×C4×C13#9911yescharacteristic
155C8×C13—82no—
156C8×C13—82no—
157C2×#123C4×C1311yescharacteristic
158C2×C4×D4C22×C1311yescharacteristic
159C22×C4⋊C4C4×C1311yescharacteristic
160#432—21no—
161#407—21no—
162#389—21no—
163#388—21no—
164#387—21no—
165#386C4×C1311yescharacteristic
166#385—21no—
167#385C22×C1311yescharacteristic
168#381C22×C1311yescharacteristic
169C4×C22⋊C4C4×C1311yescharacteristic
170#324—21no—
171#323—21no—
172#323C22×C1312yes—
173#323C22×C1312yes—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—81no—
188C22×C13#40711yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41311yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—42no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—42no—
199C4×C13—81no—
200C4×C13—81no—
201C22×D4C2×C4×C1311yescharacteristic
202C23×C4C2×C4×C1311yescharacteristic
203C23×C4C2×C4×C1311yescharacteristic
204C23×C4C2×C4×C1311yescharacteristic
205C23×C4D4×C1311yescharacteristic
206C2×M16—41no—
207#123—22no—
208#123—22no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4D4×C1311yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4C2×C4×C1311yescharacteristic
221C2×C22⋊C4C2×C4×C1311yescharacteristic
222C2×C22⋊C4D4×C1311yescharacteristic
223C2×C22⋊C4C23×C1311yescharacteristic
224C2×C42—21no—
225C2×C42D4×C1311yescharacteristic
226C4⋊C8—41no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230#97—41no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—41no—
239C2×C13—41no—
240C2×C13—81no—
241C2×C13#146511yescharacteristic
242C2×C13#212111yescharacteristic
243C2×C13#212311yescharacteristic
244C24C13×C22⋊C411yescharacteristic
245C24C22×C4×C1311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C13×C22⋊C411yescharacteristic
266C22×C4C13×C22⋊C411yescharacteristic
267C22×C4C13×C22⋊C411yescharacteristic
268C22×C4C13×M1612yescomplemented
269C22×C4C2×D4×C1311yescharacteristic
270C22×C4C2×D4×C1311yescharacteristic
271M16—82no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—24no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—81no—
280C22⋊C4—24no—
281C22⋊C4—21no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—81no—
286C22⋊C4C13×M1612yescomplemented
287C42—21no—
288C42—21no—
289C42—81no—
290C13#1152811yescharacteristic, direct product factor, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×C13×C22⋊C411yescharacteristic
301C23C2×C13×M1611yescharacteristic
302C23C2×C13×M1611yescharacteristic
303D4—42no—
304D4—42no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—82no—
334C2×C4C13×#9911yescharacteristic
335C2×C4C13×#9911yescharacteristic
336C8—82no—
337C8—82no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—42no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22C13×#40711yescharacteristic
353C22C2×C13×#9911yescharacteristic
354C22C13×#41311yescharacteristic
355C4—21no—
356C4—21no—
357C4—42no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—42no—
363C4—81no—
364C4—81no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2C13×#146511yescharacteristic
371C2C13×#212111yescharacteristic
372C2C13×#212311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC22×D4×C13C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1326C2semidirect
5. C13×#1317C2semidirect
58. #11528C13direct (N × H)
83. C22×C4×C13M16semidirect
101. C13×C22⋊C4M16semidirect
108. #1326C2×C13semidirect
109. #1317C2×C13semidirect
268. C22×C4C13×M16semidirect
286. C22⋊C4C13×M16semidirect
290. C13#11528direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23222
C13×#14662
C13×#14652
C13×#13262
C13×#13172
#1152813