Finite Group Databasebeta

← C13×#11550 #15697889

Subgroups — C13×#11550 #15697889

Order 3328.

408 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2500C211yesmaximal, characteristic
2C13×#1464C211yesmaximal, characteristic, complemented
3C13×#1458C211yesmaximal, characteristic, complemented
4C13×#1324C212yesmaximal, complemented
5C13×#1318C212yesmaximal, complemented
6C2×C13×#121C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#432—21no—
9C13×#431—21no—
10C13×#394—21no—
11C13×#394—21no—
12C13×#390C411yescharacteristic
13C13×#390C2211yescharacteristic
14C13×#388—21no—
15C13×#388—21no—
16C13×#384C411yescharacteristic
17C13×#382C2211yescharacteristic
18C4×C13×C22⋊C4C411yescharacteristic
19C13×#324C2212yes—
20C13×#324C2212yes—
21C13×#323—21no—
22C13×#323—21no—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C13×#121—41no—
27C13×#121—41no—
28C13×#117—41no—
29C13×#117—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
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×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C13×C4⋊C8—41no—
48C13×C4⋊C8—41no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×#97—41no—
52C4×C8×C13—41no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#11550C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13—21no—
58C24×C13C22⋊C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—81no—
64C2×D4×C13—81no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C2×C8×C13—42no—
79C2×C8×C13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—81no—
84C13×C4⋊C4—81no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—22no—
99C42×C13—41no—
100#2500C2×C1311yescharacteristic
101#1464C2×C1311yescharacteristic, complemented
102#1458C2×C1311yescharacteristic, complemented
103#1324C2×C1312yescomplemented
104#1318C2×C1312yescomplemented
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13C2×C22⋊C411yescharacteristic
118D4×C13—82no—
119D4×C13—84no—
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—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
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—41no—
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13#9911yescharacteristic
145C2×C4×C13#13112yes—
146C8×C13—82no—
147C8×C13—82no—
148C2×#121C4×C1311yescharacteristic
149C2×#117C22×C1311yescharacteristic
150#432—21no—
151#431—21no—
152#394—21no—
153#394—21no—
154#390C4×C1311yescharacteristic
155#390C22×C1311yescharacteristic
156#388—21no—
157#388—21no—
158#384C4×C1311yescharacteristic
159#382C22×C1311yescharacteristic
160C4×C22⋊C4C4×C1311yescharacteristic
161#324C22×C1312yes—
162#324C22×C1312yes—
163#323—21no—
164#323—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13#40811yescharacteristic
180C22×C13C2×#9911yescharacteristic
181C22×C13#41311yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—42no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—81no—
191C4×C13—81no—
192C22×D4—21no—
193C22×D4C2×C4×C1311yescharacteristic
194C23×C4C2×C4×C1311yescharacteristic
195#121—41no—
196#121—41no—
197#117—41no—
198#117—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C1311yescharacteristic
202C2×C4⋊C4C2×C4×C1311yescharacteristic
203C2×C4⋊C4C23×C1311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4D4×C1311yescharacteristic
211C2×C22⋊C4D4×C1311yescharacteristic
212C2×C42C2×C4×C1311yescharacteristic
213C2×C42C2×C4×C1311yescharacteristic
214C2×C42D4×C1311yescharacteristic
215C2×C42D4×C1311yescharacteristic
216C4⋊C8—41no—
217C4⋊C8—41no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220#97—41no—
221C4×C8—41no—
222#95—21no—
223#95—21no—
224#95—21no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—81no—
228C2×C13—161no—
229C2×C13#146811yescharacteristic
230C2×C13#212611yescharacteristic
231C2×C13#213411yescharacteristic
232C24—21no—
233C24C13×C22⋊C411yescharacteristic
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—42no—
238C2×D4—81no—
239C2×D4—81no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4C13×C22⋊C411yescharacteristic
248C22×C4C13×C22⋊C411yescharacteristic
249C22×C4C13×C22⋊C411yescharacteristic
250C22×C4C22×C4×C1311yescharacteristic
251C22×C4C2×D4×C1311yescharacteristic
252C22×C4C2×D4×C1311yescharacteristic
253C2×C8—42no—
254C2×C8—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—22no—
274C42—41no—
275C13#1155011yescharacteristic, direct product factor, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×C13×C22⋊C411yescharacteristic
289D4—82no—
290D4—84no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4C13×#9911yescharacteristic
315C2×C4C13×#9911yescharacteristic
316C2×C4C13×#13112yes—
317C8—82no—
318C8—82no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C13×#40811yescharacteristic
334C22C2×C13×#9911yescharacteristic
335C22C13×#41311yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—42no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—161no—
350C2C13×#146811yescharacteristic
351C2C13×#212611yescharacteristic
352C2C13×#213411yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC2×C13×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1464C2semidirect
3. C13×#1458C2semidirect
4. C13×#1324C2semidirect
5. C13×#1318C2semidirect
56. #11550C13direct (N × H)
101. #1464C2×C13semidirect
102. #1458C2×C13semidirect
103. #1324C2×C13semidirect
104. #1318C2×C13semidirect
275. C13#11550direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25002
C13×#14642
C13×#14582
C13×#13242
C13×#13182
#1155013