Finite Group Databasebeta

← C13×#9449 #15695788

Subgroups — C13×#9449 #15695788

Order 3328.

490 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2973C211yesmaximal, characteristic
2C13×#2566C211yesmaximal, characteristic
3C13×#1534C212yesmaximal, complemented
4C13×#1466C211yesmaximal, characteristic
5C13×#1285C212yesmaximal, complemented
6C2×C13×#125C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#435—24no—
9C13×#432C2212yes—
10C13×#432C2212yes—
11C13×#407—21no—
12C2×C13×C22⋊C8—21no—
13C13×#396—21no—
14C13×#396—21no—
15C13×#390C411yescharacteristic
16C13×#390C411yescharacteristic
17C13×#385—21no—
18C13×#385—21no—
19C13×#384C411yescharacteristic
20C13×#382C411yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C13×#330—24no—
23C13×#323—21no—
24C13×#323—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C2×C13×M16—22no—
29C22×C8×C13—22no—
30C13×#125—22no—
31C13×#125—22no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
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⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13C2×C411yescharacteristic
50C2×C42×C13C2311yescharacteristic
51C13×C4⋊C8—22no—
52C13×C4⋊C8—22no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8—22no—
56C13×C22⋊C8—22no—
57C13×#97—22no—
58C13×#97D414yes—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95—21no—
62#9449C1311yesmaximal, characteristic, direct product factor, Sylow
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—41no—
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—21no—
75C22×C4×C13—21no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×M16—82no—
84C2×C8×C13—24no—
85C2×C8×C13—42no—
86C2×C8×C13—82no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—81no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—81no—
101C13×C22⋊C4—81no—
102C42×C13—41no—
103C42×C13—41no—
104C42×C13C2×D412yes—
105C42×C13#4112yes—
106#2973C2×C1311yescharacteristic
107#2566C2×C1311yescharacteristic
108#1534C2×C1312yescomplemented
109#1466C2×C1311yescharacteristic
110#1285C2×C1312yescomplemented
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#10112yes—
121C23×C13C2×C22⋊C411yescharacteristic
122D4×C13—44no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
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—41no—
144C2×C4×C13—41no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13C4×D412yes—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12112yes—
150C2×C4×C13#12311yescharacteristic
151C8×C13—44no—
152C8×C13—82no—
153C2×#125C22×C1311yescharacteristic
154C2×C4×D4C22×C1311yescharacteristic
155#435—24no—
156#432C22×C1312yes—
157#432C22×C1312yes—
158#407—21no—
159C2×C22⋊C8—21no—
160#396—21no—
161#396—21no—
162#390C4×C1311yescharacteristic
163#390C4×C1311yescharacteristic
164#385—21no—
165#385—21no—
166#384C4×C1311yescharacteristic
167#382C4×C1311yescharacteristic
168C4×C4⋊C4C22×C1311yescharacteristic
169#330—24no—
170#323—21no—
171#323—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—22no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#38611yescharacteristic
185C22×C13C2×#10111yescharacteristic
186C22×C13#41311yescharacteristic
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C22×D4C2×C4×C1311yescharacteristic
198C23×C4D4×C1311yescharacteristic
199C23×C4D4×C1311yescharacteristic
200C2×M16—22no—
201C22×C8—22no—
202#125—22no—
203#125—22no—
204C4×D4—22no—
205C4×D4—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×C4×C1311yescharacteristic
212C2×C4⋊C4C2×C4×C1311yescharacteristic
213C2×C4⋊C4C2×C4×C1311yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4D4×C1311yescharacteristic
219C2×C22⋊C4D4×C1311yescharacteristic
220C2×C42C2×C4×C1311yescharacteristic
221C2×C42C2×C4×C1311yescharacteristic
222C2×C42C23×C1311yescharacteristic
223C4⋊C8—22no—
224C4⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229#97—22no—
230#97D4×C1314yes—
231#95—21no—
232#95—21no—
233#95—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—42no—
237C2×C13—81no—
238C2×C13#188411yescharacteristic
239C2×C13#190111yescharacteristic
240C2×C13#191111yescharacteristic
241C24C13×C22⋊C411yescharacteristic
242C24C13×C22⋊C411yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C13×C22⋊C411yescharacteristic
257C22×C4C13×C22⋊C411yescharacteristic
258C22×C4C22×C4×C1311yescharacteristic
259C22×C4C2×D4×C1311yescharacteristic
260C22×C4C2×D4×C1311yescharacteristic
261M16—82no—
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—82no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C42—41no—
281C42—41no—
282C42C2×D4×C1312yes—
283C42C13×#4112yes—
284C13#944911yescharacteristic, direct product factor, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C13×#10112yes—
295C23C2×C13×C22⋊C411yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
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×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4C4×D4×C1312yes—
322C2×C4C13×#12011yescharacteristic
323C2×C4C13×#12112yes—
324C2×C4C13×#12311yescharacteristic
325C8—44no—
326C8—82no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22C13×#38611yescharacteristic
340C22C2×C13×#10111yescharacteristic
341C22C13×#41311yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2C13×#188411yescharacteristic
357C2C13×#190111yescharacteristic
358C2C13×#191111yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C42C23×C13
prime radicalC22×D4×C13C2×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×#1534C2semidirect
5. C13×#1285C2semidirect
62. #9449C13direct (N × H)
108. #1534C2×C13semidirect
110. #1285C2×C13semidirect
284. C13#9449direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29732
C13×#25662
C13×#15342
C13×#14662
C13×#12852
#944913