Finite Group Databasebeta

← C13×#9184 #15695523

Subgroups — C13×#9184 #15695523

Order 3328.

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

normal subgroups only

This group has 530 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×#2975C211yesmaximal, characteristic
2C13×#2638C211yesmaximal, characteristic
3C4×C13×#99C211yesmaximal, characteristic
4C13×#1508C212yesmaximal, complemented
5C13×#1284C212yesmaximal, complemented
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#436—24no—
9C13×#431—21no—
10C2×C13×#99—21no—
11C13×#407—21no—
12C13×#407C2212yes—
13C13×#398C411yescharacteristic, complemented
14C13×#397—21no—
15C13×#397C411yescharacteristic, complemented
16C13×#395C411yescharacteristic, complemented
17C13×#394—21no—
18C13×#393C411yescharacteristic, complemented
19C13×#387—21no—
20C13×#385—21no—
21C13×#381C2211yescharacteristic
22C4×C13×C22⋊C4C2212yes—
23C13×#342—21no—
24C13×#328—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C2×C13×M16—22no—
30C2×C13×M16—22no—
31C13×C22⋊Q8—22no—
32C13×C22⋊Q8—22no—
33C4×D4×C13—22no—
34C4×D4×C13—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C42×C13—22no—
48C2×C42×C13D411yescharacteristic
49C13×C4⋊C8—22no—
50C13×#99—24no—
51C13×C22⋊C8—22no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8D414yes—
54C4×C8×C13—22no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60C13×#95—22no—
61C13×#95C2×C411yescharacteristic
62C13×#95C2×C411yescharacteristic
63#9184C1311yesmaximal, characteristic, direct product factor, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—81no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—42no—
78C22×C4×C13—81no—
79C22×C4×C13—81no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D412yes—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13#4112yes—
87C13×M16—82no—
88C13×M16—82no—
89C2×C8×C13—24no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—81no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—24no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—81no—
103C13×C22⋊C4—81no—
104C42×C13—21no—
105C42×C13—21no—
106C42×C13—82no—
107#2975C2×C1311yescharacteristic
108#2638C2×C1311yescharacteristic
109C4×#99C2×C1311yescharacteristic
110#1508C2×C1312yescomplemented
111#1284C2×C1312yescomplemented
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13#12112yes—
123Q8×C13—82no—
124D4×C13—44no—
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—42no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—44no—
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—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—81no—
150C2×C4×C13—82no—
151C2×C4×C13—82no—
152C2×C4×C13#10412yes—
153C2×C4×C13C4×D412yes—
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12311yescharacteristic
156C8×C13—44no—
157C2×C22⋊Q8C22×C1311yescharacteristic
158C2×C4×D4C22×C1311yescharacteristic
159#436—24no—
160#431—21no—
161C2×#99—21no—
162#407—21no—
163#407C22×C1312yes—
164#398C4×C1311yescharacteristic, complemented
165#397—21no—
166#397C4×C1311yescharacteristic, complemented
167#395C4×C1311yescharacteristic, complemented
168#394—21no—
169#393C4×C1311yescharacteristic, complemented
170#387—21no—
171#385—21no—
172#381C22×C1311yescharacteristic
173C4×C22⋊C4C22×C1312yes—
174#342—21no—
175#328—24no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—42no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#38611yescharacteristic
189C22×C13C2×#10411yescharacteristic
190C22×C13#42111yescharacteristic
191C4×C13—22no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—84no—
200C4×C13—81no—
201C4×C13—81no—
202C22×Q8C2×C4×C1311yescharacteristic
203C22×D4D4×C1311yescharacteristic
204C23×C4D4×C1311yescharacteristic
205C23×C4C23×C1311yescharacteristic
206C2×M16—22no—
207C2×M16—22no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C1311yescharacteristic
216C2×C4⋊C4C2×C4×C1311yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4C2×C4×C1311yescharacteristic
223C2×C22⋊C4D4×C1311yescharacteristic
224C2×C42—22no—
225C2×C42D4×C1311yescharacteristic
226C4⋊C8—22no—
227#99—24no—
228C22⋊C8—22no—
229C22⋊C8—22no—
230C22⋊C8D4×C1314yes—
231C4×C8—22no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—22no—
238#95C2×C4×C1311yescharacteristic
239#95C2×C4×C1311yescharacteristic
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—42no—
243C2×C13—81no—
244C2×C13#187111yescharacteristic
245C2×C13#190911yescharacteristic
246C2×C13#191311yescharacteristic
247C24C13×C22⋊C411yescharacteristic
248C24C2×D4×C1311yescharacteristic
249C2×Q8—22no—
250C2×Q8—81no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C13×C22⋊C411yescharacteristic
264C22×C4C13×C22⋊C411yescharacteristic
265C22×C4C13×C22⋊C411yescharacteristic
266C22×C4C22×C4×C1311yescharacteristic
267C22×C4C2×D4×C1312yes—
268C22×C4C2×D4×C1311yescharacteristic
269C22×C4C13×#4112yes—
270M16—82no—
271M16—82no—
272C2×C8—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—81no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—24no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—81no—
286C22⋊C4—81no—
287C42—21no—
288C42—21no—
289C42—82no—
290C13#918411yescharacteristic, 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
301C23C13×#12112yes—
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4C13×#10412yes—
332C2×C4C4×D4×C1312yes—
333C2×C4C13×#12011yescharacteristic
334C2×C4C13×#12311yescharacteristic
335C8—44no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C13×#38611yescharacteristic
349C22C2×C13×#10411yescharacteristic
350C22C13×#42111yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—84no—
360C4—81no—
361C4—81no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2C13×#187111yescharacteristic
367C2C13×#190911yescharacteristic
368C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1508C2semidirect
5. C13×#1284C2semidirect
13. C13×#398C4semidirect
15. C13×#397C4semidirect
16. C13×#395C4semidirect
18. C13×#393C4semidirect
63. #9184C13direct (N × H)
110. #1508C2×C13semidirect
111. #1284C2×C13semidirect
164. #398C4×C13semidirect
166. #397C4×C13semidirect
167. #395C4×C13semidirect
169. #393C4×C13semidirect
290. C13#9184direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29752
C13×#26382
C4×C13×#992
C13×#15082
C13×#12842
#918413