Finite Group Databasebeta

← C13×#11756 #15698095

Subgroups — C13×#11756 #15698095

Order 3328.

444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2599C211yesmaximal, characteristic
2C13×#1740C211yesmaximal, characteristic
3C13×#1464C211yesmaximal, characteristic
4C13×#1351C212yesmaximal
5C13×#1344C212yesmaximal
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C13×#117—21no—
8C2×C13×#117C2211yescharacteristic
9C13×#432—21no—
10C13×#398C411yescharacteristic, complemented
11C13×#397C2211yescharacteristic
12C13×#395C411yescharacteristic, complemented
13C13×#393C2211yescharacteristic
14C13×#388—21no—
15C13×#387—21no—
16C13×#387—21no—
17C13×#385—21no—
18C13×#383C411yescharacteristic, complemented
19C13×#342—21no—
20C13×#342C2212yes—
21C13×#324—21no—
22C13×#323C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C13×#117—24no—
28C13×#117—41no—
29C13×#117—41no—
30C13×#117—42no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4C2311yescharacteristic
43C2×C42×C13—21no—
44C2×C42×C13—41no—
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C13×C4⋊C8—41no—
48C13×C22⋊C8—22no—
49C13×#97—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95C2×C411yescharacteristic
57C13×#95C2×C411yescharacteristic
58#11756C1311yesmaximal, characteristic, direct product factor, Sylow
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C2×C8×C13—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—44no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C22⋊C4—24no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—41no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—42no—
99C42×C13—44no—
100#2599C2×C1311yescharacteristic
101#1740C2×C1311yescharacteristic
102#1464C2×C1311yescharacteristic
103#1351C2×C1312yes—
104#1344C2×C1312yes—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13AGL(1,ℤ/8)11yescharacteristic
111C23×C13#13711yescharacteristic
112Q8×C13—42no—
113Q8×C13—42no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
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—44no—
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—82no—
144C2×C4×C13—82no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#10412yes—
148C8×C13—82no—
149C2×C4×Q8C4×C1311yescharacteristic, complemented
150C2×#117—21no—
151C2×#117C22×C1311yescharacteristic
152#432—21no—
153#398C4×C1311yescharacteristic, complemented
154#397C22×C1311yescharacteristic
155#395C4×C1311yescharacteristic, complemented
156#393C22×C1311yescharacteristic
157#388—21no—
158#387—21no—
159#387—21no—
160#385—21no—
161#383C4×C1311yescharacteristic, complemented
162#342—21no—
163#342C22×C1312yes—
164#324—21no—
165#323C22×C1312yes—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13C2×#9911yescharacteristic
176C22×C13#41711yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—41no—
182C4×C13—42no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—84no—
189C4×C13—81no—
190C22×Q8C2×C4×C1311yescharacteristic
191C23×C4D4×C1311yescharacteristic
192C4×Q8—41no—
193C4×Q8—41no—
194#117—24no—
195#117—41no—
196#117—41no—
197#117—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4C2×C4×C1311yescharacteristic
203C2×C4⋊C4C2×C4×C1311yescharacteristic
204C2×C4⋊C4D4×C1311yescharacteristic
205C2×C22⋊C4—22no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4D4×C1311yescharacteristic
209C2×C22⋊C4C23×C1311yescharacteristic
210C2×C42—21no—
211C2×C42—41no—
212C2×C42C2×C4×C1311yescharacteristic
213C2×C42D4×C1311yescharacteristic
214C4⋊C8—41no—
215C22⋊C8—22no—
216#97—41no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95C2×C4×C1311yescharacteristic
224#95C2×C4×C1311yescharacteristic
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—41no—
228C2×C13—41no—
229C2×C13#150411yescharacteristic
230C2×C13#212011yescharacteristic
231C2×C13#212911yescharacteristic
232C24C2×D4×C1311yescharacteristic
233C2×Q8—42no—
234C2×Q8—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4C13×C22⋊C411yescharacteristic
246C22×C4C13×C22⋊C411yescharacteristic
247C22×C4C13×C22⋊C411yescharacteristic
248C22×C4C13×C22⋊C411yescharacteristic
249C22×C4C22×C4×C1311yescharacteristic
250C22×C4C2×D4×C1311yescharacteristic
251C2×C8—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C22⋊C4—24no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—42no—
272C42—44no—
273C13#1175611yescharacteristic, direct product factor, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23C2×C13×C22⋊C411yescharacteristic
279C23C13×AGL(1,ℤ/8)11yescharacteristic
280C23C13×#13711yescharacteristic
281Q8—42no—
282Q8—42no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—44no—
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—82no—
313C2×C4—82no—
314C2×C4C13×#9911yescharacteristic
315C2×C4C13×#9911yescharacteristic
316C2×C4C13×#10412yes—
317C8—82no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22C2×C13×#9911yescharacteristic
328C22C13×#41711yescharacteristic
329C22C2×C13×#10411yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—42no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—84no—
341C4—81no—
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2C13×#150411yescharacteristic
347C2C13×#212011yescharacteristic
348C2C13×#212911yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
6. C2×C4×Q8×C13C4semidirect
10. C13×#398C4semidirect
12. C13×#395C4semidirect
18. C13×#383C4semidirect
58. #11756C13direct (N × H)
149. C2×C4×Q8C4×C13semidirect
153. #398C4×C13semidirect
155. #395C4×C13semidirect
161. #383C4×C13semidirect
273. C13#11756direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25992
C13×#17402
C13×#14642
C13×#13512
C13×#13442
#1175613