Finite Group Databasebeta

← C13×#9444 #15695783

Subgroups — C13×#9444 #15695783

Order 3328.

474 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic
2C13×#2499C211yesmaximal, characteristic
3C13×#1820C211yesmaximal, characteristic
4C13×#1511C212yesmaximal
5C13×#1284C212yesmaximal
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#433—24no—
9C13×#423—21no—
10C13×#407C2212yes—
11C4×C13×M16—21no—
12C13×#397—21no—
13C13×#397—21no—
14C13×#391C411yescharacteristic, complemented
15C13×#391C411yescharacteristic, complemented
16C13×#387—21no—
17C13×#387—21no—
18C13×#384C411yescharacteristic, complemented
19C13×#382C411yescharacteristic, complemented
20C13×#381C2212yes—
21C4×C13×C22⋊C4C2211yescharacteristic
22C13×#342—21no—
23C13×#342—21no—
24C13×#328—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C2×C13×M16—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C13×#117—22no—
31C13×#117—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
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—24no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8D414yes—
50C13×#97—22no—
51C4×C8×C13—22no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—22no—
60C13×#95—22no—
61#9444C1311yesmaximal, characteristic, direct product factor, Sylow
62C24×C13C2×D411yescharacteristic
63C2×Q8×C13—22no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—42no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13#4112yes—
81C13×M16—42no—
82C13×M16—42no—
83C2×C8×C13—24no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—41no—
102C42×C13—41no—
103#2921C2×C1311yescharacteristic
104#2499C2×C1311yescharacteristic
105#1820C2×C1311yescharacteristic
106#1511C2×C1312yes—
107#1284C2×C1312yes—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13C2×C22⋊C411yescharacteristic
113C23×C13#12112yes—
114Q8×C13—82no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—22no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
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—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—82no—
142C2×C4×C13—82no—
143C2×C4×C13—82no—
144C2×C4×C13C4×D412yes—
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12311yescharacteristic
147C8×C13—44no—
148C2×C22⋊Q8C22×C1311yescharacteristic
149C2×#117C22×C1311yescharacteristic
150#433—24no—
151#423—21no—
152#407C22×C1312yes—
153C4×M16—21no—
154#397—21no—
155#397—21no—
156#391C4×C1311yescharacteristic, complemented
157#391C4×C1311yescharacteristic, complemented
158#387—21no—
159#387—21no—
160#384C4×C1311yescharacteristic, complemented
161#382C4×C1311yescharacteristic, complemented
162#381C22×C1312yes—
163C4×C22⋊C4C22×C1311yescharacteristic
164#342—21no—
165#342—21no—
166#328—24no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13#38611yescharacteristic
175C22×C13#41011yescharacteristic
176C22×C13#41011yescharacteristic
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—42no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—162no—
189C22×Q8C2×C4×C1311yescharacteristic
190C23×C4C23×C1311yescharacteristic
191C2×M16—22no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194#117—22no—
195#117—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C2×C4×C1311yescharacteristic
200C2×C4⋊C4C2×C4×C1311yescharacteristic
201C2×C4⋊C4C2×C4×C1311yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4D4×C1311yescharacteristic
206C2×C22⋊C4D4×C1311yescharacteristic
207C2×C42C2×C4×C1311yescharacteristic
208C2×C42C2×C4×C1311yescharacteristic
209C2×C42D4×C1311yescharacteristic
210C2×C42D4×C1311yescharacteristic
211C4⋊C8—24no—
212C22⋊C8—22no—
213C22⋊C8D4×C1314yes—
214#97—22no—
215C4×C8—22no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—22no—
224#95—22no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—42no—
228C2×C13#188411yescharacteristic
229C2×C13#189911yescharacteristic
230C2×C13#190911yescharacteristic
231C24C2×D4×C1311yescharacteristic
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4C13×C22⋊C411yescharacteristic
243C22×C4C13×C22⋊C411yescharacteristic
244C22×C4C13×C22⋊C411yescharacteristic
245C22×C4C13×C22⋊C411yescharacteristic
246C22×C4C22×C4×C1311yescharacteristic
247C22×C4C2×D4×C1311yescharacteristic
248C22×C4C2×D4×C1312yes—
249C22×C4C13×#4112yes—
250M16—42no—
251M16—42no—
252C2×C8—24no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—41no—
271C42—41no—
272C13#944411yescharacteristic, direct product factor, Sylow
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23C2×C13×C22⋊C411yescharacteristic
278C23C13×#12112yes—
279Q8—82no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4C4×D4×C1312yes—
310C2×C4C13×#12011yescharacteristic
311C2×C4C13×#12311yescharacteristic
312C8—44no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22C13×#38611yescharacteristic
321C22C13×#41011yescharacteristic
322C22C13×#41011yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—162no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C13×#188411yescharacteristic
339C2C13×#189911yescharacteristic
340C2C13×#190911yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
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
14. C13×#391C4semidirect
15. C13×#391C4semidirect
18. C13×#384C4semidirect
19. C13×#382C4semidirect
61. #9444C13direct (N × H)
156. #391C4×C13semidirect
157. #391C4×C13semidirect
160. #384C4×C13semidirect
161. #382C4×C13semidirect
272. C13#9444direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#29212
C13×#24992
C13×#18202
C13×#15112
C13×#12842
#944413