Finite Group Databasebeta

← C13×#11499 #15697838

Subgroups — C13×#11499 #15697838

Order 3328.

1866 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 1866 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
1C2×C13×#379C211yesmaximal, characteristic
2C13×#1462C212yesmaximal, complemented
3C13×#1316C214yesmaximal, complemented
4C26×C13C411yescharacteristic
5C22×C13×C22⋊C4—22no—
6C22×C13×C22⋊C4C411yescharacteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#407—22no—
9C13×#379—22no—
10C13×#379C412yes—
11C13×#379C2212yes—
12C13×#323—22no—
13C13×#323C2214yescomplemented
14C25×C13—21no—
15C25×C13—21no—
16C25×C13—24no—
17C25×C13—48no—
18C25×C13—42no—
19C25×C13—42no—
20C25×C13C2×C411yescharacteristic
21C25×C13C2×C412yes—
22C23×C4×C13—21no—
23C23×C4×C13D412yes—
24C2×C13×M16—42no—
25C2×C13×C22⋊C4—21no—
26C2×C13×C22⋊C4—24no—
27C2×C13×C22⋊C4—24no—
28C2×C13×C22⋊C4—42no—
29C2×C13×C22⋊C4—48no—
30C2×C13×C22⋊C4—42no—
31C2×C13×C22⋊C4C2×C412yes—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D412yes—
34C2×C13×C22⋊C4C2311yescharacteristic
35C13×C22⋊C8—24no—
36C13×C22⋊C8—42no—
37#11499C1311yesmaximal, characteristic, direct product factor, Sylow
38C24×C13—28no—
39C24×C13—24no—
40C24×C13—22no—
41C24×C13—22no—
42C24×C13—22no—
43C24×C13—22no—
44C24×C13—24no—
45C24×C13—22no—
46C24×C13—44no—
47C24×C13—48no—
48C24×C13—42no—
49C24×C13—42no—
50C24×C13—44no—
51C24×C13—42no—
52C24×C13—48no—
53C24×C13—432no—
54C24×C13—416no—
55C24×C13—42no—
56C24×C13—48no—
57C24×C13—432no—
58C24×C13—416no—
59C24×C13—48no—
60C24×C13—42no—
61C24×C13—42no—
62C24×C13C22⋊C411yescharacteristic
63C24×C13C22⋊C411yescharacteristic
64C24×C13M1614yescomplemented
65C24×C13C22×C411yescharacteristic
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—44no—
70C22×C4×C13—44no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C2×D412yes—
74C13×M16—84no—
75C2×C8×C13—44no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—48no—
80C13×C22⋊C4—48no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C2×#379C2×C1311yescharacteristic
84#1462C2×C1312yescomplemented
85#1316C2×C1314yescomplemented
86C23×C13—24no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—28no—
90C23×C13—216no—
91C23×C13—28no—
92C23×C13—21no—
93C23×C13—24no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—48no—
98C23×C13—416no—
99C23×C13—48no—
100C23×C13—48no—
101C23×C13—44no—
102C23×C13—48no—
103C23×C13—44no—
104C23×C13—48no—
105C23×C13—48no—
106C23×C13—416no—
107C23×C13—48no—
108C23×C13—44no—
109C23×C13—42no—
110C23×C13—48no—
111C23×C13—44no—
112C23×C13—42no—
113C23×C13—416no—
114C23×C13—416no—
115C23×C13—464no—
116C23×C13—464no—
117C23×C13—48no—
118C23×C13—416no—
119C23×C13—48no—
120C23×C13—44no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—48no—
124C23×C13#9912yes—
125C23×C13#10012yes—
126C23×C13C2×C22⋊C411yescharacteristic
127C23×C13C2×M1612yes—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—44no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—44no—
134C2×C4×C13—42no—
135C2×C4×C13—82no—
136C2×C4×C13—84no—
137C8×C13—84no—
138C26C4×C1311yescharacteristic
139C22×C22⋊C4—22no—
140C22×C22⋊C4C4×C1311yescharacteristic
141C22×C22⋊C4C22×C1311yescharacteristic
142#407—22no—
143#379—22no—
144#379C4×C1312yes—
145#379C22×C1312yes—
146#323—22no—
147#323C22×C1314yescomplemented
148C22×C13—24no—
149C22×C13—24no—
150C22×C13—22no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13—28no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—48no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—44no—
162C22×C13—432no—
163C22×C13—416no—
164C22×C13—48no—
165C22×C13—432no—
166C22×C13—416no—
167C22×C13—48no—
168C22×C13—48no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—44no—
172C22×C13AΣL(1,𝔽16)14yes—
173C22×C13#40711yescharacteristic
174C22×C13C2×#9911yescharacteristic
175C22×C13C2×#10011yescharacteristic
176C4×C13—42no—
177C4×C13—42no—
178C4×C13—82no—
179C25—21no—
180C25—21no—
181C25—24no—
182C25—48no—
183C25—42no—
184C25—42no—
185C25C2×C4×C1311yescharacteristic
186C25C2×C4×C1312yes—
187C23×C4—21no—
188C23×C4D4×C1312yes—
189C2×M16—42no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—42no—
194C2×C22⋊C4—48no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4C2×C4×C1312yes—
197C2×C22⋊C4C2×C4×C1311yescharacteristic
198C2×C22⋊C4D4×C1312yes—
199C2×C22⋊C4C23×C1311yescharacteristic
200C22⋊C8—24no—
201C22⋊C8—42no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13—24no—
205C2×C13—48no—
206C2×C13—42no—
207C2×C13—42no—
208C2×C13#146211yescharacteristic
209C2×C13C2×AΣL(1,𝔽16)12yes—
210C24—28no—
211C24—24no—
212C24—22no—
213C24—22no—
214C24—22no—
215C24—22no—
216C24—24no—
217C24—22no—
218C24—44no—
219C24—48no—
220C24—42no—
221C24—42no—
222C24—42no—
223C24—44no—
224C24—48no—
225C24—432no—
226C24—416no—
227C24—42no—
228C24—48no—
229C24—416no—
230C24—432no—
231C24—48no—
232C24—42no—
233C24—42no—
234C24C13×C22⋊C411yescharacteristic
235C24C13×C22⋊C411yescharacteristic
236C24C13×M1614yescomplemented
237C24C22×C4×C1311yescharacteristic
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—42no—
244C22×C4C13×C22⋊C412yes—
245C22×C4C2×D4×C1312yes—
246M16—84no—
247C2×C8—44no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—41no—
251C22⋊C4—48no—
252C22⋊C4—48no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C13#1149911yescharacteristic, direct product factor, Sylow
256C23—21no—
257C23—21no—
258C23—24no—
259C23—28no—
260C23—216no—
261C23—28no—
262C23—21no—
263C23—24no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—42no—
268C23—48no—
269C23—44no—
270C23—42no—
271C23—48no—
272C23—416no—
273C23—48no—
274C23—48no—
275C23—44no—
276C23—48no—
277C23—44no—
278C23—48no—
279C23—48no—
280C23—416no—
281C23—48no—
282C23—44no—
283C23—48no—
284C23—416no—
285C23—416no—
286C23—464no—
287C23—464no—
288C23—48no—
289C23—416no—
290C23—42no—
291C23—42no—
292C23—48no—
293C23—44no—
294C23C13×#9912yes—
295C23C13×#10012yes—
296C23C2×C13×C22⋊C411yescharacteristic
297C23C2×C13×M1612yes—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—84no—
307C8—84no—
308C22—24no—
309C22—24no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—28no—
314C22—22no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—48no—
319C22—42no—
320C22—42no—
321C22—44no—
322C22—432no—
323C22—416no—
324C22—48no—
325C22—48no—
326C22—416no—
327C22—432no—
328C22—48no—
329C22—42no—
330C22—42no—
331C22—44no—
332C22C13×AΣL(1,𝔽16)14yes—
333C22C13×#40711yescharacteristic
334C22C2×C13×#9911yescharacteristic
335C22C2×C13×#10011yescharacteristic
336C4—42no—
337C4—42no—
338C4—82no—
339C2—21no—
340C2—21no—
341C2—24no—
342C2—48no—
343C2—42no—
344C2—42no—
345C2C13×#146211yescharacteristic
346C2C2×C13×AΣL(1,𝔽16)12yes—
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC2×C22⋊C4C23×C13
prime radicalC26×C13C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#1462C2semidirect
3. C13×#1316C2semidirect
13. C13×#323C22semidirect
37. #11499C13direct (N × H)
64. C24×C13M16semidirect
84. #1462C2×C13semidirect
85. #1316C2×C13semidirect
147. #323C22×C13semidirect
236. C24C13×M16semidirect
255. C13#11499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3792
C13×#14622
C13×#13162
#1149913