Finite Group Databasebeta

← C13×#13964 #15700303

Subgroups — C13×#13964 #15700303

Order 3328.

1342 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#383C211yesmaximal, characteristic
2C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
3C2×C13×#376C211yesmaximal, characteristic
4C13×#1441C214yesmaximal
5C13×#1436C214yesmaximal
6C13×C4⋊#95C212yesmaximal
7C13×#1434C212yesmaximal
8C22×C13×C4⋊C4C2214yes—
9C22×C13×C4⋊C4C2212yes—
10C22×C42×C13C2212yes—
11C22×C42×C13C2211yescharacteristic
12C22×C42×C13C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C13×#383—24no—
15C4×C13×C4⋊C4C418yescomplemented
16C13×#376—24no—
17C2×C13×#95C2212yes—
18C2×C13×#95C2212yes—
19C2×C13×#95C2212yes—
20C2×C13×#95C2212yes—
21C2×C13×#95C2212yes—
22C2×C13×#95C2214yes—
23C2×C13×#95C2214yes—
24C2×C13×#95C2214yes—
25C2×C13×#95C2212yes—
26C23×C4×C13C2314yes—
27C23×C4×C13C2312yes—
28C23×C4×C13C2314yes—
29C23×C4×C13C2311yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C23×C4×C13C2312yes—
33C2×C13×C4⋊C4—24no—
34C2×C13×C4⋊C4—24no—
35C2×C13×C4⋊C4—28no—
36C2×C13×C4⋊C4—28no—
37C2×C13×C4⋊C4—44no—
38C2×C13×C4⋊C4C2×C418yes—
39C2×C42×C13—24no—
40C2×C42×C13—28no—
41C2×C42×C13—42no—
42C2×C42×C13—42no—
43C2×C42×C13C2×C414yes—
44C2×C42×C13C2×C414yes—
45C2×C42×C13C2×C414yes—
46C2×C42×C13D414yes—
47C2×C42×C13Q814yes—
48C13×#95—24no—
49C13×#95—24no—
50C13×#95—24no—
51C13×#95—24no—
52C13×#95—24no—
53C13×#95—28no—
54C13×#95—28no—
55C13×#95—44no—
56C13×#95C2×C418yes—
57#13964C1311yesmaximal, characteristic, direct product factor, Sylow
58C24×C13C2411yescharacteristic
59C22×C4×C13—24no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—24no—
63C22×C4×C13—22no—
64C22×C4×C13—24no—
65C22×C4×C13—22no—
66C22×C4×C13—24no—
67C22×C4×C13—24no—
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—24no—
73C22×C4×C13—24no—
74C22×C4×C13—24no—
75C22×C4×C13—24no—
76C22×C4×C13—24no—
77C22×C4×C13—24no—
78C22×C4×C13—24no—
79C22×C4×C13—24no—
80C22×C4×C13—24no—
81C22×C4×C13—24no—
82C22×C4×C13—24no—
83C22×C4×C13C22×C414yes—
84C22×C4×C13C22×C412yes—
85C22×C4×C13C22×C412yes—
86C22×C4×C13C22×C412yes—
87C22×C4×C13C22×C414yes—
88C22×C4×C13C2×D412yes—
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×Q812yes—
92C22×C4×C13C2×Q812yes—
93C22×C4×C13C2×Q812yes—
94C22×C4×C13#4118yes—
95C22×C4×C13#4114yes—
96C22×C4×C13#4114yes—
97C13×C4⋊C4—216no—
98C13×C4⋊C4—416no—
99C42×C13—216no—
100C42×C13—44no—
101C42×C13—44no—
102C42×C13C4⋊C4116yescomplemented
103C2×#383C2×C1311yescharacteristic
104C2×C4×C4⋊C4C2×C1311yescharacteristic
105C2×#376C2×C1311yescharacteristic
106#1441C2×C1314yes—
107#1436C2×C1314yes—
108C4⋊#95C2×C1312yes—
109#1434C2×C1312yes—
110C23×C13C23×C411yescharacteristic
111C23×C13C22×D411yescharacteristic
112C23×C13C22×Q811yescharacteristic
113C23×C13C2×#4112yes—
114C23×C13C2×#4112yes—
115C23×C13C2×#4114yes—
116C23×C13H(5,𝔽2)12yes—
117C23×C132−1+412yes—
118C2×C4×C13—24no—
119C2×C4×C13—24no—
120C2×C4×C13—24no—
121C2×C4×C13—22no—
122C2×C4×C13—24no—
123C2×C4×C13—22no—
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—24no—
129C2×C4×C13—24no—
130C2×C4×C13—24no—
131C2×C4×C13—28no—
132C2×C4×C13—28no—
133C2×C4×C13—24no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—28no—
137C2×C4×C13—28no—
138C2×C4×C13—28no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
141C2×C4×C13—44no—
142C2×C4×C13—44no—
143C2×C4×C13—44no—
144C2×C4×C13—44no—
145C2×C4×C13—44no—
146C2×C4×C13—44no—
147C2×C4×C13—44no—
148C2×C4×C13—44no—
149C2×C4×C13—44no—
150C2×C4×C13—44no—
151C2×C4×C13—44no—
152C2×C4×C13C2×C4⋊C414yes—
153C2×C4×C13C2×C4⋊C414yes—
154C2×C4×C13C2×C4⋊C414yes—
155C2×C4×C13#11718yes—
156C22×C4⋊C4C22×C1314yes—
157C22×C4⋊C4C22×C1312yes—
158C22×C42C22×C1312yes—
159C22×C42C22×C1311yescharacteristic
160C22×C42C22×C1311yescharacteristic
161C22×C42C22×C1311yescharacteristic
162#383—24no—
163C4×C4⋊C4C4×C1318yescomplemented
164#376—24no—
165C2×#95C22×C1312yes—
166C2×#95C22×C1312yes—
167C2×#95C22×C1314yes—
168C2×#95C22×C1314yes—
169C2×#95C22×C1312yes—
170C2×#95C22×C1312yes—
171C2×#95C22×C1312yes—
172C2×#95C22×C1314yes—
173C2×#95C22×C1312yes—
174C22×C13C22×C4⋊C411yescharacteristic
175C22×C13C2×#11712yes—
176C22×C13C4×#4112yes—
177C22×C13#51811yescharacteristic
178C22×C13#51911yescharacteristic
179C22×C13#52512yes—
180C22×C13#53212yes—
181C22×C13#53311yescharacteristic
182C22×C13#53312yes—
183C22×C13#53311yescharacteristic
184C22×C13#53712yes—
185C22×C13#54412yes—
186C22×C13#55114yes—
187C22×C13#55214yes—
188C22×C13#55314yes—
189C22×C13#55614yes—
190C4×C13—24no—
191C4×C13—28no—
192C4×C13—24no—
193C4×C13—24no—
194C4×C13—48no—
195C4×C13—44no—
196C4×C13—84no—
197C23×C4C23×C1314yes—
198C23×C4C23×C1312yes—
199C23×C4C23×C1314yes—
200C23×C4C23×C1311yescharacteristic
201C23×C4C23×C1311yescharacteristic
202C23×C4C23×C1311yescharacteristic
203C23×C4C23×C1312yes—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—28no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4C2×C4×C1318yes—
210C2×C42—24no—
211C2×C42—28no—
212C2×C42—42no—
213C2×C42—42no—
214C2×C42C2×C4×C1314yes—
215C2×C42C2×C4×C1314yes—
216C2×C42C2×C4×C1314yes—
217C2×C42D4×C1314yes—
218C2×C42Q8×C1314yes—
219#95—24no—
220#95—24no—
221#95—24no—
222#95—24no—
223#95—24no—
224#95—28no—
225#95—28no—
226#95—44no—
227#95C2×C4×C1318yes—
228C2×C13#228511yescharacteristic
229C2×C13#229611yescharacteristic
230C2×C13#231611yescharacteristic
231C2×C13#235312yes—
232C2×C13#235612yes—
233C2×C13#260114yes—
234C2×C13#260512yes—
235C2×C13#260612yes—
236C24C24×C1311yescharacteristic
237C22×C4—24no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—22no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4C22×C4×C1314yes—
262C22×C4C22×C4×C1312yes—
263C22×C4C22×C4×C1312yes—
264C22×C4C22×C4×C1312yes—
265C22×C4C22×C4×C1314yes—
266C22×C4C2×D4×C1312yes—
267C22×C4C2×D4×C1312yes—
268C22×C4C2×D4×C1312yes—
269C22×C4C2×Q8×C1312yes—
270C22×C4C2×Q8×C1312yes—
271C22×C4C2×Q8×C1312yes—
272C22×C4C13×#4118yes—
273C22×C4C13×#4114yes—
274C22×C4C13×#4114yes—
275C4⋊C4—216no—
276C4⋊C4—416no—
277C42—216no—
278C42—44no—
279C42—44no—
280C42C13×C4⋊C4116yescomplemented
281C13#1396411yescharacteristic, direct product factor, Sylow
282C23C23×C4×C1311yescharacteristic
283C23C22×D4×C1311yescharacteristic
284C23C22×Q8×C1311yescharacteristic
285C23C2×C13×#4112yes—
286C23C2×C13×#4112yes—
287C23C2×C13×#4114yes—
288C23C13×H(5,𝔽2)12yes—
289C23C13×2−1+412yes—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—28no—
310C2×C4—28no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4C2×C13×C4⋊C414yes—
325C2×C4C2×C13×C4⋊C414yes—
326C2×C4C2×C13×C4⋊C414yes—
327C2×C4C13×#11718yes—
328C22C22×C13×C4⋊C411yescharacteristic
329C22C2×C13×#11712yes—
330C22C4×C13×#4112yes—
331C22C13×#51811yescharacteristic
332C22C13×#51911yescharacteristic
333C22C13×#52512yes—
334C22C13×#53212yes—
335C22C13×#53311yescharacteristic
336C22C13×#53311yescharacteristic
337C22C13×#53312yes—
338C22C13×#53712yes—
339C22C13×#54412yes—
340C22C13×#55114yes—
341C22C13×#55214yes—
342C22C13×#55314yes—
343C22C13×#55614yes—
344C4—24no—
345C4—24no—
346C4—24no—
347C4—28no—
348C4—48no—
349C4—44no—
350C4—84no—
351C2C13×#228511yescharacteristic
352C2C13×#229611yescharacteristic
353C2C13×#231611yescharacteristic
354C2C13×#235312yes—
355C2C13×#235612yes—
356C2C13×#260114yes—
357C2C13×#260512yes—
358C2C13×#260612yes—
subgroupG/H
center, socle, prime radicalC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
15. C4×C13×C4⋊C4C4semidirect
57. #13964C13direct (N × H)
102. C42×C13C4⋊C4semidirect
163. C4×C4⋊C4C4×C13semidirect
280. C42C13×C4⋊C4semidirect
281. C13#13964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3832
C2×C4×C13×C4⋊C42
C2×C13×#3762
C13×#14412
C13×#14362
C13×C4⋊#952
C13×#14342
#1396413