Finite Group Databasebeta

← C13×#15026 #15701365

Subgroups — C13×#15026 #15701365

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#385C211yesmaximal, characteristic
2C22×C13×#95C211yesmaximal, characteristic
3C13×#1443C214yesmaximal, complemented
4C13×#1442C214yesmaximal, complemented
5C13×C22⋊#95C212yesmaximal
6C13×C22⋊#95C211yesmaximal, characteristic
7C13×C22⋊#95C212yesmaximal
8C24×C4×C13C2212yes—
9C24×C4×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2212yes—
11C22×C13×C22⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4C2212yes—
13C22×C13×C22⋊C4C2211yescharacteristic
14C13×#385—24no—
15C2×C13×#95—24no—
16C2×C13×#95C2214yes—
17C2×C13×#95C2212yes—
18C2×C13×#95C2214yes—
19C2×C13×#95C2214yes—
20C2×C13×#95C2214yes—
21C2×C13×#95C2214yes—
22C2×C13×#95C2214yes—
23C25×C13C2311yescharacteristic
24C23×C4×C13—24no—
25C23×C4×C13—24no—
26C23×C4×C13—28no—
27C23×C4×C13—24no—
28C23×C4×C13—24no—
29C23×C4×C13—44no—
30C23×C4×C13—44no—
31C23×C4×C13D414yes—
32C23×C4×C13C2311yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C23×C4×C13C2314yes—
35C23×C4×C13C2312yes—
36C23×C4×C13C2312yes—
37C23×C4×C13C2314yes—
38C2×C13×C4⋊C4—24no—
39C2×C13×C4⋊C4—44no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—24no—
44C2×C13×C22⋊C4—24no—
45C2×C13×C22⋊C4—24no—
46C2×C13×C22⋊C4—24no—
47C2×C13×C22⋊C4Q814yes—
48C13×#95—24no—
49C13×#95—28no—
50C13×#95—28no—
51C13×#95—28no—
52C13×#95—44no—
53C13×#95—44no—
54C13×#95—44no—
55#15026C1311yesmaximal, characteristic, direct product factor, Sylow
56C24×C13—24no—
57C24×C13—24no—
58C24×C13C2×D412yes—
59C24×C13C2×Q812yes—
60C24×C13#4112yes—
61C24×C13#4114yes—
62C24×C13#4114yes—
63C24×C13C2411yescharacteristic
64C22×C4×C13—216no—
65C22×C4×C13—28no—
66C22×C4×C13—24no—
67C22×C4×C13—22no—
68C22×C4×C13—24no—
69C22×C4×C13—22no—
70C22×C4×C13—24no—
71C22×C4×C13—24no—
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—21no—
80C22×C4×C13—21no—
81C22×C4×C13—24no—
82C22×C4×C13—24no—
83C22×C4×C13—24no—
84C22×C4×C13—22no—
85C22×C4×C13—22no—
86C22×C4×C13—24no—
87C22×C4×C13—24no—
88C22×C4×C13—24no—
89C22×C4×C13—24no—
90C22×C4×C13—24no—
91C22×C4×C13—24no—
92C22×C4×C13—48no—
93C22×C4×C13—416no—
94C22×C4×C13—416no—
95C22×C4×C13—48no—
96C22×C4×C13—416no—
97C22×C4×C13—48no—
98C22×C4×C13C2×D414yes—
99C22×C4×C13C2×Q814yes—
100C22×C4×C13#4118yes—
101C13×C4⋊C4—48no—
102C13×C22⋊C4—28no—
103C13×C22⋊C4—44no—
104C13×C22⋊C4—48no—
105C2×#385C2×C1311yescharacteristic
106C22×#95C2×C1311yescharacteristic
107#1443C2×C1314yescomplemented
108#1442C2×C1314yescomplemented
109C22⋊#95C2×C1311yescharacteristic
110C22⋊#95C2×C1312yes—
111C22⋊#95C2×C1312yes—
112C23×C13—24no—
113C23×C13—28no—
114C23×C13—24no—
115C23×C13—28no—
116C23×C13—28no—
117C23×C13—28no—
118C23×C13—28no—
119C23×C13—28no—
120C23×C13C22⋊Q814yes—
121C23×C13#12314yes—
122C23×C13#12414yes—
123C23×C13#12518yes—
124C23×C13#12618yes—
125C23×C13C22×D411yescharacteristic
126C23×C13C22×Q811yescharacteristic
127C23×C13C2×#4111yescharacteristic
128C23×C13C2×#4112yes—
129C23×C13C2×#4114yes—
130C23×C13C2×#4112yes—
131C23×C13H(5,𝔽2)14yes—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13—28no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—28no—
138C2×C4×C13—28no—
139C2×C4×C13—28no—
140C2×C4×C13—432no—
141C2×C4×C13—416no—
142C2×C4×C13—42no—
143C2×C4×C13—44no—
144C2×C4×C13—42no—
145C2×C4×C13—44no—
146C2×C4×C13—48no—
147C2×C4×C13—44no—
148C2×C4×C13—44no—
149C2×C4×C13—44no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—44no—
154C2×C4×C13—44no—
155C2×C4×C13—44no—
156C2×C4×C13—42no—
157C2×C4×C13—44no—
158C2×C4×C13—44no—
159C2×C4×C13—44no—
160C2×C4×C13—44no—
161C2×C4×C13—44no—
162C2×C4×C13—44no—
163C24×C4C22×C1312yes—
164C24×C4C22×C1311yescharacteristic
165C22×C4⋊C4C22×C1312yes—
166C22×C22⋊C4C22×C1312yes—
167C22×C22⋊C4C22×C1311yescharacteristic
168C22×C22⋊C4C22×C1311yescharacteristic
169#385—24no—
170C2×#95—24no—
171C2×#95C22×C1314yes—
172C2×#95C22×C1314yes—
173C2×#95C22×C1314yes—
174C2×#95C22×C1312yes—
175C2×#95C22×C1314yes—
176C2×#95C22×C1314yes—
177C2×#95C22×C1314yes—
178C22×C13—28no—
179C22×C13—28no—
180C22×C13—24no—
181C22×C13—24no—
182C22×C13—216no—
183C22×C13—216no—
184C22×C13#40018yes—
185C22×C13C2×C22⋊Q811yescharacteristic
186C22×C13C2×#12311yescharacteristic
187C22×C13#52512yes—
188C22×C13C2×#12411yescharacteristic
189C22×C13C2×#12512yes—
190C22×C13C2×#12612yes—
191C22×C13#52914yes—
192C22×C13#53412yes—
193C22×C13#53814yes—
194C22×C13#55114yes—
195C22×C13#55114yes—
196C22×C13#55314yes—
197C22×C13#55414yes—
198C4×C13—48no—
199C4×C13—44no—
200C4×C13—44no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—84no—
204C25C23×C1311yescharacteristic
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—28no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—44no—
211C23×C4—44no—
212C23×C4D4×C1314yes—
213C23×C4C23×C1311yescharacteristic
214C23×C4C23×C1311yescharacteristic
215C23×C4C23×C1314yes—
216C23×C4C23×C1312yes—
217C23×C4C23×C1312yes—
218C23×C4C23×C1314yes—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—44no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—24no—
226C2×C22⋊C4—24no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4Q8×C1314yes—
229#95—28no—
230#95—24no—
231#95—28no—
232#95—28no—
233#95—44no—
234#95—44no—
235#95—44no—
236C2×C13—28no—
237C2×C13C2×#40011yescharacteristic
238C2×C13#250514yes—
239C2×C13#251014yes—
240C2×C13#256112yes—
241C2×C13#257912yes—
242C2×C13#262211yescharacteristic
243C2×C13#285311yescharacteristic
244C24—24no—
245C24—24no—
246C24C2×D4×C1312yes—
247C24C2×Q8×C1312yes—
248C24C13×#4112yes—
249C24C13×#4114yes—
250C24C13×#4114yes—
251C24C24×C1311yescharacteristic
252C22×C4—216no—
253C22×C4—28no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—48no—
281C22×C4—416no—
282C22×C4—416no—
283C22×C4—48no—
284C22×C4—416no—
285C22×C4—48no—
286C22×C4C2×D4×C1314yes—
287C22×C4C2×Q8×C1314yes—
288C22×C4C13×#4118yes—
289C4⋊C4—48no—
290C22⋊C4—28no—
291C22⋊C4—44no—
292C22⋊C4—48no—
293C13#1502611yescharacteristic, direct product factor, Sylow
294C23—24no—
295C23—28no—
296C23—24no—
297C23—28no—
298C23—28no—
299C23—28no—
300C23—28no—
301C23—28no—
302C23C13×C22⋊Q814yes—
303C23C13×#12314yes—
304C23C13×#12414yes—
305C23C13×#12518yes—
306C23C13×#12618yes—
307C23C22×D4×C1311yescharacteristic
308C23C22×Q8×C1311yescharacteristic
309C23C2×C13×#4111yescharacteristic
310C23C2×C13×#4112yes—
311C23C2×C13×#4114yes—
312C23C2×C13×#4112yes—
313C23C13×H(5,𝔽2)14yes—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—28no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4—28no—
322C2×C4—432no—
323C2×C4—416no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—48no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C22—216no—
346C22—216no—
347C22—28no—
348C22—28no—
349C22—24no—
350C22—24no—
351C22C13×#40018yes—
352C22C2×C13×C22⋊Q811yescharacteristic
353C22C2×C13×#12311yescharacteristic
354C22C13×#52512yes—
355C22C2×C13×#12411yescharacteristic
356C22C2×C13×#12512yes—
357C22C2×C13×#12612yes—
358C22C13×#52914yes—
359C22C13×#53412yes—
360C22C13×#53814yes—
361C22C13×#55114yes—
362C22C13×#55114yes—
363C22C13×#55314yes—
364C22C13×#55414yes—
365C4—48no—
366C4—44no—
367C4—44no—
368C4—84no—
369C4—81no—
370C4—81no—
371C2—28no—
372C2C2×C13×#40011yescharacteristic
373C2C13×#250514yes—
374C2C13×#251014yes—
375C2C13×#256112yes—
376C2C13×#257912yes—
377C2C13×#262211yescharacteristic
378C2C13×#285311yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1443C2semidirect
4. C13×#1442C2semidirect
55. #15026C13direct (N × H)
107. #1443C2×C13semidirect
108. #1442C2×C13semidirect
293. C13#15026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3852
C22×C13×#952
C13×#14432
C13×#14422
C13×C22⋊#952
#1502613