Finite Group Databasebeta

← C13×#13297 #15699636

Subgroups — C13×#13297 #15699636

Order 3328.

488 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
1C13×#2579C211yesmaximal, characteristic
2C13×#1800C211yesmaximal, characteristic
3C4×C13×#99C211yesmaximal, characteristic
4C13×#1390C212yesmaximal
5C13×#1390C212yesmaximal
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C13×#423—21no—
9C2×C13×#100C2212yes—
10C2×C13×#99C2212yes—
11C13×#398—21no—
12C13×#396—21no—
13C13×#387—21no—
14C13×#386C2211yescharacteristic
15C13×#386C2211yescharacteristic
16C13×#385—21no—
17C13×#385C411yescharacteristic, complemented
18C13×#385C411yescharacteristic, complemented
19C13×#380C411yescharacteristic, complemented
20C4×C13×C22⋊C4—21no—
21C13×#343—21no—
22C13×#342—21no—
23C22×D4×C13C2311yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C2×C13×M16—22no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4—41no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C42×C13—41no—
47C2×C42×C13D411yescharacteristic
48C13×C4⋊C8—41no—
49C13×C4⋊C8—41no—
50C13×#100—24no—
51C13×#99—22no—
52C13×#99Q814yes—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—41no—
59#13297C1311yesmaximal, characteristic, direct product factor, Sylow
60C24×C13C22×C411yescharacteristic
61C24×C13C2×D411yescharacteristic
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13C2×Q812yes—
65C2×D4×C13#4112yes—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—42no—
75C22×C4×C13—41no—
76C22×C4×C13—42no—
77C22×C4×C13—41no—
78C22×C4×C13—81no—
79C22×C4×C13—81no—
80C22×C4×C13—81no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×M16—42no—
87C13×M16—42no—
88C2×C8×C13—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—81no—
96C13×C22⋊C4—24no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C42×C13—21no—
105C42×C13—21no—
106C42×C13—82no—
107#2579C2×C1311yescharacteristic
108#1800C2×C1311yescharacteristic
109C4×#99C2×C1311yescharacteristic
110#1390C2×C1312yes—
111#1390C2×C1312yes—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C4×Q812yes—
122C23×C13C22⋊Q812yes—
123D4×C13—42no—
124D4×C13—42no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—44no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13—82no—
156C2×C4×C13#9911yescharacteristic
157C2×C4×C13#9911yescharacteristic
158C2×C4×C13#12411yescharacteristic
159C2×C4×C13C4⋊Q811yescharacteristic
160C8×C13—82no—
161C2×C4×D4C22×C1311yescharacteristic
162C22×C4⋊C4C4×C1311yescharacteristic, complemented
163#423—21no—
164C2×#100C22×C1312yes—
165C2×#99C22×C1312yes—
166#398—21no—
167#396—21no—
168#387—21no—
169#386C22×C1311yescharacteristic
170#386C22×C1311yescharacteristic
171#385—21no—
172#385C4×C1311yescharacteristic, complemented
173#385C4×C1311yescharacteristic, complemented
174#380C4×C1311yescharacteristic, complemented
175C4×C22⋊C4—21no—
176#343—21no—
177#342—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—81no—
190C22×C13#39111yescharacteristic
191C22×C13C2×#9911yescharacteristic
192C22×C13#41011yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—41no—
198C4×C13—42no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13—84no—
204C4×C13—81no—
205C22×D4C23×C1311yescharacteristic
206C23×C4C2×C4×C1311yescharacteristic
207C23×C4C2×C4×C1311yescharacteristic
208C23×C4C2×C4×C1311yescharacteristic
209C23×C4D4×C1311yescharacteristic
210C2×M16—22no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4D4×C1311yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4C2×C4×C1311yescharacteristic
225C2×C22⋊C4C2×C4×C1311yescharacteristic
226C2×C22⋊C4C2×C4×C1311yescharacteristic
227C2×C22⋊C4D4×C1311yescharacteristic
228C2×C42—41no—
229C2×C42D4×C1311yescharacteristic
230C4⋊C8—41no—
231C4⋊C8—41no—
232#100—24no—
233#99—22no—
234#99Q8×C1314yes—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—41no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13—42no—
244C2×C13—42no—
245C2×C13#199611yescharacteristic
246C2×C13#212011yescharacteristic
247C2×C13#212111yescharacteristic
248C24C22×C4×C1311yescharacteristic
249C24C2×D4×C1311yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4C2×Q8×C1312yes—
253C2×D4C13×#4112yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4C13×C22⋊C411yescharacteristic
270C22×C4C13×C22⋊C411yescharacteristic
271C22×C4C13×C22⋊C411yescharacteristic
272C22×C4C13×C22⋊C411yescharacteristic
273C22×C4C2×D4×C1311yescharacteristic
274M16—42no—
275M16—42no—
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C22⋊C4—24no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C42—21no—
293C42—21no—
294C42—82no—
295C13#1329711yescharacteristic, direct product factor, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C2×C13×C22⋊C411yescharacteristic
305C23C4×Q8×C1312yes—
306C23C13×C22⋊Q812yes—
307D4—42no—
308D4—42no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4C13×#9911yescharacteristic
341C2×C4C13×#9911yescharacteristic
342C2×C4C13×#12411yescharacteristic
343C2×C4C13×C4⋊Q811yescharacteristic
344C8—82no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22C13×#39111yescharacteristic
358C22C2×C13×#9911yescharacteristic
359C22C13×#41011yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—42no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C4—84no—
371C4—81no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2C13×#199611yescharacteristic
377C2C13×#212011yescharacteristic
378C2C13×#212111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
7. C22×C13×C4⋊C4C4semidirect
17. C13×#385C4semidirect
18. C13×#385C4semidirect
19. C13×#380C4semidirect
59. #13297C13direct (N × H)
162. C22×C4⋊C4C4×C13semidirect
172. #385C4×C13semidirect
173. #385C4×C13semidirect
174. #380C4×C13semidirect
295. C13#13297direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25792
C13×#18002
C4×C13×#992
C13×#13902
#1329713