Finite Group Databasebeta

← C13×#13300 #15699639

Subgroups — C13×#13300 #15699639

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2566C211yesmaximal, characteristic
2C13×#1799C211yesmaximal, characteristic
3C4×C13×#99C211yesmaximal, characteristic
4C13×#1393C212yesmaximal
5C13×#1393C212yesmaximal
6C2×C13×#125C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C2×C13×#99C2212yes—
9C2×C13×#99C2212yes—
10C13×#396—21no—
11C13×#396—21no—
12C13×#390C2211yescharacteristic
13C13×#390C2211yescharacteristic
14C13×#385—21no—
15C13×#385—21no—
16C13×#384C411yescharacteristic, complemented
17C13×#382C411yescharacteristic, complemented
18C13×#380—21no—
19C4×C13×C4⋊C4C411yescharacteristic, complemented
20C4×C13×C22⋊C4—21no—
21C13×#342—21no—
22C13×#342—21no—
23C22×D4×C13C2311yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C13×#125—41no—
27C13×#125—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C42×C13—41no—
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13C2×C411yescharacteristic
50C2×C42×C13C2×C411yescharacteristic
51C13×#99—22no—
52C13×#99—24no—
53C13×#99Q814yes—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—41no—
58C13×#95—41no—
59#13300C1311yesmaximal, characteristic, direct product factor, Sylow
60C24×C13C2×D411yescharacteristic
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—42no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—82no—
93C13×C22⋊C4—24no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—81no—
102C13×C22⋊C4—81no—
103C42×C13—21no—
104C42×C13—21no—
105C42×C13—41no—
106C42×C13—41no—
107C42×C13—82no—
108#2566C2×C1311yescharacteristic
109#1799C2×C1311yescharacteristic
110C4×#99C2×C1311yescharacteristic
111#1393C2×C1312yes—
112#1393C2×C1312yes—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13C22⋊Q812yes—
123C23×C13#12411yescharacteristic
124C23×C13C4⋊Q811yescharacteristic
125D4×C13—42no—
126D4×C13—42no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—22no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—44no—
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—41no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13—82no—
156C2×C4×C13—82no—
157C2×C4×C13—82no—
158C2×C4×C13#9911yescharacteristic
159C2×C4×C13#9911yescharacteristic
160C2×C4×C13C4×Q812yes—
161C2×#125C4×C1311yescharacteristic, complemented
162C2×C4×D4C22×C1311yescharacteristic
163C2×#99C22×C1312yes—
164C2×#99C22×C1312yes—
165#396—21no—
166#396—21no—
167#390C22×C1311yescharacteristic
168#390C22×C1311yescharacteristic
169#385—21no—
170#385—21no—
171#384C4×C1311yescharacteristic, complemented
172#382C4×C1311yescharacteristic, complemented
173#380—21no—
174C4×C4⋊C4C4×C1311yescharacteristic, complemented
175C4×C22⋊C4—21no—
176#342—21no—
177#342—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13#39111yescharacteristic
193C22×C13C2×#9911yescharacteristic
194C22×C13#41011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—81no—
203C4×C13—84no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13—162no—
207C22×D4C23×C1311yescharacteristic
208C23×C4D4×C1311yescharacteristic
209C23×C4D4×C1311yescharacteristic
210#125—41no—
211#125—41no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4C2×C4×C1311yescharacteristic
221C2×C4⋊C4C2×C4×C1311yescharacteristic
222C2×C4⋊C4C2×C4×C1311yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4D4×C1311yescharacteristic
230C2×C22⋊C4D4×C1311yescharacteristic
231C2×C42—41no—
232C2×C42C2×C4×C1311yescharacteristic
233C2×C42C2×C4×C1311yescharacteristic
234C2×C42C2×C4×C1311yescharacteristic
235#99—22no—
236#99—24no—
237#99Q8×C1314yes—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—41no—
242#95—41no—
243C2×C13—21no—
244C2×C13—21no—
245C2×C13—42no—
246C2×C13—41no—
247C2×C13—41no—
248C2×C13#199611yescharacteristic
249C2×C13#212611yescharacteristic
250C2×C13#212711yescharacteristic
251C24C2×D4×C1311yescharacteristic
252C24C2×D4×C1311yescharacteristic
253C2×D4—41no—
254C2×D4—41no—
255C2×D4C2×Q8×C1312yes—
256C2×D4C13×#4112yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4C13×C22⋊C411yescharacteristic
270C22×C4C13×C22⋊C411yescharacteristic
271C22×C4C13×C22⋊C411yescharacteristic
272C22×C4C13×C22⋊C411yescharacteristic
273C22×C4C22×C4×C1311yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C4⋊C4—82no—
284C22⋊C4—24no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C42—21no—
295C42—21no—
296C42—41no—
297C42—41no—
298C42—82no—
299C13#1330011yescharacteristic, direct product factor, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23C2×C13×C22⋊C411yescharacteristic
309C23C13×C22⋊Q812yes—
310C23C13×#12411yescharacteristic
311C23C13×C4⋊Q811yescharacteristic
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4C13×#9911yescharacteristic
346C2×C4C13×#9911yescharacteristic
347C2×C4C4×Q8×C1312yes—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22C13×#39111yescharacteristic
363C22C2×C13×#9911yescharacteristic
364C22C13×#41011yescharacteristic
365C4—22no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—81no—
373C4—84no—
374C4—81no—
375C4—81no—
376C4—162no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—41no—
381C2—41no—
382C2C13×#199611yescharacteristic
383C2C13×#212611yescharacteristic
384C2C13×#212711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ 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
6. C2×C13×#125C4semidirect
16. C13×#384C4semidirect
17. C13×#382C4semidirect
19. C4×C13×C4⋊C4C4semidirect
59. #13300C13direct (N × H)
161. C2×#125C4×C13semidirect
171. #384C4×C13semidirect
172. #382C4×C13semidirect
174. C4×C4⋊C4C4×C13semidirect
299. C13#13300direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25662
C13×#17992
C4×C13×#992
C13×#13932
#1330013