Finite Group Databasebeta

← C13×#8998 #15695337

Subgroups — C13×#8998 #15695337

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3172C211yesmaximal, characteristic
2C13×#2995C211yesmaximal, characteristic
3C13×#1995C211yesmaximal, characteristic, complemented
4C13×#1500C211yesmaximal, characteristic
5C13×#1497C211yesmaximal, characteristic, complemented
6C13×#1300C211yesmaximal, characteristic, complemented
7C13×#1299C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#497C411yescharacteristic, complemented
12C13×#491C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#470—21no—
15C13×#468—21no—
16C13×#446—21no—
17C4×C13×Q16—21no—
18C4×C13×SD16—21no—
19C13×#436—21no—
20C13×#435—21no—
21C13×#435—21no—
22C13×#433—21no—
23C13×#432C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#424—21no—
26C13×#423C2211yescharacteristic
27C4×C13×M16C2211yescharacteristic
28C13×#376C2211yescharacteristic
29C13×#339—21no—
30C13×#339—21no—
31C13×#328—21no—
32C13×#327—21no—
33C13×Q8⋊C8—21no—
34C13×Q8⋊C8—21no—
35C2×C13×Q16—21no—
36C2×C13×SD16—21no—
37C2×C13×M16—21no—
38C2×C13×M16—21no—
39C2×C13×M16D411yescharacteristic
40C2×C13×M16D411yescharacteristic
41C22×C8×C13—21no—
42C13×C4⋊Q8C2×C411yescharacteristic
43C13×C4⋊Q8C2×C411yescharacteristic
44C13×#126—21no—
45C13×#125—21no—
46C13×#125C2×C411yescharacteristic
47C13×#124C2×C411yescharacteristic
48C13×#123—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8D411yescharacteristic
52C13×#121D411yescharacteristic
53C4×Q8×C13—21no—
54C4×Q8×C13—21no—
55C4×Q8×C13D411yescharacteristic
56C4×D4×C13—21no—
57C4×D4×C13D411yescharacteristic
58C13×#117—21no—
59C13×#117—21no—
60C2×C42×C13—21no—
61C2×C42×C13C2311yescharacteristic
62C13×#107—21no—
63C13×#106—21no—
64C13×C4⋊C8—21no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8D411yescharacteristic
70C13×C4⋊C8D411yescharacteristic
71C13×#103—21no—
72C13×#103—21no—
73C13×#103—21no—
74C13×#102—21no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×#97—21no—
80C13×#97—21no—
81C13×#97C2×C411yescharacteristic
82C13×#97C2×C411yescharacteristic
83C4×C8×C13—21no—
84C4×C8×C13—21no—
85C4×C8×C13—21no—
86C13×#95—21no—
87C13×#95—21no—
88#8998C1311yesmaximal, characteristic, direct product factor, Sylow
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13C22⋊C411yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13C22⋊C411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13#4111yescharacteristic
99C13×Q16—42no—
100C13×SD16—42no—
101C13×M16—42no—
102C13×M16—41no—
103C13×M16—41no—
104C13×M16—81no—
105C2×C8×C13—21no—
106C2×C8×C13—21no—
107C2×C8×C13—21no—
108C2×C8×C13—21no—
109C2×C8×C13—21no—
110C2×C8×C13—21no—
111C2×C8×C13—41no—
112C2×C8×C13—81no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4C22⋊C411yescharacteristic
124C13×C4⋊C4C22⋊C411yescharacteristic
125C13×C22⋊C4—21no—
126C13×C22⋊C4—21no—
127C13×C22⋊C4—21no—
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—41no—
131C42×C13—21no—
132C42×C13—22no—
133C42×C13—41no—
134C42×C13—41no—
135C42×C13C22×C411yescharacteristic
136C42×C13C2×D411yescharacteristic
137C42×C13C2×D411yescharacteristic
138C42×C13#4111yescharacteristic
139#3172C2×C1311yescharacteristic
140#2995C2×C1311yescharacteristic
141#1995C2×C1311yescharacteristic, complemented
142#1500C2×C1311yescharacteristic
143#1497C2×C1311yescharacteristic, complemented
144#1300C2×C1311yescharacteristic, complemented
145#1299C2×C1311yescharacteristic, complemented
146C23×C13—21no—
147C23×C13#12111yescharacteristic
148Q8×C13—41no—
149Q8×C13—41no—
150Q8×C13—41no—
151Q8×C13—42no—
152D4×C13—41no—
153D4×C13—81no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13C2×C22⋊C411yescharacteristic
169C2×C4×C13C4×D411yescharacteristic
170C2×C4×C13C4×D411yescharacteristic
171C2×C4×C13#12011yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12311yescharacteristic
174C8×C13—22no—
175C8×C13—41no—
176C8×C13—41no—
177C8×C13—41no—
178C8×C13—41no—
179C8×C13—41no—
180C8×C13—81no—
181#533C22×C1311yescharacteristic
182#529C22×C1311yescharacteristic
183#501C4×C1311yescharacteristic, complemented
184#497C4×C1311yescharacteristic, complemented
185#491C4×C1311yescharacteristic, complemented
186#489C4×C1311yescharacteristic, complemented
187#470—21no—
188#468—21no—
189#446—21no—
190C4×Q16—21no—
191C4×SD16—21no—
192#436—21no—
193#435—21no—
194#435—21no—
195#433—21no—
196#432C22×C1311yescharacteristic
197#431C22×C1311yescharacteristic
198#424—21no—
199#423C22×C1311yescharacteristic
200C4×M16C22×C1311yescharacteristic
201#376C22×C1311yescharacteristic
202#339—21no—
203#339—21no—
204#328—21no—
205#327—21no—
206Q8⋊C8—21no—
207Q8⋊C8—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13#38611yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—82no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13#45511yescharacteristic
227C4×C13#45611yescharacteristic
228C2×Q16—21no—
229C2×SD16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16D4×C1311yescharacteristic
233C2×M16D4×C1311yescharacteristic
234C22×C8—21no—
235C4⋊Q8C2×C4×C1311yescharacteristic
236C4⋊Q8C2×C4×C1311yescharacteristic
237#126—21no—
238#125—21no—
239#125C2×C4×C1311yescharacteristic
240#124C2×C4×C1311yescharacteristic
241#123—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8D4×C1311yescharacteristic
245#121D4×C1311yescharacteristic
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8D4×C1311yescharacteristic
249C4×D4—21no—
250C4×D4D4×C1311yescharacteristic
251#117—21no—
252#117—21no—
253C2×C42—21no—
254C2×C42C23×C1311yescharacteristic
255#107—21no—
256#106—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C1311yescharacteristic
263C4⋊C8D4×C1311yescharacteristic
264#103—21no—
265#103—21no—
266#103—21no—
267#102—21no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272#97—21no—
273#97—21no—
274#97C2×C4×C1311yescharacteristic
275#97C2×C4×C1311yescharacteristic
276C4×C8—21no—
277C4×C8—21no—
278C4×C8—21no—
279#95—21no—
280#95—21no—
281C2×C13—41no—
282C2×C13—81no—
283C2×C13#188111yescharacteristic
284C2×C13#188211yescharacteristic
285C2×C13#188411yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8C13×C22⋊C411yescharacteristic
289C2×D4—21no—
290C2×D4C13×C22⋊C411yescharacteristic
291C22×C4—21no—
292C22×C4—41no—
293C22×C4C2×D4×C1311yescharacteristic
294C22×C4C2×D4×C1311yescharacteristic
295C22×C4C13×#4111yescharacteristic
296Q16—42no—
297SD16—42no—
298M16—42no—
299M16—41no—
300M16—41no—
301M16—81no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—41no—
309C2×C8—81no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4C13×C22⋊C411yescharacteristic
321C4⋊C4C13×C22⋊C411yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—22no—
330C42—41no—
331C42—41no—
332C42C22×C4×C1311yescharacteristic
333C42C2×D4×C1311yescharacteristic
334C42C2×D4×C1311yescharacteristic
335C42C13×#4111yescharacteristic
336C13#899811yescharacteristic, direct product factor, Sylow
337C23—21no—
338C23C13×#12111yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—42no—
343D4—41no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C13×C22⋊C411yescharacteristic
360C2×C4C4×D4×C1311yescharacteristic
361C2×C4C4×D4×C1311yescharacteristic
362C2×C4C13×#12011yescharacteristic
363C2×C4C13×#12111yescharacteristic
364C2×C4C13×#12311yescharacteristic
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—41no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22C13×#38611yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4C13×#45511yescharacteristic
391C4C13×#45611yescharacteristic
392C2—41no—
393C2—81no—
394C2C13×#188111yescharacteristic
395C2C13×#188211yescharacteristic
396C2C13×#188411yescharacteristic
subgroupG/H
centerC2×C4×C13#120
commutatorC42C22×C4×C13
Frattini, cosocleC2×C42C23×C13
socleC22×C13#386
prime radicalC13×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1995C2semidirect
5. C13×#1497C2semidirect
6. C13×#1300C2semidirect
7. C13×#1299C2semidirect
10. C13×#501C4semidirect
11. C13×#497C4semidirect
12. C13×#491C4semidirect
13. C13×#489C4semidirect
88. #8998C13direct (N × H)
141. #1995C2×C13semidirect
143. #1497C2×C13semidirect
144. #1300C2×C13semidirect
145. #1299C2×C13semidirect
183. #501C4×C13semidirect
184. #497C4×C13semidirect
185. #491C4×C13semidirect
186. #489C4×C13semidirect
336. C13#8998direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#31722
C13×#29952
C13×#19952
C13×#15002
C13×#14972
C13×#13002
C13×#12992
#899813